题目: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.
思路:动态规划
使用动态规划,此时刻的数值等于左边的数值加上上边的数值。
公式到,编程自然迎刃而解。
代码:
class Solution { public: //https://leetcode.com/problems/unique-paths/ int uniquePaths(int m, int n) { if(m==0||n==0){ return 0; } int sum[m][n]; for(int i=0;i<m;i++){ sum[i][0]=1;//一直往下走只有一条路 } for(int i=0;i<n;i++){ sum[0][i]=1;//一直往右走只有一条路 } for(int i=1;i<m;i++){ for(int j=1;j<n;j++){ sum[i][j]=sum[i-1][j]+sum[i][j-1]; } } return sum[m-1][n-1]; } };