From 41cddb5fb5535a22a9d75eb4a1f95ed4a8c19383 Mon Sep 17 00:00:00 2001 From: yanglbme Date: Mon, 25 Nov 2024 09:02:00 +0800 Subject: [PATCH] feat: add solutions to lc problem: No.0743 No.0743.Network Delay Time --- .../0743.Network Delay Time/README.md | 563 ++++++----------- .../0743.Network Delay Time/README_EN.md | 565 ++++++------------ .../0743.Network Delay Time/Solution.cpp | 13 +- .../0743.Network Delay Time/Solution.go | 28 +- .../0743.Network Delay Time/Solution.java | 23 +- .../0743.Network Delay Time/Solution.py | 9 +- .../0743.Network Delay Time/Solution.ts | 23 + .../0743.Network Delay Time/Solution2.cpp | 36 +- .../0743.Network Delay Time/Solution2.go | 79 +-- .../0743.Network Delay Time/Solution2.java | 43 +- .../0743.Network Delay Time/Solution2.py | 21 +- .../0743.Network Delay Time/Solution2.ts | 24 + .../0743.Network Delay Time/Solution3.cpp | 18 - .../0743.Network Delay Time/Solution3.go | 21 - .../0743.Network Delay Time/Solution3.java | 22 - .../0743.Network Delay Time/Solution3.py | 11 - .../0743.Network Delay Time/Solution4.cpp | 35 -- .../0743.Network Delay Time/Solution4.go | 37 -- .../0743.Network Delay Time/Solution4.java | 41 -- .../0743.Network Delay Time/Solution4.py | 23 - .../Solution.go | 4 +- 21 files changed, 536 insertions(+), 1103 deletions(-) create mode 100644 solution/0700-0799/0743.Network Delay Time/Solution.ts create mode 100644 solution/0700-0799/0743.Network Delay Time/Solution2.ts delete mode 100644 solution/0700-0799/0743.Network Delay Time/Solution3.cpp delete mode 100644 solution/0700-0799/0743.Network Delay Time/Solution3.go delete mode 100644 solution/0700-0799/0743.Network Delay Time/Solution3.java delete mode 100644 solution/0700-0799/0743.Network Delay Time/Solution3.py delete mode 100644 solution/0700-0799/0743.Network Delay Time/Solution4.cpp delete mode 100644 solution/0700-0799/0743.Network Delay Time/Solution4.go delete mode 100644 solution/0700-0799/0743.Network Delay Time/Solution4.java delete mode 100644 solution/0700-0799/0743.Network Delay Time/Solution4.py diff --git a/solution/0700-0799/0743.Network Delay Time/README.md b/solution/0700-0799/0743.Network Delay Time/README.md index 3590db1d02302..7030693378b19 100644 --- a/solution/0700-0799/0743.Network Delay Time/README.md +++ b/solution/0700-0799/0743.Network Delay Time/README.md @@ -73,7 +73,15 @@ tags: ### 方法一：朴素 Dijkstra 算法 -时间复杂度 $O(n^2+m)$。 +我们定义 $\textit{g}[u][v]$ 表示节点 $u$ 到节点 $v$ 的边权，如果节点 $u$ 到节点 $v$ 之间没有边，则 $\textit{g}[u][v] = +\infty$。 + +我们维护一个数组 $\textit{dist}$，其中 $\textit{dist}[i]$ 表示节点 $k$ 到节点 $i$ 的最短路径长度。初始时，我们将 $\textit{dist}[i]$ 全部初始化为 $+\infty$，但 $\textit{dist}[k - 1] = 0$。定义一个数组 $\textit{vis}$，其中 $\textit{vis}[i]$ 表示节点 $i$ 是否被访问过，初始时，我们将 $\textit{vis}[i]$ 全部初始化为 $\text{false}$。 + +我们每次找到未被访问的距离最小的节点 $t$，然后以节点 $t$ 为中心进行松弛操作，即对于每个节点 $j$，如果 $\textit{dist}[j] > \textit{dist}[t] + \textit{g}[t][j]$，则更新 $\textit{dist}[j] = \textit{dist}[t] + \textit{g}[t][j]$。 + +最后，我们返回 $\textit{dist}$ 中的最大值，即为答案。如果答案为 $+\infty$，则说明存在无法到达的节点，返回 $-1$。 + +时间复杂度 $O(n^2 + m)$，空间复杂度 $O(n^2)$。其中 $n$ 和 $m$ 分别为节点数和边数。 @@ -82,13 +90,12 @@ tags: ```python class Solution: def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - vis = [False] * n - g = [[INF] * n for _ in range(n)] + g = [[inf] * n for _ in range(n)] for u, v, w in times: g[u - 1][v - 1] = w + dist = [inf] * n dist[k - 1] = 0 + vis = [False] * n for _ in range(n): t = -1 for j in range(n): @@ -98,27 +105,26 @@ class Solution: for j in range(n): dist[j] = min(dist[j], dist[t] + g[t][j]) ans = max(dist) - return -1 if ans == INF else ans + return -1 if ans == inf else ans ``` #### Java ```java class Solution { - private static final int INF = 0x3f3f; - public int networkDelayTime(int[][] times, int n, int k) { int[][] g = new int[n][n]; int[] dist = new int[n]; - boolean[] vis = new boolean[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - Arrays.fill(g[i], INF); + final int inf = 1 << 29; + Arrays.fill(dist, inf); + for (var e : g) { + Arrays.fill(e, inf); } - for (int[] t : times) { - g[t[0] - 1][t[1] - 1] = t[2]; + for (var e : times) { + g[e[0] - 1][e[1] - 1] = e[2]; } dist[k - 1] = 0; + boolean[] vis = new boolean[n]; for (int i = 0; i < n; ++i) { int t = -1; for (int j = 0; j < n; ++j) { @@ -132,10 +138,10 @@ class Solution { } } int ans = 0; - for (int d : dist) { - ans = Math.max(ans, d); + for (int x : dist) { + ans = Math.max(ans, x); } - return ans == INF ? -1 : ans; + return ans == inf ? -1 : ans; } } ``` @@ -145,14 +151,15 @@ class Solution { ```cpp class Solution { public: - const int inf = 0x3f3f; - int networkDelayTime(vector>& times, int n, int k) { + const int inf = 1 << 29; vector> g(n, vector(n, inf)); - for (auto& t : times) g[t[0] - 1][t[1] - 1] = t[2]; - vector vis(n); + for (const auto& e : times) { + g[e[0] - 1][e[1] - 1] = e[2]; + } vector dist(n, inf); dist[k - 1] = 0; + vector vis(n); for (int i = 0; i < n; ++i) { int t = -1; for (int j = 0; j < n; ++j) { @@ -165,7 +172,7 @@ public: dist[j] = min(dist[j], dist[t] + g[t][j]); } } - int ans = *max_element(dist.begin(), dist.end()); + int ans = ranges::max(dist); return ans == inf ? -1 : ans; } }; @@ -175,21 +182,25 @@ public: ```go func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f - dist := make([]int, n) - vis := make([]bool, n) + const inf = 1 << 29 g := make([][]int, n) - for i := range dist { - dist[i] = inf + for i := range g { g[i] = make([]int, n) for j := range g[i] { g[i][j] = inf } } - for _, t := range times { - g[t[0]-1][t[1]-1] = t[2] + for _, e := range times { + g[e[0]-1][e[1]-1] = e[2] + } + + dist := make([]int, n) + for i := range dist { + dist[i] = inf } dist[k-1] = 0 + + vis := make([]bool, n) for i := 0; i < n; i++ { t := -1 for j := 0; j < n; j++ { @@ -202,11 +213,39 @@ func networkDelayTime(times [][]int, n int, k int) int { dist[j] = min(dist[j], dist[t]+g[t][j]) } } - ans := slices.Max(dist) - if ans == inf { - return -1 + + if ans := slices.Max(dist); ans != inf { + return ans } - return ans + return -1 +} +``` + +#### TypeScript + +```ts +function networkDelayTime(times: number[][], n: number, k: number): number { + const g: number[][] = Array.from({ length: n }, () => Array(n).fill(Infinity)); + for (const [u, v, w] of times) { + g[u - 1][v - 1] = w; + } + const dist: number[] = Array(n).fill(Infinity); + dist[k - 1] = 0; + const vis: boolean[] = Array(n).fill(false); + for (let i = 0; i < n; ++i) { + let t = -1; + for (let j = 0; j < n; ++j) { + if (!vis[j] && (t === -1 || dist[j] < dist[t])) { + t = j; + } + } + vis[t] = true; + for (let j = 0; j < n; ++j) { + dist[j] = Math.min(dist[j], dist[t] + g[t][j]); + } + } + const ans = Math.max(...dist); + return ans === Infinity ? -1 : ans; } ``` @@ -218,7 +257,15 @@ func networkDelayTime(times [][]int, n int, k int) int { ### 方法二：堆优化 Dijkstra 算法 -时间复杂度 $O(m\log n)$。 +我们可以使用优先队列（堆）来优化朴素 Dijkstra 算法。 + +我们定义 $\textit{g}[u]$ 表示节点 $u$ 的所有邻接边，而 $\textit{dist}[u]$ 表示节点 $k$ 到节点 $u$ 的最短路径长度。初始时，我们将 $\textit{dist}[u]$ 全部初始化为 $+\infty$，但 $\textit{dist}[k - 1] = 0$。 + +定义一个优先队列 $\textit{pq}$，其中每个元素为 $(\textit{d}, u)$，表示节点 $u$ 到节点 $k$ 的距离为 $\textit{d}$。我们每次从 $\textit{pq}$ 中取出距离最小的节点 $(\textit{d}, u)$。如果 $\textit{d} > \textit{dist}[u]$，则跳过该节点。否则，我们遍历节点 $u$ 的所有邻接边，对于每个邻接边 $(v, w)$，如果 $\textit{dist}[v] > \textit{dist}[u] + w$，则更新 $\textit{dist}[v] = \textit{dist}[u] + w$，并将 $(\textit{dist}[v], v)$ 加入 $\textit{pq}$。 + +最后，我们返回 $\textit{dist}$ 中的最大值，即为答案。如果答案为 $+\infty$，则说明存在无法到达的节点，返回 $-1$。 + +时间复杂度 $O(m \times \log m + n)$，空间复杂度 $O(n + m)$。其中 $n$ 和 $m$ 分别为节点数和边数。 @@ -227,58 +274,56 @@ func networkDelayTime(times [][]int, n int, k int) int { ```python class Solution: def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - g = defaultdict(list) + g = [[] for _ in range(n)] for u, v, w in times: g[u - 1].append((v - 1, w)) - dist = [INF] * n + dist = [inf] * n dist[k - 1] = 0 - q = [(0, k - 1)] - while q: - _, u = heappop(q) + pq = [(0, k - 1)] + while pq: + d, u = heappop(pq) + if d > dist[u]: + continue for v, w in g[u]: - if dist[v] > dist[u] + w: - dist[v] = dist[u] + w - heappush(q, (dist[v], v)) + if (nd := d + w) < dist[v]: + dist[v] = nd + heappush(pq, (nd, v)) ans = max(dist) - return -1 if ans == INF else ans + return -1 if ans == inf else ans ``` #### Java ```java class Solution { - private static final int INF = 0x3f3f; - public int networkDelayTime(int[][] times, int n, int k) { + final int inf = 1 << 29; List[] g = new List[n]; - int[] dist = new int[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - g[i] = new ArrayList<>(); - } - for (int[] t : times) { - g[t[0] - 1].add(new int[] {t[1] - 1, t[2]}); + Arrays.setAll(g, i -> new ArrayList<>()); + for (var e : times) { + g[e[0] - 1].add(new int[] {e[1] - 1, e[2]}); } + int[] dist = new int[n]; + Arrays.fill(dist, inf); dist[k - 1] = 0; - PriorityQueue q = new PriorityQueue<>(Comparator.comparingInt(a -> a[0])); - q.offer(new int[] {0, k - 1}); - while (!q.isEmpty()) { - int[] p = q.poll(); - int u = p[1]; - for (int[] ne : g[u]) { - int v = ne[0], w = ne[1]; + PriorityQueue pq = new PriorityQueue<>(Comparator.comparingInt(a -> a[0])); + pq.offer(new int[] {0, k - 1}); + while (!pq.isEmpty()) { + var p = pq.poll(); + int d = p[0], u = p[1]; + if (d > dist[u]) { + continue; + } + for (var e : g[u]) { + int v = e[0], w = e[1]; if (dist[v] > dist[u] + w) { dist[v] = dist[u] + w; - q.offer(new int[] {dist[v], v}); + pq.offer(new int[] {dist[v], v}); } } } - int ans = 0; - for (int d : dist) { - ans = Math.max(ans, d); - } - return ans == INF ? -1 : ans; + int ans = Arrays.stream(dist).max().getAsInt(); + return ans == inf ? -1 : ans; } } ``` @@ -288,166 +333,34 @@ class Solution { ```cpp class Solution { public: - const int inf = 0x3f3f; - int networkDelayTime(vector>& times, int n, int k) { - vector>> g(n); - for (auto& t : times) g[t[0] - 1].push_back({t[1] - 1, t[2]}); + const int inf = 1 << 29; + using pii = pair; + vector> g(n); + for (auto& edge : times) { + g[edge[0] - 1].emplace_back(edge[1] - 1, edge[2]); + } + vector dist(n, inf); dist[k - 1] = 0; - priority_queue, vector>, greater>> q; - q.push({0, k - 1}); - while (!q.empty()) { - auto p = q.top(); - q.pop(); - int u = p[1]; - for (auto& ne : g[u]) { - int v = ne[0], w = ne[1]; + priority_queue, greater<>> pq; + pq.emplace(0, k - 1); + + while (!pq.empty()) { + auto [d, u] = pq.top(); + pq.pop(); + if (d > dist[u]) { + continue; + } + for (auto& [v, w] : g[u]) { if (dist[v] > dist[u] + w) { dist[v] = dist[u] + w; - q.push({dist[v], v}); + pq.emplace(dist[v], v); } } } - int ans = *max_element(dist.begin(), dist.end()); - return ans == inf ? -1 : ans; - } -}; -``` - -#### Go - -```go -const Inf = 0x3f3f3f3f - -type pair struct { - first int - second int -} - -var _ heap.Interface = (*pairs)(nil) - -type pairs []pair - -func (a pairs) Len() int { return len(a) } -func (a pairs) Less(i int, j int) bool { - return a[i].first < a[j].first || a[i].first == a[j].first && a[i].second < a[j].second -} -func (a pairs) Swap(i int, j int) { a[i], a[j] = a[j], a[i] } -func (a *pairs) Push(x any) { *a = append(*a, x.(pair)) } -func (a *pairs) Pop() any { l := len(*a); t := (*a)[l-1]; *a = (*a)[:l-1]; return t } - -func networkDelayTime(times [][]int, n int, k int) int { - graph := make([]pairs, n) - for _, time := range times { - from, to, time := time[0]-1, time[1]-1, time[2] - graph[from] = append(graph[from], pair{to, time}) - } - - dis := make([]int, n) - for i := range dis { - dis[i] = Inf - } - dis[k-1] = 0 - - vis := make([]bool, n) - h := make(pairs, 0) - heap.Push(&h, pair{0, k - 1}) - for len(h) > 0 { - from := heap.Pop(&h).(pair).second - if vis[from] { - continue - } - vis[from] = true - for _, e := range graph[from] { - to, d := e.first, dis[from]+e.second - if d < dis[to] { - dis[to] = d - heap.Push(&h, pair{d, to}) - } - } - } - ans := slices.Max(dis) - if ans == Inf { - return -1 - } - return ans -} -``` - - - - - - - -### 方法三：Bellman Ford 算法 - -时间复杂度 $O(nm)$。 - - -#### Python3 - -```python -class Solution: - def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - dist[k - 1] = 0 - for _ in range(n): - backup = dist[:] - for u, v, w in times: - dist[v - 1] = min(dist[v - 1], dist[u - 1] + w) - ans = max(dist) - return -1 if ans == INF else ans -``` - -#### Java - -```java -class Solution { - private static final int INF = 0x3f3f; - - public int networkDelayTime(int[][] times, int n, int k) { - int[] dist = new int[n]; - int[] backup = new int[n]; - Arrays.fill(dist, INF); - dist[k - 1] = 0; - for (int i = 0; i < n; ++i) { - System.arraycopy(dist, 0, backup, 0, n); - for (int[] t : times) { - int u = t[0] - 1, v = t[1] - 1, w = t[2]; - dist[v] = Math.min(dist[v], backup[u] + w); - } - } - int ans = 0; - for (int i = 0; i < n; ++i) { - ans = Math.max(ans, dist[i]); - } - return ans == INF ? -1 : ans; - } -} -``` - -#### C++ - -```cpp -class Solution { -public: - int inf = 0x3f3f; - - int networkDelayTime(vector>& times, int n, int k) { - vector dist(n, inf); - dist[k - 1] = 0; - for (int i = 0; i < n; ++i) { - vector backup = dist; - for (auto& e : times) { - int u = e[0] - 1, v = e[1] - 1, w = e[2]; - dist[v] = min(dist[v], backup[u] + w); - } - } - int ans = *max_element(dist.begin(), dist.end()); + int ans = ranges::max(dist); return ans == inf ? -1 : ans; } }; @@ -457,191 +370,75 @@ public: ```go func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f + g := make([][][2]int, n) + for _, e := range times { + u, v, w := e[0]-1, e[1]-1, e[2] + g[u] = append(g[u], [2]int{v, w}) + } dist := make([]int, n) - backup := make([]int, n) + const inf int = 1 << 29 for i := range dist { dist[i] = inf } dist[k-1] = 0 - for i := 0; i < n; i++ { - copy(backup, dist) - for _, e := range times { - u, v, w := e[0]-1, e[1]-1, e[2] - dist[v] = min(dist[v], backup[u]+w) + pq := hp{{0, k - 1}} + for len(pq) > 0 { + p := heap.Pop(&pq).