LeetCode 64. Minimum Path Sum

题目如下：

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：

因为只能往右或往下走，所以可以初始化当res[m][0], res[0][n]这些边界情况

然后，每一步结果为当前值＋min(上边一步，左边一步)，即res[i][j] = grid[i][j] + min(res[i-1][j], res[i][j-1])

本体代码：

/**
 * Created by yuanxu on 17/4/13.
 */
public class DP64 {

    public static int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int res[][] = new int[m][n];

        // boundary conditions
        res[0][0] = grid[0][0];
        for (int i=1; i<m; i++) {
            res[i][0] = grid[i][0] + res[i-1][0];
        }
        for (int j=1; j<n; j++) {
            res[0][j] = grid[0][j] + res[0][j-1];
        }

        // dp
        for (int i=1; i<m; i++) {
            for (int j=1; j<n; j++) {
                res[i][j] = grid[i][j] + (res[i-1][j] < res[i][j-1] ? res[i-1][j] : res[i][j-1]);
            }
        }

        return res[m-1][n-1];
    }

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

网上的解答有空间复杂度为0的：

public class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;// row
        int n = grid[0].length; // column
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (i == 0 && j != 0) {
                    grid[i][j] = grid[i][j] + grid[i][j - 1];
                } else if (i != 0 && j == 0) {
                    grid[i][j] = grid[i][j] + grid[i - 1][j];
                } else if (i == 0 && j == 0) {
                    grid[i][j] = grid[i][j];
                } else {
                    grid[i][j] = Math.min(grid[i][j - 1], grid[i - 1][j])
                            + grid[i][j];
                }
            }
        }

        return grid[m - 1][n - 1];
    }
}

ref: https://discuss.leetcode.com/topic/5459/my-java-solution-using-dp-and-no-extra-space