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MinPathSum.java
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52 lines (49 loc) · 1.6 KB
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package com.lga.algorithm.tag.homework.Week_05;
/**
* 64. 最小路径和
* <p>
* https://leetcode-cn.com/problems/minimum-path-sum/
*/
public class MinPathSum {
/**
* 常规dp
* 时间复杂度O（n^2）
* 空间复杂度O（n）
* @param grid
* @return
*/
public int minPathSum(int[][] grid) {
if (grid == null || grid.length < 1) return 0;
int y = grid.length;
int x = grid[0].length;
int[][] dp = new int[y][x];
for (int i = 0; i < y; i++) {
for (int j = 0; j < x; j++) {
if (i == 0 && j == 0) dp[i][j] = grid[i][j];
else if (i == 0) dp[i][j] = dp[i][j - 1] + grid[i][j];
else if (j == 0) dp[i][j] = dp[i - 1][j] + grid[i][j];
else dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
}
}
return dp[y - 1][x - 1];
}
/**
* 优化常规dp。可以不需要额外的空间来保存状态
* @param grid
* @return
*/
public int minPathSum_1(int[][] grid) {
if (grid == null || grid.length < 1) return 0;
int y = grid.length;
int x = grid[0].length;
for (int i = 0; i < y; i++) {
for (int j = 0; j < x; j++) {
if (i == 0 && j == 0) continue;
else if (i == 0) grid[i][j] = grid[i][j - 1] + grid[i][j];
else if (j == 0) grid[i][j] = grid[i - 1][j] + grid[i][j];
else grid[i][j] = Math.min(grid[i - 1][j], grid[i][j - 1]) + grid[i][j];
}
}
return grid[y - 1][x - 1];
}
}