(pair) + d, u := p.x, p.i + if d > dist[u] { + continue + } + for _, e := range g[u] { + v, w := e[0], e[1] + if nd := d + w; nd < dist[v] { + dist[v] = nd + heap.Push(&pq, pair{nd, v}) + } } } - ans := slices.Max(dist) - if ans == inf { - return -1 + if ans := slices.Max(dist); ans < inf { + return ans } - return ans -} -``` - - - - - - + return -1 -### 方法四 +} - +type pair struct{ x, i int } +type hp []pair -#### Python3 - -```python -class Solution: - def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - vis = [False] * n - g = defaultdict(list) - for u, v, w in times: - g[u - 1].append((v - 1, w)) - k -= 1 - dist[k] = 0 - q = deque([k]) - vis[k] = True - while q: - u = q.popleft() - vis[u] = False - for v, w in g[u]: - if dist[v] > dist[u] + w: - dist[v] = dist[u] + w - if not vis[v]: - q.append(v) - vis[v] = True - ans = max(dist) - return -1 if ans == INF else ans +func (h hp) Len() int { return len(h) } +func (h hp) Less(i, j int) bool { return h[i].x < h[j].x } +func (h hp) Swap(i, j int) { h[i], h[j] = h[j], h[i] } +func (h *hp) Push(x any) { *h = append(*h, x.(pair)) } +func (h *hp) Pop() (x any) { a := *h; x = a[len(a)-1]; *h = a[:len(a)-1]; return } ``` -#### Java - -```java -class Solution { - private static final int INF = 0x3f3f; +#### TypeScript - public int networkDelayTime(int[][] times, int n, int k) { - int[] dist = new int[n]; - boolean[] vis = new boolean[n]; - List[] g = new List[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - g[i] = new ArrayList<>(); - } - for (int[] t : times) { - int u = t[0] - 1, v = t[1] - 1, w = t[2]; - g[u].add(new int[] {v, w}); - } - --k; - dist[k] = 0; - Deque q = new ArrayDeque<>(); - q.offer(k); - vis[k] = true; - while (!q.isEmpty()) { - int u = q.poll(); - vis[u] = false; - for (int[] ne : g[u]) { - int v = ne[0], w = ne[1]; - if (dist[v] > dist[u] + w) { - dist[v] = dist[u] + w; - if (!vis[v]) { - q.offer(v); - vis[v] = true; - } - } - } - } - int ans = 0; - for (int i = 0; i < n; ++i) { - ans = Math.max(ans, dist[i]); - } - return ans == INF ? -1 : ans; +```ts +function networkDelayTime(times: number[][], n: number, k: number): number { + const g: [number, number][][] = Array.from({ length: n }, () => []); + for (const [u, v, w] of times) { + g[u - 1].push([v - 1, w]); } -} -``` - -#### C++ - -```cpp -class Solution { -public: - const int inf = 0x3f3f; - - int networkDelayTime(vector>& times, int n, int k) { - vector dist(n, inf); - vector>> g(n); - for (auto& e : times) { - int u = e[0] - 1, v = e[1] - 1, w = e[2]; - g[u].push_back({v, w}); + const dist: number[] = Array(n).fill(Infinity); + dist[k - 1] = 0; + const pq = new MinPriorityQueue({ priority: v => v[0] }); + pq.enqueue([0, k - 1]); + while (!pq.isEmpty()) { + const [d, u] = pq.dequeue().element; + if (d > dist[u]) { + continue; } - vector vis(n); - --k; - queue q{{k}}; - vis[k] = true; - dist[k] = 0; - while (!q.empty()) { - int u = q.front(); - q.pop(); - vis[u] = false; - for (auto& ne : g[u]) { - int v = ne[0], w = ne[1]; - if (dist[v] > dist[u] + w) { - dist[v] = dist[u] + w; - if (!vis[v]) { - q.push(v); - vis[v] = true; - } - } + for (const [v, w] of g[u]) { + if (dist[v] > dist[u] + w) { + dist[v] = dist[u] + w; + pq.enqueue([dist[v], v]); } } - int ans = *max_element(dist.begin(), dist.end()); - return ans == inf ? -1 : ans; } -}; -``` - -#### Go - -```go -func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f - dist := make([]int, n) - vis := make([]bool, n) - g := make([][][]int, n) - for i := range dist { - dist[i] = inf - } - for _, t := range times { - u, v, w := t[0]-1, t[1]-1, t[2] - g[u] = append(g[u], []int{v, w}) - } - k-- - dist[k] = 0 - q := []int{k} - vis[k] = true - for len(q) > 0 { - u := q[0] - q = q[1:] - vis[u] = false - for _, ne := range g[u] { - v, w := ne[0], ne[1] - if dist[v] > dist[u]+w { - dist[v] = dist[u] + w - if !vis[v] { - q = append(q, v) - vis[v] = true - } - } - } - } - ans := slices.Max(dist) - if ans == inf { - return -1 - } - return ans + const ans = Math.max(...dist); + return ans === Infinity ? -1 : ans; } ``` diff --git a/solution/0700-0799/0743.Network Delay Time/README_EN.md b/solution/0700-0799/0743.Network Delay Time/README_EN.md index 7b3c47657d4e5..271a9fdb4db44 100644 --- a/solution/0700-0799/0743.Network Delay Time/README_EN.md +++ b/solution/0700-0799/0743.Network Delay Time/README_EN.md @@ -65,7 +65,17 @@ tags: -### Solution 1 +### Solution 1: Naive Dijkstra Algorithm + +We define $\textit{g}[u][v]$ to represent the edge weight from node $u$ to node $v$. If there is no edge between node $u$ and node $v$, then $\textit{g}[u][v] = +\infty$. + +We maintain an array $\textit{dist}$, where $\textit{dist}[i]$ represents the shortest path length from node $k$ to node $i$. Initially, we set all $\textit{dist}[i]$ to $+\infty$, except for $\textit{dist}[k - 1] = 0$. We define an array $\textit{vis}$, where $\textit{vis}[i]$ indicates whether node $i$ has been visited. Initially, we set all $\textit{vis}[i]$ to $\text{false}$. + +Each time, we find the unvisited node $t$ with the smallest distance, and then perform relaxation operations centered on node $t$. For each node $j$, if $\textit{dist}[j] > \textit{dist}[t] + \textit{g}[t][j]$, we update $\textit{dist}[j] = \textit{dist}[t] + \textit{g}[t][j]$. + +Finally, we return the maximum value in $\textit{dist}$ as the answer. If the answer is $+\infty$, it means there are unreachable nodes, and we return $-1$. + +The time complexity is $O(n^2 + m)$, and the space complexity is $O(n^2)$. Here, $n$ and $m$ are the number of nodes and edges, respectively. @@ -74,13 +84,12 @@ tags: ```python class Solution: def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - vis = [False] * n - g = [[INF] * n for _ in range(n)] + g = [[inf] * n for _ in range(n)] for u, v, w in times: g[u - 1][v - 1] = w + dist = [inf] * n dist[k - 1] = 0 + vis = [False] * n for _ in range(n): t = -1 for j in range(n): @@ -90,27 +99,26 @@ class Solution: for j in range(n): dist[j] = min(dist[j], dist[t] + g[t][j]) ans = max(dist) - return -1 if ans == INF else ans + return -1 if ans == inf else ans ``` #### Java ```java class Solution { - private static final int INF = 0x3f3f; - public int networkDelayTime(int[][] times, int n, int k) { int[][] g = new int[n][n]; int[] dist = new int[n]; - boolean[] vis = new boolean[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - Arrays.fill(g[i], INF); + final int inf = 1 << 29; + Arrays.fill(dist, inf); + for (var e : g) { + Arrays.fill(e, inf); } - for (int[] t : times) { - g[t[0] - 1][t[1] - 1] = t[2]; + for (var e : times) { + g[e[0] - 1][e[1] - 1] = e[2]; } dist[k - 1] = 0; + boolean[] vis = new boolean[n]; for (int i = 0; i < n; ++i) { int t = -1; for (int j = 0; j < n; ++j) { @@ -124,10 +132,10 @@ class Solution { } } int ans = 0; - for (int d : dist) { - ans = Math.max(ans, d); + for (int x : dist) { + ans = Math.max(ans, x); } - return ans == INF ? -1 : ans; + return ans == inf ? -1 : ans; } } ``` @@ -137,14 +145,15 @@ class Solution { ```cpp class Solution { public: - const int inf = 0x3f3f; - int networkDelayTime(vector>& times, int n, int k) { + const int inf = 1 << 29; vector> g(n, vector(n, inf)); - for (auto& t : times) g[t[0] - 1][t[1] - 1] = t[2]; - vector vis(n); + for (const auto& e : times) { + g[e[0] - 1][e[1] - 1] = e[2]; + } vector dist(n, inf); dist[k - 1] = 0; + vector vis(n); for (int i = 0; i < n; ++i) { int t = -1; for (int j = 0; j < n; ++j) { @@ -157,7 +166,7 @@ public: dist[j] = min(dist[j], dist[t] + g[t][j]); } } - int ans = *max_element(dist.begin(), dist.end()); + int ans = ranges::max(dist); return ans == inf ? -1 : ans; } }; @@ -167,21 +176,25 @@ public: ```go func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f - dist := make([]int, n) - vis := make([]bool, n) + const inf = 1 << 29 g := make([][]int, n) - for i := range dist { - dist[i] = inf + for i := range g { g[i] = make([]int, n) for j := range g[i] { g[i][j] = inf } } - for _, t := range times { - g[t[0]-1][t[1]-1] = t[2] + for _, e := range times { + g[e[0]-1][e[1]-1] = e[2] + } + + dist := make([]int, n) + for i := range dist { + dist[i] = inf } dist[k-1] = 0 + + vis := make([]bool, n) for i := 0; i < n; i++ { t := -1 for j := 0; j < n; j++ { @@ -194,11 +207,39 @@ func networkDelayTime(times [][]int, n int, k int) int { dist[j] = min(dist[j], dist[t]+g[t][j]) } } - ans := slices.Max(dist) - if ans == inf { - return -1 + + if ans := slices.Max(dist); ans != inf { + return ans } - return ans + return -1 +} +``` + +#### TypeScript + +```ts +function networkDelayTime(times: number[][], n: number, k: number): number { + const g: number[][] = Array.from({ length: n }, () => Array(n).fill(Infinity)); + for (const [u, v, w] of times) { + g[u - 1][v - 1] = w; + } + const dist: number[] = Array(n).fill(Infinity); + dist[k - 1] = 0; + const vis: boolean[] = Array(n).fill(false); + for (let i = 0; i < n; ++i) { + let t = -1; + for (let j = 0; j < n; ++j) { + if (!vis[j] && (t === -1 || dist[j] < dist[t])) { + t = j; + } + } + vis[t] = true; + for (let j = 0; j < n; ++j) { + dist[j] = Math.min(dist[j], dist[t] + g[t][j]); + } + } + const ans = Math.max(...dist); + return ans === Infinity ? -1 : ans; } ``` @@ -208,7 +249,17 @@ func networkDelayTime(times [][]int, n int, k int) int { -### Solution 2 +### Solution 2: Heap-Optimized Dijkstra Algorithm + +We can use a priority queue (heap) to optimize the naive Dijkstra algorithm. + +We define $\textit{g}[u]$ to represent all adjacent edges of node $u$, and $\textit{dist}[u]$ to represent the shortest path length from node $k$ to node $u$. Initially, we set all $\textit{dist}[u]$ to $+\infty$, except for $\textit{dist}[k - 1] = 0$. + +We define a priority queue $\textit{pq}$, where each element is $(\textit{d}, u)$, representing the distance $\textit{d}$ from node $u$ to node $k$. Each time, we take out the node $(\textit{d}, u)$ with the smallest distance from $\textit{pq}$. If $\textit{d} > $\textit{dist}[u]$, we skip this node. Otherwise, we traverse all adjacent edges of node $u$. For each adjacent edge $(v, w)$, if $\textit{dist}[v] > \textit{dist}[u] + w$, we update $\textit{dist}[v] = \textit{dist}[u] + w$ and add $(\textit{dist}[v], v)$ to $\textit{pq}$. + +Finally, we return the maximum value in $\textit{dist}$ as the answer. If the answer is $+\infty$, it means there are unreachable nodes, and we return $-1$. + +The time complexity is $O(m \times \log m + n)$, and the space complexity is $O(n + m)$. Here, $n$ and $m$ are the number of nodes and edges, respectively. @@ -217,58 +268,56 @@ func networkDelayTime(times [][]int, n int, k int) int { ```python class Solution: def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - g = defaultdict(list) + g = [[] for _ in range(n)] for u, v, w in times: g[u - 1].append((v - 1, w)) - dist = [INF] * n + dist = [inf] * n dist[k - 1] = 0 - q = [(0, k - 1)] - while q: - _, u = heappop(q) + pq = [(0, k - 1)] + while pq: + d, u = heappop(pq) + if d > dist[u]: + continue for v, w in g[u]: - if dist[v] > dist[u] + w: - dist[v] = dist[u] + w - heappush(q, (dist[v], v)) + if (nd := d + w) < dist[v]: + dist[v] = nd + heappush(pq, (nd, v)) ans = max(dist) - return -1 if ans == INF else ans + return -1 if ans == inf else ans ``` #### Java ```java class Solution { - private static final int INF = 0x3f3f; - public int networkDelayTime(int[][] times, int n, int k) { + final int inf = 1 << 29; List[] g = new List[n]; - int[] dist = new int[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - g[i] = new ArrayList<>(); - } - for (int[] t : times) { - g[t[0] - 1].add(new int[] {t[1] - 1, t[2]}); + Arrays.setAll(g, i -> new ArrayList<>()); + for (var e : times) { + g[e[0] - 1].add(new int[] {e[1] - 1, e[2]}); } + int[] dist = new int[n]; + Arrays.fill(dist, inf); dist[k - 1] = 0; - PriorityQueue q = new PriorityQueue<>(Comparator.comparingInt(a -> a[0])); - q.offer(new int[] {0, k - 1}); - while (!q.isEmpty()) { - int[] p = q.poll(); - int u = p[1]; - for (int[] ne : g[u]) { - int v = ne[0], w = ne[1]; + PriorityQueue pq = new PriorityQueue<>(Comparator.comparingInt(a -> a[0])); + pq.offer(new int[] {0, k - 1}); + while (!pq.isEmpty()) { + var p = pq.poll(); + int d = p[0], u = p[1]; + if (d > dist[u]) { + continue; + } + for (var e : g[u]) { + int v = e[0], w = e[1]; if (dist[v] > dist[u] + w) { dist[v] = dist[u] + w; - q.offer(new int[] {dist[v], v}); + pq.offer(new int[] {dist[v], v}); } } } - int ans = 0; - for (int d : dist) { - ans = Math.max(ans, d); - } - return ans == INF ? -1 : ans; + int ans = Arrays.stream(dist).max().getAsInt(); + return ans == inf ? -1 : ans; } } ``` @@ -278,164 +327,34 @@ class Solution { ```cpp class Solution { public: - const int inf = 0x3f3f; - int networkDelayTime(vector>& times, int n, int k) { - vector>> g(n); - for (auto& t : times) g[t[0] - 1].push_back({t[1] - 1, t[2]}); + const int inf = 1 << 29; + using pii = pair; + vector> g(n); + for (auto& edge : times) { + g[edge[0] - 1].emplace_back(edge[1] - 1, edge[2]); + } + vector dist(n, inf); dist[k - 1] = 0; - priority_queue, vector>, greater>> q; - q.push({0, k - 1}); - while (!q.empty()) { - auto p = q.top(); - q.pop(); - int u = p[1]; - for (auto& ne : g[u]) { - int v = ne[0], w = ne[1]; + priority_queue, greater<>> pq; + pq.emplace(0, k - 1); + + while (!pq.empty()) { + auto [d, u] = pq.top(); + pq.pop(); + if (d > dist[u]) { + continue; + } + for (auto& [v, w] : g[u]) { if (dist[v] > dist[u] + w) { dist[v] = dist[u] + w; - q.push({dist[v], v}); + pq.emplace(dist[v], v); } } } - int ans = *max_element(dist.begin(), dist.end()); - return ans == inf ? -1 : ans; - } -}; -``` - -#### Go - -```go -const Inf = 0x3f3f3f3f - -type pair struct { - first int - second int -} - -var _ heap.Interface = (*pairs)(nil) - -type pairs []pair - -func (a pairs) Len() int { return len(a) } -func (a pairs) Less(i int, j int) bool { - return a[i].first < a[j].first || a[i].first == a[j].first && a[i].second < a[j].second -} -func (a pairs) Swap(i int, j int) { a[i], a[j] = a[j], a[i] } -func (a *pairs) Push(x any) { *a = append(*a, x.