A. Vanya and Cubes

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492A. Vanya and Cubes
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Vanya got n cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes, and so on. Thus, the i-th level of the pyramid must have 1 + 2 + … + (i - 1) + i cubes.
Vanya wants to know what is the maximum height of the pyramid that he can make using the given cubes.

Input
The first line contains integer n (1 ≤ n ≤ 104) — the number of cubes given to Vanya.

Output
Print the maximum possible height of the pyramid in the single line.

Examples
Input

1

Output

1

Input

25

Output

4

题意：Vanya有n个立方体。他决定用它们建造一座金字塔。Vanya想要构建金字塔如下:金字塔的顶层必须由1个立方体组成，第二层必须由1 + 2 = 3个立方体组成，第三层必须有1 + 2 + 3 = 6个立方体，依此类推。因此，金字塔的第i层必须有1 + 2 +…+ (i - 1) + i个立方体。Vanya想知道他能用给定的立方体做出的金字塔的最大高度是多少。

思路1：使用数学公式求解
思路2：递归求解
具体看代码

AC代码1

#include
#include
#include
using namespace std;
int main()
{ int i,n,sum;
	cin>>n;
	sum=0;
	i=0;
	while(1)
	{
		i++;
		sum=i*(i+1)*(i+2)/6;
		if(sum>n)
		{
			break;
		}
	}
	cout<<i-1<<endl;
	return 0;
}

AC代码2

#include 
#include 
#include 
using namespace std;
int main() {
int a[210],sum[210];int n,h=0;
     cin>>n;
    a[0]=0;
    for(int i=1;i<210;i++){
    a[i]=a[i-1]+i;
    }sum[0]=0;
    for(int i=1;i<210;i++){
    sum[i]=sum[i-1]+a[i];
    }
    while(n>=sum[h]) h++;
    cout <<h-1<< endl;
    return 0;
}