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.
n = 5 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ Because the 3rd row is incomplete, we return 2.
n = 8 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ Because the 4th row is incomplete, we return 3.
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.
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).