From 99d8b346b0a32c1a1c0f7c8db72ddbe369a1f0e4 Mon Sep 17 00:00:00 2001 From: yanglbme Date: Wed, 20 Sep 2023 08:45:57 +0800 Subject: [PATCH] feat: add solutions to lcp problems: No.06,07 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * No.06.拿硬币 * No.07.传递信息 --- .../README.md" | 75 ++++---- .../Solution.c" | 18 +- .../Solution.cpp" | 16 +- .../Solution.go" | 9 +- .../Solution.java" | 16 +- .../Solution.php" | 8 +- .../Solution.py" | 6 +- .../Solution.rs" | 5 + .../Solution.ts" | 4 +- .../README.md" | 163 +++++++++++++++++- .../Solution.cpp" | 16 ++ .../Solution.go" | 13 ++ .../Solution.java" | 27 +-- .../Solution.py" | 17 +- .../Solution.ts" | 12 ++ 15 files changed, 306 insertions(+), 99 deletions(-) create mode 100644 "lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.rs" create mode 100644 "lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.cpp" create mode 100644 "lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.go" create mode 100644 "lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.ts" diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/README.md" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/README.md" index 7a7bbda366870..0612321f5df16 100644 --- "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/README.md" +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/README.md" @@ -35,6 +35,14 @@ +**方法一：数学** + +我们可以发现，每堆力扣币拿完的最少次数，等于该堆力扣币数量除以 $2$ 向上取整的结果之和。 + +因此，我们只需要遍历每堆力扣币 $x_i$，计算每堆力扣币拿完的最少次数 $\left \lceil x_i/2 \right \rceil$，然后累加即可。 + +时间复杂度 $O(n)$，其中 $n$ 是数组 $coins$ 的长度。空间复杂度 $O(1)$。 + ### **Python3** @@ -44,7 +52,7 @@ ```python class Solution: def minCount(self, coins: List[int]) -> int: - return sum((coin + 1) // 2 for coin in coins) + return sum((x + 1) >> 1 for x in coins) ``` ### **Java** @@ -55,8 +63,8 @@ class Solution: class Solution { public int minCount(int[] coins) { int ans = 0; - for (int coin : coins) { - ans += (coin + 1) / 2; + for (int x : coins) { + ans += (x + 1) >> 1; } return ans; } @@ -70,7 +78,9 @@ class Solution { public: int minCount(vector& coins) { int ans = 0; - for (int coin : coins) ans += (coin + 1) / 2; + for (int x : coins) { + ans += (x + 1) >> 1; + } return ans; } }; @@ -79,38 +89,43 @@ public: ### **Go** ```go -func minCount(coins []int) int { - ans := 0 - for _, coin := range coins { - ans += (coin + 1) / 2 +func minCount(coins []int) (ans int) { + for _, x := range coins { + ans += (x + 1) >> 1 } - return ans + return } ``` -### **C** +### **TypeScript** -```c -int minCount(int* coins, int coinsSize) { - int res = 0; - for (int i = 0; i < coinsSize; i++) { - int coin = coins[i]; - if (coin % 2 == 1) { - res++; - } - res += coin / 2; +```ts +function minCount(coins: number[]): number { + let ans = 0; + for (const x of coins) { + ans += (x + 1) >> 1; } - return res; + return ans; } ``` -### **TypeScript** +### **Rust** -```ts -function minCount(coins: number[]): number { - let ans = 0; - for (const coin of coins) { - ans += Math.floor((coin + 1) / 2); +```rust +impl Solution { + pub fn min_count(coins: Vec) -> i32 { + coins.iter().map(|&x| (x + 1) >> 1).sum::() + } +} +``` + +### **C** + +```c +int minCount(int* coins, int coinsSize) { + int ans = 0; + for (int i = 0; i < coinsSize; ++i) { + ans += (coins[i] + 1) >> 1; } return ans; } @@ -125,11 +140,11 @@ class Solution { * @return Integer */ function minCount($coins) { - $cnt = 0; - for ($i = 0; $i < count($coins); $i++) { - $cnt += floor($coins[$i] / 2) + ($coins[$i] % 2); + $ans = 0; + foreach ($coins as $x) { + $ans += $x + 1 >> 1; } - return $cnt; + return $ans; } } ``` diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.c" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.c" index f6298086d63be..574ebaec9fd13 100644 --- "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.c" +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.c" @@ -1,11 +1,7 @@ -int minCount(int* coins, int coinsSize) { - int res = 0; - for (int i = 0; i < coinsSize; i++) { - int coin = coins[i]; - if (coin % 2 == 1) { - res++; - } - res += coin / 2; - } - return res; -} +int minCount(int* coins, int coinsSize) { + int ans = 0; + for (int i = 0; i < coinsSize; ++i) { + ans += (coins[i] + 1) >> 1; + } + return ans; +} diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.cpp" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.cpp" index 23010356078b0..df83766f5bd46 100644 --- "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.cpp" +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.cpp" @@ -1,8 +1,10 @@ -class Solution { -public: - int minCount(vector& coins) { - int ans = 0; - for (int coin : coins) ans += (coin + 1) / 2; - return ans; - } +class Solution { +public: + int minCount(vector& coins) { + int ans = 0; + for (int x : coins) { + ans += (x + 1) >> 1; + } + return ans; + } }; \ No newline at end of file diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.go" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.go" index 7c0f5389b52e9..6b139b2bcc349 100644 --- "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.go" +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.go" @@ -1,7 +1,6 @@ -func minCount(coins []int) int { - ans := 0 - for _, coin := range coins { - ans += (coin + 1) / 2 +func minCount(coins []int) (ans int) { + for _, x := range coins { + ans += (x + 1) >> 1 } - return ans + return } \ No newline at end of file diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.java" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.java" index fa339a8766214..d161f48579e3a 100644 --- "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.java" +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.java" @@ -1,9 +1,9 @@ -class Solution { - public int minCount(int[] coins) { - int ans = 0; - for (int coin : coins) { - ans += (coin + 1) / 2; - } - return ans; - } +class Solution { + public int minCount(int[] coins) { + int ans = 0; + for (int x : coins) { + ans += (x + 1) >> 1; + } + return ans; + } } \ No newline at end of file diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.php" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.php" index 9cc0ed5669ddc..fad936e2ae3a4 100644 --- "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.php" +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.php" @@ -4,10 +4,10 @@ class Solution { * @return Integer */ function minCount($coins) { - $cnt = 0; - for ($i = 0; $i < count($coins); $i++) { - $cnt += floor($coins[$i] / 2) + ($coins[$i] % 2); + $ans = 0; + foreach ($coins as $x) { + $ans += $x + 1 >> 1; } - return $cnt; + return $ans; } } \ No newline at end of file diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.py" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.py" index 5907837660eb2..353670e0c9cae 100644 --- "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.py" +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.py" @@ -1,3 +1,3 @@ -class Solution: - def minCount(self, coins: List[int]) -> int: - return sum((coin + 1) // 2 for coin in coins) +class Solution: + def minCount(self, coins: List[int]) -> int: + return sum((x + 1) >> 1 for x in coins) diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.rs" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.rs" new file mode 100644 index 0000000000000..a7e6073350592 --- /dev/null +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.rs" @@ -0,0 +1,5 @@ +impl Solution { + pub fn min_count(coins: Vec) -> i32 { + coins.iter().map(|&x| (x + 1) >> 1).sum::() + } +} \ No newline at end of file diff --git "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.ts" "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.ts" index 