feat: add solutions to lc problems

* No.0787.Cheapest Flights Within K Stops
* No.0868.Binary Gap

Author: yanglbme

solution/0700-0799/0787.Cheapest Flights Within K Stops/README.md

@@ -58,14 +58,29 @@ src = 0, dst = 2, k = 0
 
 <!-- 这里可写通用的实现逻辑 -->
 
-DFS + 记忆化搜索。
+**方法一：Bellman Ford 算法**
+
+**方法二：DFS + 记忆化搜索**
 
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
+```python
+class Solution:
+    def findCheapestPrice(self, n: int, flights: List[List[int]], src: int, dst: int, k: int) -> int:
+        INF = 0x3f3f3f3f
+        dist = [INF] * n
+        dist[src] = 0
+        for _ in range(k + 1):
+            backup = dist.copy()
+            for f, t, p in flights:
+                dist[t] = min(dist[t], backup[f] + p)
+        return -1 if dist[dst] == INF else dist[dst]
+```
+
 ```python
 from functools import lru_cache
 
@@ -95,6 +110,27 @@ class Solution:
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
+```java
+class Solution {
+    private static final int INF = 0x3f3f3f3f;
+
+    public int findCheapestPrice(int n, int[][] flights, int src, int dst, int k) {
+        int[] dist = new int[n];
+        int[] backup = new int[n];
+        Arrays.fill(dist, INF);
+        dist[src] = 0;
+        for (int i = 0; i < k + 1; ++i) {
+            System.arraycopy(dist, 0, backup, 0, n);
+            for (int[] e : flights) {
+                int f = e[0], t = e[1], p = e[2];
+                dist[t] = Math.min(dist[t], backup[f] + p);
+            }
+        }
+        return dist[dst] == INF ? -1 : dist[dst];
+    }
+}
+```
+
 ```java
 class Solution {
     private int[][] memo;
@@ -141,6 +177,28 @@ class Solution {
 
 ### **C++**
 
+```cpp
+class Solution {
+public:
+    int findCheapestPrice(int n, vector<vector<int>>& flights, int src, int dst, int k) {
+        const int inf = 0x3f3f3f3f;
+        vector<int> dist(n, inf);
+        vector<int> backup;
+        dist[src] = 0;
+        for (int i = 0; i < k + 1; ++i)
+        {
+            backup = dist;
+            for (auto& e : flights)
+            {
+                int f = e[0], t = e[1], p = e[2];
+                dist[t] = min(dist[t], backup[f] + p);
+            }
+        }
+        return dist[dst] == inf ? -1 : dist[dst];
+    }
+};
+```
+
 ```cpp
 class Solution {
 public:
@@ -175,6 +233,36 @@ public:
 
 ### **Go**
 
+```go
+func findCheapestPrice(n int, flights [][]int, src int, dst int, k int) int {
+	const inf = 0x3f3f3f3f
+	dist := make([]int, n)
+	backup := make([]int, n)
+	for i := range dist {
+		dist[i] = inf
+	}
+	dist[src] = 0
+	for i := 0; i < k+1; i++ {
+		copy(backup, dist)
+		for _, e := range flights {
+			f, t, p := e[0], e[1], e[2]
+			dist[t] = min(dist[t], backup[f]+p)
+		}
+	}
+	if dist[dst] == inf {
+		return -1
+	}
+	return dist[dst]
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+```
+
 ```go
 func findCheapestPrice(n int, flights [][]int, src int, dst int, k int) int {
 	n += 10

solution/0700-0799/0787.Cheapest Flights Within K Stops/README_EN.md

@@ -61,6 +61,19 @@ The optimal path with no stops from city 0 to 2 is marked in red and has cost 50
 
 ### **Python3**
 
+```python
+class Solution:
+    def findCheapestPrice(self, n: int, flights: List[List[int]], src: int, dst: int, k: int) -> int:
+        INF = 0x3f3f3f3f
+        dist = [INF] * n
+        dist[src] = 0
+        for _ in range(k + 1):
+            backup = dist.copy()
+            for f, t, p in flights:
+                dist[t] = min(dist[t], backup[f] + p)
+        return -1 if dist[dst] == INF else dist[dst]
+```
+
 ```python
 from functools import lru_cache
 
@@ -88,6 +101,27 @@ class Solution:
 
 ### **Java**
 
+```java
+class Solution {
+    private static final int INF = 0x3f3f3f3f;
+
+    public int findCheapestPrice(int n, int[][] flights, int src, int dst, int k) {
+        int[] dist = new int[n];
+        int[] backup = new int[n];
+        Arrays.fill(dist, INF);
+        dist[src] = 0;
+        for (int i = 0; i < k + 1; ++i) {
+            System.arraycopy(dist, 0, backup, 0, n);
+            for (int[] e : flights) {
+                int f = e[0], t = e[1], p = e[2];
+                dist[t] = Math.min(dist[t], backup[f] + p);
+            }
+        }
+        return dist[dst] == INF ? -1 : dist[dst];
+    }
+}
+```
+
 ```java
 class Solution {
     private int[][] memo;
@@ -134,6 +168,28 @@ class Solution {
 
