062. Unique Paths

Difficulty: Medium

Frequency: N/A

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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My solution:

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Code:

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

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Another solution:

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Things to learn: