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 = 5The coins can form the following rows:¤¤ ¤¤ ¤Because the 3rd row is incomplete, we return 2.Example 2:n = 8The 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

1 public class Solution { 2     public int arrangeCoins(int n) { 3         long sum = 0; 4         int count = 0; 5         while (true) { 6             sum = sum + count; 7             if (n < sum) break; 8             count++; 9         }10         return count - 1;11     }12 }

 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

1 public class Solution { 2     public int arrangeCoins(int n) { 3         int l=1, r=n; 4         while (l <= r) { 5             int m = l + (r-l)/2; 6             if (0.5*m+0.5*m*m > n) { 7                 r = m - 1;  8             } 9             else l = m + 1;10         }11         return r;12     }13 }