0ef82440a05b5..31666f18a1651 100644 --- "a/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.ts" +++ "b/lcp/LCP 06. \346\213\277\347\241\254\345\270\201/Solution.ts" @@ -1,7 +1,7 @@ function minCount(coins: number[]): number { let ans = 0; - for (const coin of coins) { - ans += Math.floor((coin + 1) / 2); + for (const x of coins) { + ans += (x + 1) >> 1; } return ans; } diff --git "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/README.md" "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/README.md" index 0400bc1804a0c..4832e1bfe824d 100644 --- "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/README.md" +++ "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/README.md" @@ -49,6 +49,16 @@ **方法一：动态规划** +我们定义 $f[i][j]$ 表示经过 $i$ 轮传递到编号 $j$ 的方案数，那么最终答案即为 $f[k][n-1]$。初始时 $f[0][0]=1$，其余均为 $0$。 + +当 $i \gt 0$ 时，对于每个玩家 $b$，考虑所有传递到他的玩家 $a$，有 $f[i][b]=\sum_{a \to b} f[i-1][a]$，其中 $a \to b$ 表示所有满足 $a$ 可以传递到 $b$ 的玩家 $a$。 + +最终答案即为 $f[k][n-1]$。 + +我们注意到 $f[i][b]$ 只与 $f[i-1][a]$ 有关，根据状态转移方程，我们可以使用滚动数组的方式，将空间复杂度优化到 $O(n)$。 + +时间复杂度 $O(k \times m)$，空间复杂度 $O(n)$，其中 $m$ 为 $relation$ 的长度。 + ### **Python3** @@ -58,12 +68,24 @@ ```python class Solution: def numWays(self, n: int, relation: List[List[int]], k: int) -> int: - dp = [[0] * n for _ in range(k + 1)] - dp[0][0] = 1 + f = [[0] * n for _ in range(k + 1)] + f[0][0] = 1 for i in range(1, k + 1): for a, b in relation: - dp[i][b] += dp[i - 1][a] - return dp[-1][-1] + f[i][b] += f[i - 1][a] + return f[-1][-1] +``` + +```python +class Solution: + def numWays(self, n: int, relation: List[List[int]], k: int) -> int: + f = [1] + [0] * (n - 1) + for _ in range(k): + g = [0] * n + for a, b in relation: + g[b] += f[a] + f = g + return f[-1] ``` ### **Java** @@ -73,15 +95,138 @@ class Solution: ```java class Solution { public int numWays(int n, int[][] relation, int k) { - int[][] dp = new int[k + 1][n]; - dp[0][0] = 1; - for (int i = 1; i <= k; i++) { + int[][] f = new int[k + 1][n]; + f[0][0] = 1; + for (int i = 1; i <= k; ++i) { + for (int[] r : relation) { + int a = r[0], b = r[1]; + f[i][b] += f[i - 1][a]; + } + } + return f[k][n - 1]; + } +} +``` + +```java +class Solution { + public int numWays(int n, int[][] relation, int k) { + int[] f = new int[n]; + f[0] = 1; + while (k-- > 0) { + int[] g = new int[n]; for (int[] r : relation) { - dp[i][r[1]] += dp[i - 1][r[0]]; + int a = r[0], b = r[1]; + g[b] += f[a]; } + f = g; + } + return f[n - 1]; + } +} +``` + +### **C++** + +```cpp +class Solution { +public: + int numWays(int n, vector>& relation, int k) { + int f[k + 1][n]; + memset(f, 0, sizeof(f)); + f[0][0] = 1; + for (int i = 1; i <= k; ++i) { + for (auto& r : relation) { + int a = r[0], b = r[1]; + f[i][b] += f[i - 1][a]; + } + } + return f[k][n - 1]; + } +}; +``` + +```cpp +class Solution { +public: + int numWays(int n, vector>& relation, int k) { + vector f(n); + f[0] = 1; + while (k--) { + vector g(n); + for (auto& r : relation) { + int a = r[0], b = r[1]; + g[b] += f[a]; + } + f = move(g); + } + return f[n - 1]; + } +}; +``` + +### **Go** + +```go +func numWays(n int, relation [][]int, k int) int { + f := make([][]int, k+1) + for i := range f { + f[i] = make([]int, n) + } + f[0][0] = 1 + for i := 1; i <= k; i++ { + for _, r := range relation { + a, b := r[0], r[1] + f[i][b] += f[i-1][a] + } + } + return f[k][n-1] +} +``` + +```go +func numWays(n int, relation [][]int, k int) int { + f := make([]int, n) + f[0] = 1 + for ; k > 0; k-- { + g := make([]int, n) + for _, r := range relation { + a, b := r[0], r[1] + g[b] += f[a] + } + f = g + } + return f[n-1] +} +``` + +### **TypeScript** + +```ts +function numWays(n: number, relation: number[][], k: number): number { + const f: number[][] = new Array(k + 1).fill(0).map(() => new