 ### **C++**
 
+```cpp
+class Solution {
+public:
+    int findCheapestPrice(int n, vector<vector<int>>& flights, int src, int dst, int k) {
+        const int inf = 0x3f3f3f3f;
+        vector<int> dist(n, inf);
+        vector<int> backup;
+        dist[src] = 0;
+        for (int i = 0; i < k + 1; ++i)
+        {
+            backup = dist;
+            for (auto& e : flights)
+            {
+                int f = e[0], t = e[1], p = e[2];
+                dist[t] = min(dist[t], backup[f] + p);
+            }
+        }
+        return dist[dst] == inf ? -1 : dist[dst];
+    }
+};
+```
+
 ```cpp
 class Solution {
 public:
@@ -168,6 +224,36 @@ public:
 
 ### **Go**
 
+```go
+func findCheapestPrice(n int, flights [][]int, src int, dst int, k int) int {
+	const inf = 0x3f3f3f3f
+	dist := make([]int, n)
+	backup := make([]int, n)
+	for i := range dist {
+		dist[i] = inf
+	}
+	dist[src] = 0
+	for i := 0; i < k+1; i++ {
+		copy(backup, dist)
+		for _, e := range flights {
+			f, t, p := e[0], e[1], e[2]
+			dist[t] = min(dist[t], backup[f]+p)
+		}
+	}
+	if dist[dst] == inf {
+		return -1
+	}
+	return dist[dst]
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+```
+
 ```go
 func findCheapestPrice(n int, flights [][]int, src int, dst int, k int) int {
 	n += 10

solution/0700-0799/0787.Cheapest Flights Within K Stops/Solution.cpp

@@ -1,29 +1,19 @@
-class Solution {
-public:
-    vector<vector<int>> memo;
-    vector<vector<int>> g;
-    int dst;
-    int inf = 1e6;
-
-    int findCheapestPrice(int n, vector<vector<int>>& flights, int src, int dst, int k) {
-        n += 10;
-        memo.resize(n, vector<int>(n, -1));
-        g.resize(n, vector<int>(n));
-        for (auto& e : flights) g[e[0]][e[1]] = e[2];
-        this->dst = dst;
-        int ans = dfs(src, k + 1);
-        return ans >= inf ? -1 : ans;
-    }
-
-    int dfs(int u, int k) {
-        if (memo[u][k] != -1) return memo[u][k];
-        if (u == dst) return 0;
-        if (k <= 0) return inf;
-        int ans = inf;
-        for (int v = 0; v < g[u].size(); ++v)
-            if (g[u][v] > 0)
-                ans = min(ans, dfs(v, k - 1) + g[u][v]);
-        memo[u][k] = ans;
-        return memo[u][k];
-    }
+class Solution {
+public:
+    int findCheapestPrice(int n, vector<vector<int>>& flights, int src, int dst, int k) {
+        const int inf = 0x3f3f3f3f;
+        vector<int> dist(n, inf);
+        vector<int> backup;
+        dist[src] = 0;
+        for (int i = 0; i < k + 1; ++i)
+        {
+            backup = dist;
+            for (auto& e : flights)
+            {
+                int f = e[0], t = e[1], p = e[2];
+                dist[t] = min(dist[t], backup[f] + p);
+            }
+        }
+        return dist[dst] == inf ? -1 : dist[dst];
+    }
 };

solution/0700-0799/0787.Cheapest Flights Within K Stops/Solution.go

@@ -1,49 +1,27 @@
-func findCheapestPrice(n int, flights [][]int, src int, dst int, k int) int {
-	n += 10
-	memo := make([][]int, n)
-	g := make([][]int, n)
-	for i := range memo {
-		memo[i] = make([]int, n)
-		g[i] = make([]int, n)
-		for j := range memo[i] {
-			memo[i][j] = -1
-		}
-	}
-
-	for _, e := range flights {
-		g[e[0]][e[1]] = e[2]
-	}
-	inf := int(1e6)
-	var dfs func(u, k int) int
-	dfs = func(u, k int) int {
-		if memo[u][k] != -1 {
-			return memo[u][k]
-		}
-		if u == dst {
-			return 0
-		}
-		if k <= 0 {
-			return inf
-		}
-		ans := inf
-		for v, p := range g[u] {
-			if p > 0 {
-				ans = min(ans, dfs(v, k-1)+p)
-			}
-		}
-		memo[u][k] = ans
-		return ans
-	}
-	ans := dfs(src, k+1)
-	if ans >= inf {
-		return -1
-	}
-	return ans
-}
-
-func min(a, b int) int {
-	if a < b {
-		return a
-	}
-	return b
+func findCheapestPrice(n int, flights [][]int, src int, dst int, k int) int {
+	const inf = 0x3f3f3f3f
+	dist := make([]int, n)
+	backup := make([]int, n)
+	for i := range dist {
+		dist[i] = inf
+	}
+	dist[src] = 0
+	for i := 0; i < k+1; i++ {
+		copy(backup, dist)
+		for _, e := range flights {
+			f, t, p := e[0], e[1], e[2]
+			dist[t] = min(dist[t], backup[f]+p)
+		}
+	}
+	if dist[dst] == inf {
+		return -1
+	}
+	return dist[dst]
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
 }