441. Arranging Coins

Problem Description

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:
¤
¤ ¤
¤ ¤
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 Method

Method One

    if (n <= 0)
        return 0;
    if (n < 3)
        return 1;
    if (n == 3)
        return 2;
    
    for (long i = 1; i < n ; i ++)
    {
        if (i*(i+1)/2 > n)
            return i - 1;
    }
    return 0;

Method Two

binary search

int arrangeCoins(int n)
{
    if(n == 0) 
    { 
        return 0; 
    } 
    long low = 1,  high = n; 
    while(low <= high) 
    { 
        long mid = (low + high)/2;
        if((mid+1)*mid/2 <= n) 
        { 
            low = mid +1; 
        } 
        else 
        { 
            high = mid -1; 
        } 
    }
     return low-1;
}