leetcode 62. Unique Paths

leetcode 62. Unique Paths

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

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:

1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
   Example 2:

Input: m = 7, n = 3
Output: 28

Constraints:

1 <= m, n <= 100
It's guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.

Solution

在每一个位置[i][j],robot要么从上面一个位置下来，要么从左边一个位置过来
所以其动态规划的状态转移方程为
dp[i][j]=dp[i-1][j]+dp[i][j-1]

class Solution {
public:
    int uniquePaths(int m, int n) {
        int dp[101][101];
        for(int i=0;i<=m;i++)
            dp[0][i]=0;
        for(int i=0;i<=n;i++)
            dp[i][0]=0;
        dp[0][1]=1;
        for(int i=1;i<=n;i++)
            for(int j=1;j<=m;j++)
                dp[i][j]=dp[i-1][j]+dp[i][j-1];
        return dp[n][m];
    }
};

参考链接

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