Arranging Coins

Description

You have n coins and you want to build a staircase with these coins. The staircase consists of k rows where the ith row has exactly i coins. The last row of the staircase may be incomplete.

Given the integer n, return the number of complete rows of the staircase you will build.

Example 1:

Input: n = 5 Output: 2 Explanation: Because the 3rd row is incomplete, we return 2.

Example 2:

Input: n = 8 Output: 3 Explanation: Because the 4th row is incomplete, we return 3.

Constraints:

• 1 <= n <= 231 - 1

Code

Time Complexity: $O(\log n)$, Space Complexity: $O(1)$

和 Valid Perfect Square 一樣。

class Solution {
public:
    int arrangeCoins(int n) {
        // 1 + 2 + ... + x = x * (x + 1) / 2
        long long l = 1, r = n;
        while(l < r) {
            long long m = l + (r - l) / 2;
            if((m * (m + 1) / 2) < n) {
                l = m + 1;
            } else {
                r = m;
            }
        }
        return (l * (l + 1) / 2) > n ? l - 1 : l;
    }
};

Source

• Arranging Coins - LeetCode