62. Unique Paths

Question

LeetCode Problem

Image: View on LeetCode

There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0] ). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1] ). The robot can only move either down or right at any point in time.
Given the two integers m and n , return the number of possible unique paths that the robot can take to reach the bottom-right corner .
The test cases are generated so that the answer will be less than or equal to 2 * 10 9 .
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

Constraints:

• 1 <= m, n <= 100

Solutions

int uniquePaths(int m, int n) {
	vector<vector<int>> dp(m, vector<int>(n , 0));
	for (int i = 0; i < m; ++i) {
		dp[i][0] = 1;
	}
	for (int j = 0; j < n; ++j) {
		dp[0][j] = 1;
	}
	
	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];
}