(pair)) } -func (a *pairs) Pop() any { l := len(*a); t := (*a)[l-1]; *a = (*a)[:l-1]; return t } - -func networkDelayTime(times [][]int, n int, k int) int { - graph := make([]pairs, n) - for _, time := range times { - from, to, time := time[0]-1, time[1]-1, time[2] - graph[from] = append(graph[from], pair{to, time}) - } - - dis := make([]int, n) - for i := range dis { - dis[i] = Inf - } - dis[k-1] = 0 - - vis := make([]bool, n) - h := make(pairs, 0) - heap.Push(&h, pair{0, k - 1}) - for len(h) > 0 { - from := heap.Pop(&h).(pair).second - if vis[from] { - continue - } - vis[from] = true - for _, e := range graph[from] { - to, d := e.first, dis[from]+e.second - if d < dis[to] { - dis[to] = d - heap.Push(&h, pair{d, to}) - } - } - } - ans := slices.Max(dis) - if ans == Inf { - return -1 - } - return ans -} -``` - - - - - - - -### Solution 3 - - - -#### Python3 - -```python -class Solution: - def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - dist[k - 1] = 0 - for _ in range(n): - backup = dist[:] - for u, v, w in times: - dist[v - 1] = min(dist[v - 1], dist[u - 1] + w) - ans = max(dist) - return -1 if ans == INF else ans -``` - -#### Java - -```java -class Solution { - private static final int INF = 0x3f3f; - - public int networkDelayTime(int[][] times, int n, int k) { - int[] dist = new int[n]; - int[] backup = new int[n]; - Arrays.fill(dist, INF); - dist[k - 1] = 0; - for (int i = 0; i < n; ++i) { - System.arraycopy(dist, 0, backup, 0, n); - for (int[] t : times) { - int u = t[0] - 1, v = t[1] - 1, w = t[2]; - dist[v] = Math.min(dist[v], backup[u] + w); - } - } - int ans = 0; - for (int i = 0; i < n; ++i) { - ans = Math.max(ans, dist[i]); - } - return ans == INF ? -1 : ans; - } -} -``` - -#### C++ -```cpp -class Solution { -public: - int inf = 0x3f3f; - - int networkDelayTime(vector>& times, int n, int k) { - vector dist(n, inf); - dist[k - 1] = 0; - for (int i = 0; i < n; ++i) { - vector backup = dist; - for (auto& e : times) { - int u = e[0] - 1, v = e[1] - 1, w = e[2]; - dist[v] = min(dist[v], backup[u] + w); - } - } - int ans = *max_element(dist.begin(), dist.end()); + int ans = ranges::max(dist); return ans == inf ? -1 : ans; } }; @@ -445,191 +364,75 @@ public: ```go func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f + g := make([][][2]int, n) + for _, e := range times { + u, v, w := e[0]-1, e[1]-1, e[2] + g[u] = append(g[u], [2]int{v, w}) + } dist := make([]int, n) - backup := make([]int, n) + const inf int = 1 << 29 for i := range dist { dist[i] = inf } dist[k-1] = 0 - for i := 0; i < n; i++ { - copy(backup, dist) - for _, e := range times { - u, v, w := e[0]-1, e[1]-1, e[2] - dist[v] = min(dist[v], backup[u]+w) + pq := hp{{0, k - 1}} + for len(pq) > 0 { + p := heap.Pop(&pq).(pair) + d, u := p.x, p.i + if d > dist[u] { + continue + } + for _, e := range g[u] { + v, w := e[0], e[1] + if nd := d + w; nd < dist[v] { + dist[v] = nd + heap.Push(&pq, pair{nd, v}) + } } } - ans := slices.Max(dist) - if ans == inf { - return -1 + if ans := slices.Max(dist); ans < inf { + return ans } - return ans -} -``` - - - - - - + return -1 -### Solution 4 +} - +type pair struct{ x, i int } +type hp []pair -#### Python3 - -```python -class Solution: - def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - vis = [False] * n - g = defaultdict(list) - for u, v, w in times: - g[u - 1].append((v - 1, w)) - k -= 1 - dist[k] = 0 - q = deque([k]) - vis[k] = True - while q: - u = q.popleft() - vis[u] = False - for v, w in g[u]: - if dist[v] > dist[u] + w: - dist[v] = dist[u] + w - if not vis[v]: - q.append(v) - vis[v] = True - ans = max(dist) - return -1 if ans == INF else ans +func (h hp) Len() int { return len(h) } +func (h hp) Less(i, j int) bool { return h[i].x < h[j].x } +func (h hp) Swap(i, j int) { h[i], h[j] = h[j], h[i] } +func (h *hp) Push(x any) { *h = append(*h, x.(pair)) } +func (h *hp) Pop() (x any) { a := *h; x = a[len(a)-1]; *h = a[:len(a)-1]; return } ``` -#### Java - -```java -class Solution { - private static final int INF = 0x3f3f; +#### TypeScript - public int networkDelayTime(int[][] times, int n, int k) { - int[] dist = new int[n]; - boolean[] vis = new boolean[n]; - List[] g = new List[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - g[i] = new ArrayList<>(); - } - for (int[] t : times) { - int u = t[0] - 1, v = t[1] - 1, w = t[2]; - g[u].add(new int[] {v, w}); - } - --k; - dist[k] = 0; - Deque q = new ArrayDeque<>(); - q.offer(k); - vis[k] = true; - while (!q.isEmpty()) { - int u = q.poll(); - vis[u] = false; - for (int[] ne : g[u]) { - int v = ne[0], w = ne[1]; - if (dist[v] > dist[u] + w) { - dist[v] = dist[u] + w; - if (!vis[v]) { - q.offer(v); - vis[v] = true; - } - } - } - } - int ans = 0; - for (int i = 0; i < n; ++i) { - ans = Math.max(ans, dist[i]); - } - return ans == INF ? -1 : ans; +```ts +function networkDelayTime(times: number[][], n: number, k: number): number { + const g: [number, number][][] = Array.from({ length: n }, () => []); + for (const [u, v, w] of times) { + g[u - 1].push([v - 1, w]); } -} -``` - -#### C++ - -```cpp -class Solution { -public: - const int inf = 0x3f3f; - - int networkDelayTime(vector>& times, int n, int k) { - vector dist(n, inf); - vector>> g(n); - for (auto& e : times) { - int u = e[0] - 1, v = e[1] - 1, w = e[2]; - g[u].push_back({v, w}); + const dist: number[] = Array(n).fill(Infinity); + dist[k - 1] = 0; + const pq = new MinPriorityQueue({ priority: v => v[0] }); + pq.enqueue([0, k - 1]); + while (!pq.isEmpty()) { + const [d, u] = pq.dequeue().element; + if (d > dist[u]) { + continue; } - vector vis(n); - --k; - queue q{{k}}; - vis[k] = true; - dist[k] = 0; - while (!q.empty()) { - int u = q.front(); - q.pop(); - vis[u] = false; - for (auto& ne : g[u]) { - int v = ne[0], w = ne[1]; - if (dist[v] > dist[u] + w) { - dist[v] = dist[u] + w; - if (!vis[v]) { - q.push(v); - vis[v] = true; - } - } + for (const [v, w] of g[u]) { + if (dist[v] > dist[u] + w) { + dist[v] = dist[u] + w; + pq.enqueue([dist[v], v]); } } - int ans = *max_element(dist.begin(), dist.end()); - return ans == inf ? -1 : ans; } -}; -``` - -#### Go - -```go -func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f - dist := make([]int, n) - vis := make([]bool, n) - g := make([][][]int, n) - for i := range dist { - dist[i] = inf - } - for _, t := range times { - u, v, w := t[0]-1, t[1]-1, t[2] - g[u] = append(g[u], []int{v, w}) - } - k-- - dist[k] = 