LeetCode 441 Arranging Coins
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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 = 5The coins can form the following rows:¤¤ ¤¤ ¤Because the 3rd row is incomplete, we return 2.
Example 2:
n = 8The coins can form the following rows:¤¤ ¤¤ ¤ ¤¤ ¤Because the 4th row is incomplete, we return 3.
设所求的结果为x,则1+2+3+4+……+x = n,(1+x)x/2=n,(1+x)x =2n, x^2+x-2n = 0; 这是一个方程啊,记得当年的求根公式是x =(-b+sqrt(b^2 - 4ac) )/2 其中a是x^2的系数1,b是x的系数1,c是后面的常数项-2n,则x = -1+sqrt(1+8n); x向下取整即答案;
public int arrangeCoins(int n) {return (int) Math.floor((-1 + Math.sqrt(1 + 8L * n)) / 2.0);}
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