ArrangeCoinII.java

// 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.

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