【DP】一共有多少种走法

题目描述

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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

递推式：到grid[i][j]有两种走法，从上面走下来，从左边走过来。

所以gridNum[i][j]=gridNum[i-1][j]+gridNum[i][j-1];

矩阵第一行跟第一列均为1。

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