leetcode Unique Paths/Minimum Path Sum

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

因为只能向下或者向右走，所依某一点的值就是上面方格的值 和左边的值 相加

dynamic programming.

public class Solution {
    public int uniquePaths(int m, int n) {
        int[][] grid=new int[100][100];
        for(int i=0;i<m;i++){
        	grid[i][0]=1;
        }
        for(int j=0;j<n;j++){
        	grid[0][j]=1;
        }
        for(int i=1;i<m;i++){
        	for(int j=1;j<n;j++){
        		grid[i][j]=grid[i-1][j]+grid[i][j-1];
        	}
        }
        return grid[m-1][n-1];
    }
}

　　

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 Solution {
    public int minPathSum(int[][] grid) {
        if(grid==null||grid.length==0||grid[0].length==0){
        	return 0;
        }
        int m=grid.length;
        int n=grid[0].length;
        for(int i=1;i<n;i++){
        	grid[0][i]=grid[0][i-1]+grid[0][i];
        }
        for(int j=1;j<m;j++){
        	grid[j][0]=grid[j-1][0]+grid[j][0];
        }
        for(int i=1;i<m;i++){
        	for(int j=1;j<n;j++){
        		if(grid[i-1][j]<=grid[i][j-1]){
        			grid[i][j]=grid[i-1][j]+grid[i][j];
        		}
        		else{
        			grid[i][j]=grid[i][j-1]+grid[i][j];
        		}
        	}
        }
        return grid[grid.length-1][grid[0].length-1];
    }
}