整数划分问题--DFS

单点时限:1000ms

内存限制:256MB

描述

Given two positive integers N and M, please divide N into several integers A1, A2, …, Ak (k >= 1), so that:

1. 0 < A1 < A2 < … < Ak;

2. A1 + A2 + … + Ak = N;

3. A1, A2, …, Ak are different with each other;

4. The product of them P = A1 * A2 * … * Ak is a multiple of M;

How many different ways can you achieve this goal?

输入

Two integers N and M. 1 <= N <= 100, 1 <= M <= 50.

输出

Output one integer – the number of different ways to achieve this goal, module 1,000,000,007.

样例输入

7 2

样例输出

4

样例提示

There are 4 different ways to achieve this goal for the sample:

A1=1, A2=2, A3=4;

A1=1, A2=6;

A1=2, A2=5;

A1=3, A2=4.

思路就是暴力 , 把所有情况都试一下.

#include <iostream>
using namespace std;

typedef unsigned long long ull;
ull N, M;
ull r = 0;
const ull MOD = 1000000007;

void dfs (ull i, ull s, ull p) {
    if (s == N) {
        if (p % M == 0) r++;
        return;
    }
    for (ull j = i + 1; j < N - s + 1; j++) {
        dfs (j, s + j, p * j);
    }
}

int main () {
    cin >> N >> M;
    dfs (0, 0, 1);
    cout << r % MOD << endl;
    return 0;
}

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