增加带备忘录的深度优先搜索和动态规划

Author: diguage

docs/0787-cheapest-flights-within-k-stops.adoc

@@ -7,7 +7,6 @@ https://leetcode.cn/problems/cheapest-flights-within-k-stops/[LeetCode - 787. K
 
 现在给定所有的城市和航班，以及出发城市 `src` 和目的地 `dst`，你的任务是找到出一条最多经过 `k` 站中转的路线，使得从 `src` 到 `dst` 的 *价格最便宜* ，并返回该价格。 如果不存在这样的路线，则输出 `-1`。
 
-
 *示例 1：*
 
 image::images/0787-01.png[{image_attr}]
@@ -61,11 +60,10 @@ image::images/0787-03.png[{image_attr}]
 
 == 思路分析
 
-
 [[src-0787]]
 [tabs]
 ====
-一刷（回溯，超时）::
+一刷（深度优先搜索，超时）::
 +
 --
 [{java_src_attr}]
@@ -74,12 +72,21 @@ include::{sourcedir}/_0787_CheapestFlightsWithinKStops.java[tag=answer]
 ----
 --
 
+一刷（带备忘录的深度优先搜索）::
++
+--
+[{java_src_attr}]
+----
+include::{sourcedir}/_0787_CheapestFlightsWithinKStops_10.java[tag=answer]
+----
+--
+
 一刷（动态规划）::
 +
 --
 [{java_src_attr}]
 ----
-include::{sourcedir}/_0787_CheapestFlightsWithinKStops_1.java[tag=answer]
+include::{sourcedir}/_0787_CheapestFlightsWithinKStops_11.java[tag=answer]
 ----
 --
 
@@ -93,7 +100,9 @@ include::{sourcedir}/_0787_CheapestFlightsWithinKStops_1.java[tag=answer]
 // --
 ====
 
-
 == 参考资料
 
-
+. https://leetcode.cn/problems/cheapest-flights-within-k-stops/solutions/954402/k-zhan-zhong-zhuan-nei-zui-bian-yi-de-ha-abzi/[787. K 站中转内最便宜的航班 - 官方题解^]
+. https://leetcode.cn/problems/cheapest-flights-within-k-stops/solutions/955290/gong-shui-san-xie-xiang-jie-bellman-ford-dc94/[787. K 站中转内最便宜的航班 - 运用 Bellman Ford 求解有限制的最短路问题^]
+. https://leetcode.cn/problems/cheapest-flights-within-k-stops/solutions/3637197/xi-you-yuan-su-787-k-zhan-zhong-zhuan-ne-xik1/[787. K 站中转内最便宜的航班 - 「稀有猿诉」787. K 站中转内最便宜的航班「DFS/记忆化搜索」^]
+. https://leetcode.cn/problems/cheapest-flights-within-k-stops/solutions/956113/tong-ge-lai-shua-ti-la-yi-ti-si-jie-bfs-deqpt/[787. K 站中转内最便宜的航班 - 【彤哥来刷题啦】一题六解：1ms & 100% & 记忆化搜索 & DP & DP优化 & BFS & Bellman-Ford & SPFA！^]

logbook/202503.adoc

@@ -616,7 +616,7 @@ endif::[]
 |{counter:codes2503}
 |{leetcode_base_url}/cheapest-flights-within-k-stops/[787. K 站中转内最便宜的航班^]
 |{doc_base_url}/0787-cheapest-flights-within-k-stops.adoc[题解]
-|⭕️ 回溯解法通过 48 / 56 个测试用例。
+|⭕️ 深度优先搜索通过 48 / 56 个测试用例。使用带备忘录的深度优先搜索顺利通过。带备忘录的深度优先搜索，也可以优化成动态规划。
 
 
 |===

src/main/java/com/diguage/algo/leetcode/_0787_CheapestFlightsWithinKStops.java

@@ -5,6 +5,8 @@
 public class _0787_CheapestFlightsWithinKStops {
   // tag::answer[]
   /**
+   * 通过 48 / 56 个测试用例。然后超时
+   *
    * @author D瓜哥 · https://www.diguage.com
    * @since 2025-05-06 18:53:25
    */
@@ -16,13 +18,12 @@ public int findCheapestPrice(int n, int[][] flights, int src, int dst, int k) {
       int start = flight[0];
       srcMap.computeIfAbsent(start, x -> new ArrayList<>()).add(flight);
     }
-    backtrack(n, srcMap, src, dst, k + 1, 0);
+    dfs(n, srcMap, src, dst, k + 1, 0);
     return result == Integer.MAX_VALUE ? -1 : result;
   }
 
