二刷931

Author: diguage

docs/0931-minimum-falling-path-sum.adoc

@@ -1,42 +1,42 @@
 [#0931-minimum-falling-path-sum]
-= 931. Minimum Falling Path Sum
+= 931. 下降路径最小和
 
-{leetcode}/problems/minimum-falling-path-sum/[LeetCode - Minimum Falling Path Sum^]
+https://leetcode.cn/problems/minimum-falling-path-sum/[LeetCode - 931. 下降路径最小和 ^]
 
-Given a *square* array of integers `A`, we want the *minimum* sum of a _falling path_ through `A`.
+给你一个 `n x n` 的 *方形* 整数数组 `matrix` ，请你找出并返回通过 `matrix` 的 **下降路径** 的 *最小和* 。
 
-A falling path starts at any element in the first row, and chooses one element from each row.  The next row's choice must be in a column that is different from the previous row's column by at most one.
+*下降路径* 可以从第一行中的任何元素开始，并从每一行中选择一个元素。在下一行选择的元素和当前行所选元素最多相隔一列（即位于正下方或者沿对角线向左或者向右的第一个元素）。具体来说，位置 `(row, col)` 的下一个元素应当是 `(row + 1, col - 1)`、`(row + 1, col)` 或者 `(row + 1, col + 1)`。
 
- 
+*示例 1：*
 
-*Example 1:*
-
-[subs="verbatim,quotes,macros"]
-----
-*Input:* [[1,2,3],[4,5,6],[7,8,9]]
-*Output:* 12
-*Explanation:*
-The possible falling paths are:
-----
+image::images/0931-01.jpg[{image_attr}]
 
+....
+输入：matrix = [[2,1,3],[6,5,4],[7,8,9]]
+输出：13
+解释：如图所示，为和最小的两条下降路径
+....
 
-* `[1,4,7], [1,4,8], [1,5,7], [1,5,8], [1,5,9]`
-* `[2,4,7], [2,4,8], [2,5,7], [2,5,8], [2,5,9], [2,6,8], [2,6,9]`
-* `[3,5,7], [3,5,8], [3,5,9], [3,6,8], [3,6,9]`
+*示例 2：*
 
+image::images/0931-02.jpg[{image_attr}]
 
-The falling path with the smallest sum is `[1,4,7]`, so the answer is `12`.
+....
+输入：matrix = [[-19,57],[-40,-5]]
+输出：-59
+解释：如图所示，为和最小的下降路径
+....
 
- 
+*提示：*
 
-*Note:*
+* `n == matrix.length == matrix[i].length`
+* `+1 <= n <= 100+`
+* `+-100 <= matrix[i][j] <= 100+`
 
 
-* `1 <= A.length == A[0].length <= 100`
-* `-100 <= A[i][j] <= 100`
-
 == 思路分析
 
+
 [[src-0931]]
 [tabs]
 ====
@@ -49,14 +49,14 @@ include::{sourcedir}/_0931_MinimumFallingPathSum.java[tag=answer]
 ----
 --
 
-// 二刷::
-// +
-// --
-// [{java_src_attr}]
-// ----
-// include::{sourcedir}/_0931_MinimumFallingPathSum_2.java[tag=answer]
-// ----
-// --
+二刷::
++
+--
+[{java_src_attr}]
+----
+include::{sourcedir}/_0931_MinimumFallingPathSum_2.java[tag=answer]
+----
+--
 ====
 
 == 参考资料

docs/images/0931-01.jpg

@@ -325,6 +325,11 @@ endif::[]
 |{doc_base_url}/0120-triangle.adoc[题解]
 |✅ 动态规划。从底向上比从上向底效率更高。
 
+|{counter:codes2503}
+|{leetcode_base_url}/minimum-falling-path-sum/[931. 下降路径最小和^]
+|{doc_base_url}/0931-minimum-falling-path-sum.adoc[题解]
+|✅ 动态规划
+
 |===
 
 截止目前，本轮练习一共完成 {codes2503} 道题。

docs/images/0931-02.jpg

@@ -0,0 +1,35 @@
+package com.diguage.algo.leetcode;
+
+public class _0931_MinimumFallingPathSum_2 {
+  // tag::answer[]
+
+  /**
+   * @author D瓜哥 · https://www.diguage.com
+   * @since 2025-04-18 22:41:05
+   */
+  public int minFallingPathSum(int[][] matrix) {
+    int len = matrix.length;
+    if (len == 1) {
+      return matrix[0][0];
+    }
+    int result = Integer.MAX_VALUE;
+    for (int r = 1; r < len; r++) {
+      for (int c = 0; c < len; c++) {
+        int min;
+        if (c == 0) {
+          min = Math.min(matrix[r - 1][c], matrix[r - 1][c + 1]);
+        } else if (c == len - 1) {
+          min = Math.min(matrix[r - 1][c - 1], matrix[r - 1][c]);
+        } else {
+          min = Math.min(matrix[r - 1][c], Math.min(matrix[r - 1][c - 1], matrix[r - 1][c + 1]));
+        }
+        matrix[r][c] = matrix[r][c] + min;
+        if (r == len - 1) {
+          result = Math.min(result, matrix[r][c]);
+        }
+      }
+    }
+    return result;
+  }
+  // end::answer[]
+}