排列硬币问题，三种解法，java，算法练习

public class 排列硬币三种解法 {

    public static void main(String[] args) {
        System.out.println(arrangeCoins(10));
        System.out.println(arrangeCoins2(10));
        System.out.println(arrangeCoins3(10));
    }

    //  解法一  迭代
    public static int arrangeCoins(int n) {
        for (int i = 1; i <= n; i++) {
            n = n - i;
            if (n <= 1) {
                return i;
            }
        }
        return 0;
    }

    //    解法二 二分法
    public static int arrangeCoins2(int n) {
        int low = 0, high = n;
        while (low <= high) {
            int mid = (high - low) / 2 + low;
            int cost = ((mid + 1) * mid) / 2;
            if (cost == n) {
                return mid;
            } else if (cost > n) {
                high = mid - 1;
            } else {
                low = mid + 1;
            }
        }
        return high;
    }

    //    解法三 牛顿迭代
    public static int arrangeCoins3(int n) {
        if (n == 0) {
            return 0;
        }
            return (int)sqrt(n, n);
        }

        private static double sqrt ( double x, int n){
            double res=(x+(2*n-x)/x)/2;
            if(res==x){
               return x;
        }else{
                return sqrt(res,n);
            }

    }

}