Minimum Path Sum 矩阵最短路径和@LeetCode

一个矩阵要求从左上角走到右下角，只能往右或往下走。

递归，DP

非常好的练习递归和动态规划的简单题

package Level3;

import java.util.Arrays;
import java.util.Iterator;

/**
 * Minimum Path Sum 
 * 
 *  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.
 *
 */
public class S64 {

	public static void main(String[] args) {
		int[][] grid = {{1,2},{1,1}};
		System.out.println(minPathSum(grid));
		System.out.println(minPathSum2(grid));
	}

	public static int minPathSum(int[][] grid) {
		int[][] sum = new int[grid.length][grid[0].length];
		for (int[] row : sum) {
			Arrays.fill(row, Integer.MIN_VALUE);
		}
        return rec(grid, sum, grid.length-1, grid[0].length-1);
    }
	
	// 递归记忆化，从上至下。因为每次都要做判断是否已经存过，所以写的会很丑陋
	public static int rec(int[][] grid, int[][] sum, int x, int y){
		if(x==0 && y==0){
			if(sum[0][0] == Integer.MIN_VALUE){
				sum[0][0] = grid[0][0];
			}
			return sum[0][0];
		}
		if(x == 0){
			if(sum[x][y] == Integer.MIN_VALUE){
				sum[x][y-1] = rec(grid, sum, x, y-1);
				sum[x][y] = sum[x][y-1] + grid[x][y];
			}
			return sum[x][y];
		}
		if(y == 0){
			if(sum[x][y] == Integer.MIN_VALUE){
				sum[x-1][y] = rec(grid, sum, x-1, y);
				sum[x][y] = sum[x-1][y] + grid[x][y];
			}
			return sum[x][y];
		}
		
		if(sum[x][y-1] == Integer.MIN_VALUE){
			sum[x][y-1] = rec(grid, sum, x, y-1);
		}
		if(sum[x-1][y] == Integer.MIN_VALUE){
			sum[x-1][y] = rec(grid, sum, x-1, y);
		}
		sum[x][y] = Math.min(sum[x][y-1], sum[x-1][y]) + grid[x][y];
		return sum[x][y];
	}
	
	// 没有记忆的递归，超时
	public int rec(int[][] grid, int x, int y){
		if(x==0 && y==0){
			return grid[0][0];
		}
		if(x == 0){
			return rec(grid, x, y-1)+grid[x][y];
		}
		if(y == 0){
			return rec(grid, x-1, y)+grid[x][y];
		}
		return Math.min(rec(grid, x-1, y), rec(grid, x, y-1)) + grid[x][y];
	}
	
	// DP 从下至上
	public static int minPathSum2(int[][] grid) {
		int[][] sum = new int[grid.length][grid[0].length];
		sum[0][0] = grid[0][0];
		
		// 填充第一列
		for(int i=1; i

Again:

public class Solution {
    
    public int minPathSum(int[][] grid) {
        int[][] sums = new int[grid.length][grid[0].length];
        sums[0][0] = grid[0][0];
        for(int i=1; i