# 441. Arranging Coins

## Description

You have n coins and you want to build a staircase with these coins. The staircase consists of k rows where the ith row has exactly i coins. The last row of the staircase may be incomplete.

Given the integer n, return the number of complete rows of the staircase you will build.

Example 1:

Input: n = 5
Output: 2
Explanation: Because the 3rd row is incomplete, we return 2.

Example 2:

Input: n = 8
Output: 3
Explanation: Because the 4th row is incomplete, we return 3.

Constraints:

• 1 <= n <= 231 - 1

## Solutions

• class Solution {
public int arrangeCoins(int n) {
return (int) (Math.sqrt(2) * Math.sqrt(n + 0.125) - 0.5);
}
}

• using LL = long;

class Solution {
public:
int arrangeCoins(int n) {
LL left = 1, right = n;
while (left < right) {
LL mid = left + right + 1 >> 1;
LL s = (1 + mid) * mid >> 1;
if (n < s)
right = mid - 1;
else
left = mid;
}
return left;
}
};

• class Solution:
def arrangeCoins(self, n: int) -> int:
return int(math.sqrt(2) * math.sqrt(n + 0.125) - 0.5)

• func arrangeCoins(n int) int {
left, right := 1, n
for left < right {
mid := (left + right + 1) >> 1
if (1+mid)*mid/2 <= n {
left = mid
} else {
right = mid - 1
}
}
return left
}