Unique Paths.cpp

/*
Unique Paths
============

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

Example 2:
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:
Input: m = 7, n = 3
Output: 28

Example 4:
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 * 109.
*/

class Solution
{
public:
  int uniquePaths(int m, int n)
  {
    vector<vector<int>> dp(m, vector<int>(n, 0));

    for (int i = 0; i < n; ++i)
      dp[m - 1][i] = 1;
    for (int i = 0; i < m; ++i)
      dp[i][n - 1] = 1;

    for (int i = m - 2; i >= 0; --i)
    {
      for (int j = n - 2; j >= 0; --j)
      {
        dp[i][j] = dp[i + 1][j] + dp[i][j + 1];
      }
    }

    return dp[0][0];
  }
};