Leetcode-最小路徑和

64. 最小路徑和

https://leetcode-cn.com/problems/minimum-path-sum/

package com.cn.dl.leetcode;

/**
 * Created by yanshao on 2020-02-22.
 */
public class MinPathSum {

    /**
     * 簡單的動態規劃，算出每一個節點到下一個節點的路徑之和
     * */

    public int minPathSum(int[][] grid) {
        if(grid == null || grid.length == 0 ){
            return 0;
        }
        int[][] minPathSum = new int[grid.length][grid[0].length];
        minPathSum[0][0] = grid[0][0];

        //先算第一行從前一個節點到下一個節點之和
        for(int i = 1; i < grid[0].length; i++){
            minPathSum[0][i] = grid[0][i] + minPathSum[0][i-1];
        }

        //再算第一列從前一個節點到下一個節點之和
        for(int j = 1; j < grid.length; j++){
            minPathSum[j][0] = grid[j][0] + minPathSum[j - 1][0];
        }

        //接下來從（1,1）,算從上一個節點到當前節點之和
        for(int i = 1; i < grid.length; i++){
            for(int j = 1; j < grid[0].length; j++){
                minPathSum[i][j] = Math.min(minPathSum[i-1][j],minPathSum[i][j-1]) + grid[i][j];
            }
        }

        //最後（grid.length - 1,grid[0].length - 1）節點的值，就是從左上角到右下角的最短路徑
        return minPathSum[grid.length - 1][grid[0].length - 1];
    }

    public static void main(String[] args) {
        int[][] grid = new int[][]{
                {1,3,1},
                {1,5,1},
                {4,2,1}
        };
        System.out.println(new MinPathSum().minPathSum(grid));
    }
}