Leetcode 64. Minimum Path Sum

题目

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

思路

使用动态规划的思路

dp[j] = Math.min(grid[i][j] + dp[j], grid[i][j] + d[j - 1])

代码

package leetcodeArray;

public class Leetcode64MinimumPathSum {
public int minPathSum(int[][] grid) {
int hight = grid.length;
int width = grid[0].length;
int[] dp = new int[width];
dp[0] = grid[0][0];
for(int i = 1; i < width; ++i){
dp[i] = grid[0][i] + dp[i - 1];
}
for (int i = 1; i < hight; ++i) {
dp[0] = grid[i][0] + dp[0];
for (int j = 1; j < width; j++) {
dp[j] = Math.min(grid[i][j] + dp[j], grid[i][j] + dp[j - 1]);

}
}
return dp[width - 1];
}

public static void main(String[] args){
Leetcode64MinimumPathSum test = new Leetcode64MinimumPathSum();
int[][] grid = {{1,4}, {1, 1}};
System.out.println(test.minPathSum(grid));
}
}