0 - q := []int{k} - vis[k] = true - for len(q) > 0 { - u := q[0] - q = q[1:] - vis[u] = false - for _, ne := range g[u] { - v, w := ne[0], ne[1] - if dist[v] > dist[u]+w { - dist[v] = dist[u] + w - if !vis[v] { - q = append(q, v) - vis[v] = true - } - } - } - } - ans := slices.Max(dist) - if ans == inf { - return -1 - } - return ans + const ans = Math.max(...dist); + return ans === Infinity ? -1 : ans; } ``` diff --git a/solution/0700-0799/0743.Network Delay Time/Solution.cpp b/solution/0700-0799/0743.Network Delay Time/Solution.cpp index c68ed97c30279..589b43d777bc3 100644 --- a/solution/0700-0799/0743.Network Delay Time/Solution.cpp +++ b/solution/0700-0799/0743.Network Delay Time/Solution.cpp @@ -1,13 +1,14 @@ class Solution { public: - const int inf = 0x3f3f; - int networkDelayTime(vector>& times, int n, int k) { + const int inf = 1 << 29; vector> g(n, vector(n, inf)); - for (auto& t : times) g[t[0] - 1][t[1] - 1] = t[2]; - vector vis(n); + for (const auto& e : times) { + g[e[0] - 1][e[1] - 1] = e[2]; + } vector dist(n, inf); dist[k - 1] = 0; + vector vis(n); for (int i = 0; i < n; ++i) { int t = -1; for (int j = 0; j < n; ++j) { @@ -20,7 +21,7 @@ class Solution { dist[j] = min(dist[j], dist[t] + g[t][j]); } } - int ans = *max_element(dist.begin(), dist.end()); + int ans = ranges::max(dist); return ans == inf ? -1 : ans; } -}; \ No newline at end of file +}; diff --git a/solution/0700-0799/0743.Network Delay Time/Solution.go b/solution/0700-0799/0743.Network Delay Time/Solution.go index 490c5c75cc7a0..0614c61af3ffa 100644 --- a/solution/0700-0799/0743.Network Delay Time/Solution.go +++ b/solution/0700-0799/0743.Network Delay Time/Solution.go @@ -1,19 +1,23 @@ func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f - dist := make([]int, n) - vis := make([]bool, n) + const inf = 1 << 29 g := make([][]int, n) - for i := range dist { - dist[i] = inf + for i := range g { g[i] = make([]int, n) for j := range g[i] { g[i][j] = inf } } - for _, t := range times { - g[t[0]-1][t[1]-1] = t[2] + for _, e := range times { + g[e[0]-1][e[1]-1] = e[2] + } + + dist := make([]int, n) + for i := range dist { + dist[i] = inf } dist[k-1] = 0 + + vis := make([]bool, n) for i := 0; i < n; i++ { t := -1 for j := 0; j < n; j++ { @@ -26,9 +30,9 @@ func networkDelayTime(times [][]int, n int, k int) int { dist[j] = min(dist[j], dist[t]+g[t][j]) } } - ans := slices.Max(dist) - if ans == inf { - return -1 + + if ans := slices.Max(dist); ans != inf { + return ans } - return ans -} \ No newline at end of file + return -1 +} diff --git a/solution/0700-0799/0743.Network Delay Time/Solution.java b/solution/0700-0799/0743.Network Delay Time/Solution.java index 941e7ae1c3099..04bfdc47a4bc5 100644 --- a/solution/0700-0799/0743.Network Delay Time/Solution.java +++ b/solution/0700-0799/0743.Network Delay Time/Solution.java @@ -1,18 +1,17 @@ class Solution { - private static final int INF = 0x3f3f; - public int networkDelayTime(int[][] times, int n, int k) { int[][] g = new int[n][n]; int[] dist = new int[n]; - boolean[] vis = new boolean[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - Arrays.fill(g[i], INF); + final int inf = 1 << 29; + Arrays.fill(dist, inf); + for (var e : g) { + Arrays.fill(e, inf); } - for (int[] t : times) { - g[t[0] - 1][t[1] - 1] = t[2]; + for (var e : times) { + g[e[0] - 1][e[1] - 1] = e[2]; } dist[k - 1] = 0; + boolean[] vis = new boolean[n]; for (int i = 0; i < n; ++i) { int t = -1; for (int j = 0; j < n; ++j) { @@ -26,9 +25,9 @@ public int networkDelayTime(int[][] times, int n, int k) { } } int ans = 0; - for (int d : dist) { - ans = Math.max(ans, d); + for (int x : dist) { + ans = Math.max(ans, x); } - return ans == INF ? -1 : ans; + return ans == inf ? -1 : ans; } -} \ No newline at end of file +} diff --git a/solution/0700-0799/0743.Network Delay Time/Solution.py b/solution/0700-0799/0743.Network Delay Time/Solution.py index 16047a5d66c35..b26bf52aa655c 100644 --- a/solution/0700-0799/0743.Network Delay Time/Solution.py +++ b/solution/0700-0799/0743.Network Delay Time/Solution.py @@ -1,12 +1,11 @@ class Solution: def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - vis = [False] * n - g = [[INF] * n for _ in range(n)] + g = [[inf] * n for _ in range(n)] for u, v, w in times: g[u - 1][v - 1] = w + dist = [inf] * n dist[k - 1] = 0 + vis = [False] * n for _ in range(n): t = -1 for j in range(n): @@ -16,4 +15,4 @@ def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: for j in range(n): dist[j] = min(dist[j], dist[t] + g[t][j]) ans = max(dist) - return -1 if ans == INF else ans + return -1 if ans == inf else ans diff --git a/solution/0700-0799/0743.Network Delay Time/Solution.ts b/solution/0700-0799/0743.Network Delay Time/Solution.ts new file mode 100644 index 0000000000000..6102696d9b3e5 --- /dev/null +++ b/solution/0700-0799/0743.Network Delay Time/Solution.ts @@ -0,0 +1,23 @@ +function networkDelayTime(times: number[][], n: number, k: number): number { + const g: number[][] = Array.from({ length: n }, () => Array(n).fill(Infinity)); + for (const [u, v, w] of times) { + g[u - 1][v - 1] = w; + } + const dist: number[] = Array(n).fill(Infinity); + dist[k - 1] = 0; + const vis: boolean[] = Array(n).fill(false); + for (let i = 0; i < n; ++i) { + let t = -1; + for (let j = 0; j < n; ++j) { + if (!vis[j] && (t === -1 || dist[j] < dist[t])) { + t = j; + } + } + vis[t] = true; + for (let j = 0; j < n; ++j) { + dist[j] = Math.min(dist[j], dist[t] + g[t][j]); + } + } + const ans = Math.max(...dist); + return ans === Infinity ? -1 : ans; +} diff --git a/solution/0700-0799/0743.Network Delay Time/Solution2.cpp b/solution/0700-0799/0743.Network Delay Time/Solution2.cpp index 5aa9582036770..7e4bda5e91c31 100644 --- a/solution/0700-0799/0743.Network Delay Time/Solution2.cpp +++ b/solution/0700-0799/0743.Network Delay Time/Solution2.cpp @@ -1,27 +1,33 @@ class Solution { public: - const int inf = 0x3f3f; - int networkDelayTime(vector>& times, int n, int k) { - vector>> g(n); - for (auto& t : times) g[t[0] - 1].push_back({t[1] - 1, t[2]}); + const int inf = 1 << 29; + using pii = pair; + vector> g(n); + for (auto& edge : times) { + g[edge[0] - 1].emplace_back(edge[1] - 1, edge[2]); + } + vector dist(n, inf); dist[k - 1] = 0; - priority_queue, vector>, greater>> q; - q.push({0, k - 1}); - while (!q.empty()) { - auto p = q.top(); - q.pop(); - int u = p[1]; - for (auto& ne : g[u]) { - int v = ne[0], w = ne[1]; + priority_queue, greater<>> pq; + pq.emplace(0, k - 1); + + while (!pq.empty()) { + auto [d, u] = pq.top(); + pq.pop(); + if (d > dist[u]) { + continue; + } + for (auto& [v, w] : g[u]) { if (dist[v] > dist[u] + w) { dist[v] = dist[u] + w; - q.push({dist[v], v}); + pq.emplace(dist[v], v); } } } - int ans = *max_element(dist.begin(), dist.end()); + + int ans = ranges::max(dist); return ans == inf ? -1 : ans; } -}; \ No newline at end of file +}; diff --git a/solution/0700-0799/0743.Network Delay Time/Solution2.go b/solution/0700-0799/0743.Network Delay Time/Solution2.go index 01149a8fe0de9..05084001a4710 100644 --- a/solution/0700-0799/0743.Network Delay Time/Solution2.go +++ b/solution/0700-0799/0743.Network Delay Time/Solution2.go @@ -1,55 +1,42 @@ -const Inf = 0x3f3f3f3f - -type pair struct { - first int - second int -} - -var _ heap.Interface = (*pairs)(nil) - -type pairs []pair - -func (a pairs) Len() int { return len(a) } -func (a pairs) Less(i int, j int) bool { - return a[i].first < a[j].first || a[i].first == a[j].first && a[i].second < a[j].second -} -func (a pairs) Swap(i int, j int) { a[i], a[j] = a[j], a[i] } -func (a *pairs) Push(x any) { *a = append(*a, x.