LeetCode 441. Arranging Coins

Description

https://leetcode.com/problems/arranging-coins/

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:
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¤ ¤
¤ ¤ ¤
¤ ¤

Because the 4th row is incomplete, we return 3.

Explanation

The total number of coins needed to fulfil k rows is: 1 + 2 + … + k = (1 + k) * k / 2.

Therefore, we can use binary search to find what is the largest number of rows we can fulfill with n coins.

Python Solution

class Solution:
    def arrangeCoins(self, n: int) -> int:
        start = 0
        end = n
         
        while start + 1 < end:
            mid = start + (end - start) // 2
            
            
            if mid * (mid + 1) // 2 <= n:
                start = mid
            else:
                end = mid
                
        if end * (end + 1) // 2 <= n:
            return end
            
        return start
  • Time Complexity: O(logN).
  • Space Complexity: O(1).

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