2021-11-17 Daily-Challenge

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In: DailyChallenge
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Today I have done leetcode's November LeetCoding Challenge with cpp.

November LeetCoding Challenge 17

Description

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:

img

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 * 10^9.

Solution

constexpr int combination(int total, int pick) {
  long long result = 1;
  for(int i = 0; i < pick; ++i) {
    result *= (total - i);
    result /= (i + 1);
  }
  return result;
}

class Solution {
public:
  int uniquePaths(int m, int n) {
    return combination(m + n - 2, min(n - 1, m - 1));
  }
};

// Accepted
// 62/62 cases passed (0 ms)
// Your runtime beats 100 % of cpp submissions
// Your memory usage beats 88.67 % of cpp submissions (5.8 MB)
Algorithm