Leetcode: 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.

count is the # of level, sum is the accumulated coins

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

 Better Solution:

Binary Search, 因为怕溢出，所以(1+m)m/2表示成了line6那种样子. 

　用m去估计最后返回的row

0.5*m+0.5*m*m > n 表示前m row的和大于了n， 如果这个m作为返回值的话肯定是取大了，所以r减小，如果

0.5*m+0.5*m*m <= n 表示m是合适的，或者偏小了，这个时候增大l，如果l>r，r就一定落在m处

public class Solution {
    public int arrangeCoins(int n) {
        int l=1, r=n;
        while (l <= r) {
            int m = l + (r-l)/2;
            if (0.5*m+0.5*m*m > n) {
                r = m - 1; 
            }
            else l = m + 1;
        }
        return r;
    }
}