62. Unique Paths （走棋盘多少种不同的走法 动态规划）

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.

r如果用公式的话 就是 C(X+Y 选X)

 class Solution {
     public int uniquePaths(int m, int n) {
         int[][] dp = new int[m][n];

         for(int i =0;i<m;i++){
             for (int j = 0;j < n;j++){
                 if(i==0&&j==0)
                     dp[i][j]=1;
                 else if(i==0)
                     dp[i][j] = dp[i][j-1];
                 else if(j==0)
                     dp[i][j] = dp[i-1][j];
                 else
                  dp[i][j] = dp[i-1][j] + dp[i][j-1];
             }
         }
         return dp[m-1][n-1];
     }
 }

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