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.
class Solution {
public:
int arrangeCoins(int n) {
return floor(-0.5+sqrt((double)2*n+0.25));
}
};
这道题的主要考虑1+2+3+...+x<=n下，使x左边等式最接近n，并且不超过。
推导为：
-> 1+2+3+...+x = n
-> (1+x)x/2 = n
-> x^2+x = 2n
-> x^2+x+1/4 = 2n +1/4
-> (x+1/2)^2 = 2n +1/4
-> (x+0.5) = sqrt(2n+0.25)
-> x = -0.5 + sqrt(2n+0.25)
