441. Arranging Coins

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:
¤
¤ ¤
¤ ¤ ¤
¤ ¤

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

Solution

(1) Java

class Solution {
    public int arrangeCoins(int n) {
        if (n < 1) {
            return 0;
        }
        int level = 1;
        long sum = 1;
        while (sum <= n) {
            level++;
            sum = sum+level;
        }
        return level-1;
    }
}

To avoid overflow:

public class Solution {
    public int arrangeCoins(int n) {
        int i=0;
        while(n > 0){
            i+=1;
            n-=i;
        }

        return n==0 ? i : i-1;

    }
}

(2) Python

(3) Scala