Array(n).fill(0)); + f[0][0] = 1; + for (let i = 1; i <= k; ++i) { + for (const [a, b] of relation) { + f[i][b] += f[i - 1][a]; + } + } + return f[k][n - 1]; +} +``` + +```ts +function numWays(n: number, relation: number[][], k: number): number { + let f: number[] = new Array(n).fill(0); + f[0] = 1; + while (k--) { + const g: number[] = new Array(n).fill(0); + for (const [a, b] of relation) { + g[b] += f[a]; } - return dp[k][n - 1]; + f = g; } + return f[n - 1]; } ``` diff --git "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.cpp" "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.cpp" new file mode 100644 index 0000000000000..043cbd94491d0 --- /dev/null +++ "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.cpp" @@ -0,0 +1,16 @@ +class Solution { +public: + int numWays(int n, vector>& relation, int k) { + vector f(n); + f[0] = 1; + while (k--) { + vector g(n); + for (auto& r : relation) { + int a = r[0], b = r[1]; + g[b] += f[a]; + } + f = move(g); + } + return f[n - 1]; + } +}; \ No newline at end of file diff --git "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.go" "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.go" new file mode 100644 index 0000000000000..fb8b55bf50ac9 --- /dev/null +++ "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.go" @@ -0,0 +1,13 @@ +func numWays(n int, relation [][]int, k int) int { + f := make([]int, n) + f[0] = 1 + for ; k > 0; k-- { + g := make([]int, n) + for _, r := range relation { + a, b := r[0], r[1] + g[b] += f[a] + } + f = g + } + return f[n-1] +} \ No newline at end of file diff --git "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.java" "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.java" index bb4d430e55cd4..1b4b9c512f714 100644 --- "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.java" +++ "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.java" @@ -1,12 +1,15 @@ -class Solution { - public int numWays(int n, int[][] relation, int k) { - int[][] dp = new int[k + 1][n]; - dp[0][0] = 1; - for (int i = 1; i <= k; i++) { - for (int[] r : relation) { - dp[i][r[1]] += dp[i - 1][r[0]]; - } - } - return dp[k][n - 1]; - } -} +class Solution { + public int numWays(int n, int[][] relation, int k) { + int[] f = new int[n]; + f[0] = 1; + while (k-- > 0) { + int[] g = new int[n]; + for (int[] r : relation) { + int a = r[0], b = r[1]; + g[b] += f[a]; + } + f = g; + } + return f[n - 1]; + } +} \ No newline at end of file diff --git "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.py" "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.py" index a67e5411e4654..f3daa4a992089 100644 --- "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.py" +++ "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.py" @@ -1,8 +1,9 @@ -class Solution: - def numWays(self, n: int, relation: List[List[int]], k: int) -> int: - dp = [[0] * n for _ in range(k + 1)] - dp[0][0] = 1 - for i in range(1, k + 1): - for a, b in relation: - dp[i][b] += dp[i - 1][a] - return dp[-1][-1] +class Solution: + def numWays(self, n: int, relation: List[List[int]], k: int) -> int: + f = [1] + [0] * (n - 1) + for _ in range(k): + g = [0] * n + for a, b in relation: + g[b] += f[a] + f = g + return f[-1] diff --git "a/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.ts" "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.ts" new file mode 100644 index 0000000000000..76c6849eb1790 --- /dev/null +++ "b/lcp/LCP 07. \344\274\240\351\200\222\344\277\241\346\201\257/Solution.ts" @@ -0,0 +1,12 @@ +function numWays(n: number, relation: number[][], k: number): number { + let f: number[] = new Array(n).fill(0); + f[0] = 1; + while (k--) { + const g: number[] = new Array(n).fill(0); + for (const [a, b] of relation) { + g[b] += f[a]; + } + f = g; + } + return f[n - 1]; +}