LeetCode-Arranging Coins

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 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.

题意：给定一个数量的硬币，要找第k行放置k个，求最多可以放置几行（只有当一行放置足够数量的硬币，这一行才计入结果）；

解法：我们假设一共放置了n行，给定的硬币数为num，我们可以得到： $$1+2+3+4+......+n=\frac{(1+n)\ast n}{2}<=num$$ 因此，我们现在就是要找到令不等式成立的最大的那个n；

Java

class Solution { public int arrangeCoins(int n) { long result = 0; while ((1 + result) * result / 2 <= n) result++; return (int)(result-1); } }