LeetCode 441 Arranging Coins - Easy

441. Arranging Coins — Easy

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Problem

441. Arranging Coins -- Easy

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins.

Given n, find the total number of full staircase rows that can be formed.

n is a non-negative integer and fits within the range of a 32-bit signed integer.

Example 1: n = 5 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ Because the 3rd row is incomplete, we return 2.

Example 2: n = 8 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ Because the 4th row is incomplete, we return 3.

Solution

class Solution:
    def arrangeCoins(self, n: int) -> int:
        left, right = 0, n
        while left + 1 < right:
            mid = int((left + right)/2)
            mid_val = mid * (mid + 1) // 2
            if mid_val == n:
                return mid
            elif mid_val < n:
                left = mid
            else:
                right = mid
                
        if right * (right + 1) // 2 <= n:
            return right
        if left * (left + 1) // 2 <= n:
            return left