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
Companies:
Amazon, Google, Alibaba, Goldman Sachs
Related Topics:
Array, Dynamic Programming
Similar Questions:
// OJ: https://leetcode.com/problems/unique-paths/
// Author: github.com/lzl124631x
// Time: O(MN)
// Space: O(N)
class Solution {
public:
int uniquePaths(int m, int n) {
vector<int> dp(n + 1, 0);
dp[n - 1] = 1;
for (int i = m - 1; i >= 0; --i) {
for (int j = n - 1; j >= 0; --j) dp[j] += dp[j + 1];
}
return dp[0];
}
};The result is (m + n - 2)! / ((m - 1)! * (n - 1)!).
// OJ: https://leetcode.com/problems/unique-paths/
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1)
class Solution {
public:
int uniquePaths(int m, int n) {
long ans = 1;
for (int i = 1; i <= n - 1; ++i) ans = ans * (m - 1 + i) / i;
return ans;
}
};