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.

要处理mid 的越界问题

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