LeetCode:Unique Paths

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Question
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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簡単です.ステータス遷移テーブル:
m = 3, n = 7
dpプロセス
1
1
1
1
1
1
1
1
2
3
4
5
6
7
1
3
6
10
15
21
28
したがって、状態遷移方式:
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];
    }
};