LeetCode. Arranging Coins

Problem:

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.

 

-Summary-

Solved using binary search.

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

Detail explanation from the leetcode solution.

 

Complexity Analysis

- Time complexity: O(logN)

- Space complexity: O(1)

 

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