62. Unique Paths

• Difficulty: Medium

• Topics: Array, Dynamic Programming

• Similar Questions:

  • Unique Paths II

  • Minimum Path Sum

  • Dungeon Game

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?

Above is a 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

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

Example 2:

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

Solutions:

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

        return dp[n-1];
    }
};