Unique Paths Problem


Description

LeetCode Problem 62.

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?

Example 1:

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

Example 2:

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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 -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Example 3:

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

Example 4:

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Input: m = 3, n = 3
Output: 6

Constraints:

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


Sample C++ Code

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




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