原題網址：https://leetcode.com/problems/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: ¤ ¤ ¤ ¤ ¤ 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.
方法一：牛頓迭代法。
public class Solution {
private double f(double x, int n) {
return x * (1 + x) / 2 - n;
}
private double derative(double x) {
return x + 0.5;
}
public int arrangeCoins(int n) {
double x = 0;
while (true) {
double nx = x - f(x, n) / derative(x);
if (Math.abs(nx - x) < 0.01) break;
x = nx;
}
return (int)x;
}
}方法二：直接用求根公式。
public class Solution {
public int arrangeCoins(int n) {
return (int)((-1.0 + Math.sqrt(1.0 + 8.0 * n)) / 2);
}
}方法三：二分法。
public class Solution {
public int arrangeCoins(int n) {
long i = 0, j = n;
while (i <= j) {
long m = (i + j) / 2;
long sum = m * (1 + m) / 2;
if (sum > n) j = m - 1; else i = m + 1;
}
return (int)j;
}
}方法四：累加
public class Solution {
public int arrangeCoins(int n) {
int i = 0;
long sum = 0;
while (sum + i + 1 <= n) {
i++;
sum += i;
}
return i;
}
}