LeetCode-in-All
62. Unique Paths
Medium
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.
Solution
#include <vector>
class Solution {
public:
int uniquePaths(int m, int n) {
std::vector<std::vector<int>> dp(m, std::vector<int>(n, 0));
// Initialize the first column to 1
for (int i = 0; i < m; ++i) {
dp[i][0] = 1;
}
// Initialize the first row to 1
for (int j = 0; j < n; ++j) {
dp[0][j] = 1;
}
// Fill the rest of the dp array
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];
}
};