LeetCode:Unique Paths

Unique Paths

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Total Accepted: 72643  Total Submissions: 208792  Difficulty: Medium

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.

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  Array Dynamic Programming

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很简单，状态转移表：

m = 3, n = 7

dp过程

1	1	1	1	1	1	1
1	2	3	4	5	6	7
1	3	6	10	15	21	28

因此，状态转移方式：

dp[i][j] = dp[i-1][j] + dp[i][j-1]

code:

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