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: ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ 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).