HDU 5312 Sequence

Problem Description

Today, Soda has learned a sequence whose $n$-th $(n\ge 1)$ item is $3n(n-1)+1$. Now he wants to know if an integer $m$ can be represented as the sum of some items of that sequence. If possible, what are the minimum items needed?

For example, $22=19+1+1+1=7+7+7+1$.

Input

There are multiple test cases. The first line of input contains an integer $T$ (1 \le T \le 10^4)(1≤T≤10​4​​), indicating the number of test cases. For each test case:

There's a line containing an integer $m$ (1 \le m \le 10^9)(1≤m≤10​9​​).

Output

For each test case, output $-1$ if $m$ cannot be represented as the sum of some items of that sequence, otherwise output the minimum items needed.

Sample Input

10
1
2
3
4
5
6
7
8
22
10

Sample Output

1
2
3
4
5
6
1
2
4
4

打表找规律，对于1和2要特判
#include<cstdio>
#include<cmath>
#include<queue>
#include<vector>
#include<stack>
#include<map>
#include<string>
#include<cstring>
#include<algorithm>
#include<iostream>
using namespace std;
typedef long long ll;
const ll maxn = 20005;
int T, n, m, f[maxn];
map<int, int> M;

int main()
{
    for (int i = 1; i <= 20000; i++)
    {
        f[i] = 3 * i * (i - 1) + 1;
        M[f[i]] = 1;
    }
    cin >> T;
    while (T--)
    {
        scanf("%d", &n);
        m = (n - 1) % 6 + 1;
        if (m > 2) printf("%d\n", m);
        else
        {
            if (m == 1) if (M.count(n)) printf("1\n"); else printf("7\n");
            else
            {
                int flag = 0;
                for (int i = 1; f[i] + f[i] <= n; i++)
                    if (M.count(n - f[i])) { flag = 1; break; }
                if (flag) printf("2\n");else printf("8\n");
            }
        }
    }
    return 0;
}