441 Arranging Coins 排列硬币
Description:
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:
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.
题目描述:
你总共有 n 枚硬币，你需要将它们摆成一个阶梯形状，第 k 行就必须正好有 k 枚硬币。
给定一个数字 n，找出可形成完整阶梯行的总行数。
n 是一个非负整数，并且在32位有符号整型的范围内。
示例：
示例 1:
n = 5
硬币可排列成以下几行:
¤
¤ ¤
¤ ¤
因为第三行不完整，所以返回2.
示例 2:
n = 8
硬币可排列成以下几行:
¤
¤ ¤
¤ ¤ ¤
¤ ¤
因为第四行不完整，所以返回3.
思路:
返回值是找到 (i + 1) * i / 2 >= n的最小的 i
时间复杂度O(1), 空间复杂度O(1)
代码:
C++:
class Solution
{
public:
int arrangeCoins(int n)
{
return (int)(-1 + sqrt(1 + ((long)n << 3))) >> 1;
}
};
Java:
class Solution {
public int arrangeCoins(int n) {
return (int)(-1 + Math.sqrt(1 + ((long)n << 3))) >> 1;
}
}
Python:
class Solution:
def arrangeCoins(self, n: int) -> int:
return int((-1 + (1 + (n << 3)) ** 0.5)) >> 1
