441 Arranging Coins

You have n coins and you want to build a staircase with these coins. The staircase consists of k rows where the ith row has exactly i coins. The last row of the staircase may be incomplete.

Given the integer n, return the number of complete rows of the staircase you will build.

Example 1:

Input: n = 5
Output: 2
Explanation: Because the 3rd row is incomplete, we return 2.

Example 2:

Input: n = 8
Output: 3
Explanation: Because the 4th row is incomplete, we return 3.

Constraints:

• 1 <= n <= 231 - 1

这题写着简单，但是很容易overflow。首先，一眼看出这是个（1 + k) * k / 2 <= n的题。一开始为了避开java里正数除以2会round down的问题，用了（1 + k) * k <= n * 2。然后后面大数overflow了。还是套九章的模板。

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