Leetcode 441 Arranging Coins

Problem:

You had a total of n coins so want to form in a staircase shape, where every K-th Row must had E xactly 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.

Summary:

With n coins in a tower shape, the complete number of rows can be placed.

Analysis:

1. The simplest way of thinking, minus the increment of the number of coins per line, until n is a non-integer.

1 classSolution {2  Public:3     intArrangecoins (intN) {4         inti =0;5          while(N >0) {6i++;7N-=i;8         }9         Ten         returnn = =0? I:I-1; One     } A};

2. Solve the unary two-th equation: x^2 + x = 2 * N solution: x = sqrt (2 * n + 1/4)-1/2

But note that here n is a 32-bit signed integer number, 2 * n may overflow, so in the code should be handled accordingly.

1 class Solution {2public:3     int arrangecoins (int  n) {4         return sqrt (long long) 2 0.25 0.5 ; 5     }6 };

Leetcode 441 Arranging Coins