[LeetCode] 123: Unique Paths

[Problem]

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?

Note: m and n will be at most 100.

[Solution]

class Solution {
public:
int uniquePaths(int m, int n) {
// Note: The Solution object is instantiated only once and is reused by each test case.
if(m == 0 || n == 0)return 0;

// initial
int dp[m][n];
for(int i = 0; i < n; ++i){
dp[0][i] = 1;
}
for(int i = 0; i < m; ++i){
dp[i][0] = 1;
}

// dp
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];
}
};

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