-  private void backtrack(int n, Map<Integer, List<int[]>> srcMap,
-                         int src, int dst, int k, int expend) {
-
+  private void dfs(int n, Map<Integer, List<int[]>> srcMap,
+                   int src, int dst, int k, int expend) {
     if (k < 0) {
       return;
     }
@@ -37,9 +38,10 @@ private void backtrack(int n, Map<Integer, List<int[]>> srcMap,
       if (cost + expend >= result) {
         continue;
       }
-      backtrack(n, srcMap, idst, dst, k - 1, cost + expend);
+      dfs(n, srcMap, idst, dst, k - 1, cost + expend);
     }
   }
+
   // end::answer[]
   public static void main(String[] args) {
     new _0787_CheapestFlightsWithinKStops().findCheapestPrice(4,

src/main/java/com/diguage/algo/leetcode/_0787_CheapestFlightsWithinKStops_1.java

@@ -0,0 +1,55 @@
+package com.diguage.algo.leetcode;
+
+import java.util.*;
+
+public class _0787_CheapestFlightsWithinKStops_10 {
+  // tag::answer[]
+
+  /**
+   * @author D瓜哥 · https://www.diguage.com
+   * @since 2025-05-06 21:30:38
+   */
+  final int MAX = 100 * 10000 + 1;
+
+  public int findCheapestPrice(int n, int[][] flights, int src, int dst, int k) {
+    Map<Integer, List<int[]>> srcMap = new HashMap<>();
+    for (int[] flight : flights) {
+      int start = flight[0];
+      srcMap.computeIfAbsent(start, x -> new ArrayList<>()).add(flight);
+    }
+    int[][] memo = new int[n][k + 1];
+    int result = dfs(n, srcMap, src, dst, k + 1, memo);
+    return result == MAX ? -1 : result;
+  }
+
+  private int dfs(int n, Map<Integer, List<int[]>> srcMap,
+                  int src, int dst, int k, int[][] memo) {
+    if (k < 0) {
+      return MAX;
+    }
+    if (src == dst) {
+      return 0;
+    }
+    if (memo[src][k] != 0) {
+      return memo[src][k];
+    }
+    int result = MAX;
+    for (int[] flight : srcMap.getOrDefault(src, Collections.emptyList())) {
+      int idst = flight[1];
+      int cost = flight[2];
+      result = Math.min(result, dfs(n, srcMap, idst, dst, k - 1, memo) + cost);
+    }
+    memo[src][k] = result;
+    return result;
+  }
+  // end::answer[]
+  public static void main(String[] args) {
+    new _0787_CheapestFlightsWithinKStops_10().findCheapestPrice(4,
+      new int[][]{
+        {0, 1, 100},
+        {1, 2, 100},
+        {2, 0, 100},
+        {1, 3, 600},
+        {2, 3, 200}}, 0, 3, 1);
+  }
+}

src/main/java/com/diguage/algo/leetcode/_0787_CheapestFlightsWithinKStops_10.java

@@ -0,0 +1,43 @@
+package com.diguage.algo.leetcode;
+
+import java.util.Arrays;
+
+public class _0787_CheapestFlightsWithinKStops_11 {
+  // tag::answer[]
+
+  /**
+   * @author D瓜哥 · https://www.diguage.com
+   * @since 2025-05-06 21:40:38
+   */
+  public int findCheapestPrice(int n, int[][] flights, int src, int dst, int k) {
+    final int MAX = 100 * 10000 + 1;
+    int[][] dp = new int[k + 2][n];
+    for (int i = 0; i < k + 2; i++) {
+      Arrays.fill(dp[i], MAX);
+    }
+    dp[0][src] = 0;
+    for (int i = 1; i < k + 2; i++) {
+      for (int[] flight : flights) {
+        int start = flight[0];
+        int end = flight[1];
+        int cost = flight[2];
+        dp[i][end] = Math.min(dp[i][end], dp[i - 1][start] + cost);
+      }
+    }
+    int result = MAX;
+    for (int i = 1; i < k + 2; i++) {
+      result = Math.min(result, dp[i][dst]);
+    }
+    return result == MAX ? -1 : result;
+  }
+  // end::answer[]
+  public static void main(String[] args) {
+    new _0787_CheapestFlightsWithinKStops_11().findCheapestPrice(4,
+      new int[][]{
+        {0, 1, 100},
+        {1, 2, 100},
+        {2, 0, 100},
+        {1, 3, 600},
+        {2, 3, 200}}, 0, 3, 1);
+  }
+}