动态规划：二维DP

N*M个方格，每格有一定苹果，从左上角开始，能捡到多少苹果

S[i][j] = A[i][j] + max{S[i][j-1],S[i-1][j]} 注意边界条件 

并打印路径：

import java.util.*;
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        while (in.hasNext()) {//注意while处理多个case
            int m = in.nextInt();
            int n = in.nextInt();
            int[][] arr = new int[m][n];
            for(int i = 0; i < m; i++){
                for(int j = 0; j < n; j++){
                    arr[i][j] = in.nextInt();
                }
            }
            int[][] result = new int[m][n];
            int[][] path = new int[m][n];
            path[0][0] = 1;
            result[0][0] = arr[0][0];
            for(int i = 1; i < n; i++){
                result[0][i] = result[0][i-1] + arr[0][i];
            }
            for(int i = 1; i < m; i++){
                result[i][0] = result[i-1][0] + arr[i][0];
            }
            for(int i = 1; i < n; i++){
                path[0][i] = 1;
            }
            for(int i = 1; i < m; i++){
                path[i][0] = 0;
            }
            for(int i = 1; i < m; i++){
                for(int j = 1; j < n; j++){
                    if((i == 0 && j==0) || (i==1 && j==0) || (i==0 && j==1)) continue;
                    int big = 0;
                    int p = 0;
                    if(result[i][j-1]>result[i-1][j]){
                        big = result[i][j-1];
                        p = 1;
                    }else{
                        big = result[i-1][j];
                        p = 0;
                    }
                    path[i][j] = p;
                    result[i][j] = arr[i][j] + big;
                }
            }
            int a = m-1, b = n-1;
            int[] road = new int[a+b+1];
            for(int i = a+b; i >= 0; i--){
                road[i] = arr[a][b];
                if(path[a][b] == 1){
                    b--;
                }else a--;
            }
            System.out.println(Arrays.toString(road));
        }
    }
}