(pair)) } -func (a *pairs) Pop() any { l := len(*a); t := (*a)[l-1]; *a = (*a)[:l-1]; return t } - func networkDelayTime(times [][]int, n int, k int) int { - graph := make([]pairs, n) - for _, time := range times { - from, to, time := time[0]-1, time[1]-1, time[2] - graph[from] = append(graph[from], pair{to, time}) + g := make([][][2]int, n) + for _, e := range times { + u, v, w := e[0]-1, e[1]-1, e[2] + g[u] = append(g[u], [2]int{v, w}) } - - dis := make([]int, n) - for i := range dis { - dis[i] = Inf + dist := make([]int, n) + const inf int = 1 << 29 + for i := range dist { + dist[i] = inf } - dis[k-1] = 0 - - vis := make([]bool, n) - h := make(pairs, 0) - heap.Push(&h, pair{0, k - 1}) - for len(h) > 0 { - from := heap.Pop(&h).(pair).second - if vis[from] { + dist[k-1] = 0 + pq := hp{{0, k - 1}} + for len(pq) > 0 { + p := heap.Pop(&pq).(pair) + d, u := p.x, p.i + if d > dist[u] { continue } - vis[from] = true - for _, e := range graph[from] { - to, d := e.first, dis[from]+e.second - if d < dis[to] { - dis[to] = d - heap.Push(&h, pair{d, to}) + for _, e := range g[u] { + v, w := e[0], e[1] + if nd := d + w; nd < dist[v] { + dist[v] = nd + heap.Push(&pq, pair{nd, v}) } } } - ans := slices.Max(dis) - if ans == Inf { - return -1 + if ans := slices.Max(dist); ans < inf { + return ans } - return ans -} \ No newline at end of file + return -1 + +} + +type pair struct{ x, i int } +type hp []pair + +func (h hp) Len() int { return len(h) } +func (h hp) Less(i, j int) bool { return h[i].x < h[j].x } +func (h hp) Swap(i, j int) { h[i], h[j] = h[j], h[i] } +func (h *hp) Push(x any) { *h = append(*h, x.(pair)) } +func (h *hp) Pop() (x any) { a := *h; x = a[len(a)-1]; *h = a[:len(a)-1]; return } diff --git a/solution/0700-0799/0743.Network Delay Time/Solution2.java b/solution/0700-0799/0743.Network Delay Time/Solution2.java index 86ca85e907949..39c5348873cd7 100644 --- a/solution/0700-0799/0743.Network Delay Time/Solution2.java +++ b/solution/0700-0799/0743.Network Delay Time/Solution2.java @@ -1,34 +1,31 @@ class Solution { - private static final int INF = 0x3f3f; - public int networkDelayTime(int[][] times, int n, int k) { + final int inf = 1 << 29; List[] g = new List[n]; - int[] dist = new int[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - g[i] = new ArrayList<>(); - } - for (int[] t : times) { - g[t[0] - 1].add(new int[] {t[1] - 1, t[2]}); + Arrays.setAll(g, i -> new ArrayList<>()); + for (var e : times) { + g[e[0] - 1].add(new int[] {e[1] - 1, e[2]}); } + int[] dist = new int[n]; + Arrays.fill(dist, inf); dist[k - 1] = 0; - PriorityQueue q = new PriorityQueue<>(Comparator.comparingInt(a -> a[0])); - q.offer(new int[] {0, k - 1}); - while (!q.isEmpty()) { - int[] p = q.poll(); - int u = p[1]; - for (int[] ne : g[u]) { - int v = ne[0], w = ne[1]; + PriorityQueue pq = new PriorityQueue<>(Comparator.comparingInt(a -> a[0])); + pq.offer(new int[] {0, k - 1}); + while (!pq.isEmpty()) { + var p = pq.poll(); + int d = p[0], u = p[1]; + if (d > dist[u]) { + continue; + } + for (var e : g[u]) { + int v = e[0], w = e[1]; if (dist[v] > dist[u] + w) { dist[v] = dist[u] + w; - q.offer(new int[] {dist[v], v}); + pq.offer(new int[] {dist[v], v}); } } } - int ans = 0; - for (int d : dist) { - ans = Math.max(ans, d); - } - return ans == INF ? -1 : ans; + int ans = Arrays.stream(dist).max().getAsInt(); + return ans == inf ? -1 : ans; } -} \ No newline at end of file +} diff --git a/solution/0700-0799/0743.Network Delay Time/Solution2.py b/solution/0700-0799/0743.Network Delay Time/Solution2.py index 009bea471b470..d3dfae0da32dd 100644 --- a/solution/0700-0799/0743.Network Delay Time/Solution2.py +++ b/solution/0700-0799/0743.Network Delay Time/Solution2.py @@ -1,17 +1,18 @@ class Solution: def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - g = defaultdict(list) + g = [[] for _ in range(n)] for u, v, w in times: g[u - 1].append((v - 1, w)) - dist = [INF] * n + dist = [inf] * n dist[k - 1] = 0 - q = [(0, k - 1)] - while q: - _, u = heappop(q) + pq = [(0, k - 1)] + while pq: + d, u = heappop(pq) + if d > dist[u]: + continue for v, w in g[u]: - if dist[v] > dist[u] + w: - dist[v] = dist[u] + w - heappush(q, (dist[v], v)) + if (nd := d + w) < dist[v]: + dist[v] = nd + heappush(pq, (nd, v)) ans = max(dist) - return -1 if ans == INF else ans + return -1 if ans == inf else ans diff --git a/solution/0700-0799/0743.Network Delay Time/Solution2.ts b/solution/0700-0799/0743.Network Delay Time/Solution2.ts new file mode 100644 index 0000000000000..1e569b9c801ea --- /dev/null +++ b/solution/0700-0799/0743.Network Delay Time/Solution2.ts @@ -0,0 +1,24 @@ +function networkDelayTime(times: number[][], n: number, k: number): number { + const g: [number, number][][] = Array.from({ length: n }, () => []); + for (const [u, v, w] of times) { + g[u - 1].push([v - 1, w]); + } + const dist: number[] = Array(n).fill(Infinity); + dist[k - 1] = 0; + const pq = new MinPriorityQueue({ priority: v => v[0] }); + pq.enqueue([0, k - 1]); + while (!pq.isEmpty()) { + const [d, u] = pq.dequeue().element; + if (d > dist[u]) { + continue; + } + for (const [v, w] of g[u]) { + if (dist[v] > dist[u] + w) { + dist[v] = dist[u] + w; + pq.enqueue([dist[v], v]); + } + } + } + const ans = Math.max(...dist); + return ans === Infinity ? -1 : ans; +} diff --git a/solution/0700-0799/0743.Network Delay Time/Solution3.cpp b/solution/0700-0799/0743.Network Delay Time/Solution3.cpp deleted file mode 100644 index ce256623dcf49..0000000000000 --- a/solution/0700-0799/0743.Network Delay Time/Solution3.cpp +++ /dev/null @@ -1,18 +0,0 @@ -class Solution { -public: - int inf = 0x3f3f; - - int networkDelayTime(vector>& times, int n, int k) { - vector dist(n, inf); - dist[k - 1] = 0; - for (int i = 0; i < n; ++i) { - vector backup = dist; - for (auto& e : times) { - int u = e[0] - 1, v = e[1] - 1, w = e[2]; - dist[v] = min(dist[v], backup[u] + w); - } - } - int ans = *max_element(dist.begin(), dist.end()); - return ans == inf ? -1 : ans; - } -}; \ No newline at end of file diff --git a/solution/0700-0799/0743.Network Delay Time/Solution3.go