441. Arranging Coins - jiejackyzhang/leetcode-note GitHub Wiki

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:
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¤ ¤

Because the 3rd row is incomplete, we return 2.

Example 2:

n = 8

The coins can form the following rows:
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¤ ¤ ¤
¤ ¤

Because the 4th row is incomplete, we return 3.

##Approach 1: straight forward 一行一行减，当n<0时，说明最后一行不完整，res需要减1。

public class Solution {
    public int arrangeCoins(int n) {
        int res = 0, i = 1;
        while(n > 0) {
            n -= i;
            res++;
            i++;
        }
        if(n < 0) res--;
        return res;
    }
}

##Approach 2: math problem

The idea is about quadratic equation, the formula to get the sum of arithmetic progression is sum = (x + 1) * x / 2 so for this problem, if we know the the sum, then we can know the x = (-1 + sqrt(8 * n + 1)) / 2

public class Solution {
    public int arrangeCoins(int n) {
        return (int)((-1 + Math.sqrt(8 * (long)(n) + 1)) / 2);
    }
}