b/solution/0700-0799/0743.Network Delay Time/Solution3.go deleted file mode 100644 index 002be604aa819..0000000000000 --- a/solution/0700-0799/0743.Network Delay Time/Solution3.go +++ /dev/null @@ -1,21 +0,0 @@ -func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f - dist := make([]int, n) - backup := make([]int, n) - for i := range dist { - dist[i] = inf - } - dist[k-1] = 0 - for i := 0; i < n; i++ { - copy(backup, dist) - for _, e := range times { - u, v, w := e[0]-1, e[1]-1, e[2] - dist[v] = min(dist[v], backup[u]+w) - } - } - ans := slices.Max(dist) - if ans == inf { - return -1 - } - return ans -} \ No newline at end of file diff --git a/solution/0700-0799/0743.Network Delay Time/Solution3.java b/solution/0700-0799/0743.Network Delay Time/Solution3.java deleted file mode 100644 index 5a961ad640e68..0000000000000 --- a/solution/0700-0799/0743.Network Delay Time/Solution3.java +++ /dev/null @@ -1,22 +0,0 @@ -class Solution { - private static final int INF = 0x3f3f; - - public int networkDelayTime(int[][] times, int n, int k) { - int[] dist = new int[n]; - int[] backup = new int[n]; - Arrays.fill(dist, INF); - dist[k - 1] = 0; - for (int i = 0; i < n; ++i) { - System.arraycopy(dist, 0, backup, 0, n); - for (int[] t : times) { - int u = t[0] - 1, v = t[1] - 1, w = t[2]; - dist[v] = Math.min(dist[v], backup[u] + w); - } - } - int ans = 0; - for (int i = 0; i < n; ++i) { - ans = Math.max(ans, dist[i]); - } - return ans == INF ? -1 : ans; - } -} \ No newline at end of file diff --git a/solution/0700-0799/0743.Network Delay Time/Solution3.py b/solution/0700-0799/0743.Network Delay Time/Solution3.py deleted file mode 100644 index 768e9dc2e85df..0000000000000 --- a/solution/0700-0799/0743.Network Delay Time/Solution3.py +++ /dev/null @@ -1,11 +0,0 @@ -class Solution: - def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - dist[k - 1] = 0 - for _ in range(n): - backup = dist[:] - for u, v, w in times: - dist[v - 1] = min(dist[v - 1], dist[u - 1] + w) - ans = max(dist) - return -1 if ans == INF else ans diff --git a/solution/0700-0799/0743.Network Delay Time/Solution4.cpp b/solution/0700-0799/0743.Network Delay Time/Solution4.cpp deleted file mode 100644 index 7bd884c23db07..0000000000000 --- a/solution/0700-0799/0743.Network Delay Time/Solution4.cpp +++ /dev/null @@ -1,35 +0,0 @@ -class Solution { -public: - const int inf = 0x3f3f; - - int networkDelayTime(vector>& times, int n, int k) { - vector dist(n, inf); - vector>> g(n); - for (auto& e : times) { - int u = e[0] - 1, v = e[1] - 1, w = e[2]; - g[u].push_back({v, w}); - } - vector vis(n); - --k; - queue q{{k}}; - vis[k] = true; - dist[k] = 0; - while (!q.empty()) { - int u = q.front(); - q.pop(); - vis[u] = false; - for (auto& ne : g[u]) { - int v = ne[0], w = ne[1]; - if (dist[v] > dist[u] + w) { - dist[v] = dist[u] + w; - if (!vis[v]) { - q.push(v); - vis[v] = true; - } - } - } - } - int ans = *max_element(dist.begin(), dist.end()); - return ans == inf ? -1 : ans; - } -}; \ No newline at end of file diff --git a/solution/0700-0799/0743.Network Delay Time/Solution4.go b/solution/0700-0799/0743.Network Delay Time/Solution4.go deleted file mode 100644 index ccf75347f03e4..0000000000000 --- a/solution/0700-0799/0743.Network Delay Time/Solution4.go +++ /dev/null @@ -1,37 +0,0 @@ -func networkDelayTime(times [][]int, n int, k int) int { - const inf = 0x3f3f - dist := make([]int, n) - vis := make([]bool, n) - g := make([][][]int, n) - for i := range dist { - dist[i] = inf - } - for _, t := range times { - u, v, w := t[0]-1, t[1]-1, t[2] - g[u] = append(g[u], []int{v, w}) - } - k-- - dist[k] = 0 - q := []int{k} - vis[k] = true - for len(q) > 0 { - u := q[0] - q = q[1:] - vis[u] = false - for _, ne := range g[u] { - v, w := ne[0], ne[1] - if dist[v] > dist[u]+w { - dist[v] = dist[u] + w - if !vis[v] { - q = append(q, v) - vis[v] = true - } - } - } - } - ans := slices.Max(dist) - if ans == inf { - return -1 - } - return ans -} \ No newline at end of file diff --git a/solution/0700-0799/0743.Network Delay Time/Solution4.java b/solution/0700-0799/0743.Network Delay Time/Solution4.java deleted file mode 100644 index a9465a8cb408e..0000000000000 --- a/solution/0700-0799/0743.Network Delay Time/Solution4.java +++ /dev/null @@ -1,41 +0,0 @@ -class Solution { - private static final int INF = 0x3f3f; - - public int networkDelayTime(int[][] times, int n, int k) { - int[] dist = new int[n]; - boolean[] vis = new boolean[n]; - List[] g = new List[n]; - for (int i = 0; i < n; ++i) { - dist[i] = INF; - g[i] = new ArrayList<>(); - } - for (int[] t : times) { - int u = t[0] - 1, v = t[1] - 1, w = t[2]; - g[u].add(new int[] {v, w}); - } - --k; - dist[k] = 0; - Deque q = new ArrayDeque<>(); - q.offer(k); - vis[k] = true; - while (!q.isEmpty()) { - int u = q.poll(); - vis[u] = false; - for (int[] ne : g[u]) { - int v = ne[0], w = ne[1]; - if (dist[v] > dist[u] + w) { - dist[v] = dist[u] + w; - if (!vis[v]) { - q.offer(v); - vis[v] = true; - } - } - } - } - int ans = 0; - for (int i = 0; i < n; ++i) { - ans = Math.max(ans, dist[i]); - } - return ans == INF ? -1 : ans; - } -} \ No newline at end of file diff --git a/solution/0700-0799/0743.Network Delay Time/Solution4.py b/solution/0700-0799/0743.Network Delay Time/Solution4.py deleted file mode 100644 index ef237bd6aa19e..0000000000000 --- a/solution/0700-0799/0743.Network Delay Time/Solution4.py +++ /dev/null @@ -1,23 +0,0 @@ -class Solution: - def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int: - INF = 0x3F3F - dist = [INF] * n - vis = [False] * n - g = defaultdict(list) - for u, v, w in times: - g[u - 1].append((v - 1, w)) - k -= 1 - dist[k] = 0 - q = deque([k]) - vis[k] = True - while q: - u = q.popleft() - vis[u] = False - for v, w in g[u]: - if dist[v] > dist[u] + w: - dist[v] = dist[u] + w - if not vis[v]: - q.append(v) - vis[v] = True - ans = max(dist) - return -1 if ans == INF else ans diff --git a/solution/3200-3299/3266.Final Array State After K Multiplication Operations II/Solution.go b/solution/3200-3299/3266.Final Array State After K Multiplication Operations II/Solution.go index b95914be7335c..4ca706435acf2 100644 --- a/solution/3200-3299/3266.Final Array State After K Multiplication Operations II/Solution.go +++ b/solution/3200-3299/3266.Final Array State After K Multiplication Operations II/Solution.go @@ -46,7 +46,7 @@ type pair struct{ x, i int } type hp []pair func (h hp) Len() int { return len(h) } -func (h hp) Less(i, j int) bool { return h[i].x < h[j].x || h[i].x == h[j].x && h[i].i < h[j].i } +func (h hp) Less(i, j int) bool { return h[i].x < h[j].x } func (h hp) Swap(i, j int) { h[i], h[j] = h[j], h[i] } func (h *hp) Push(x any) { *h = append(*h, x.(pair)) } -func (h *hp) Pop() any { a := *h; x := a[len(a)-1]; *h = a[:len(a)-1]; return x } +func (h *hp) Pop() (x any) { a := *h; x := a[len(a)-1]; *h = a[:len(a)-1]; return }