排列搜索

设数组a包含n个元素恰好是0..n - 1的一个排列，给定b[0],b[1],b[2],b[3]问有多少个0..n-1的排列a，满足(a[a[b[0]]]*b[0]+a[a[b[1]]]*b[1]+a[a[b[2]]]*b[2]+a[a[b[3]]]*b[3])%n==k ？

输入包含5个参数：N,K,B0,B1,B2,B3，其中 4<= N<12, 0 <= K,B0,B1,B2,B3 < N。

#include <stdio.h>

#include <iostream>

#include <string>

using namespace std;

class Test {

public:

static void parse(int &n, int &k, int pos, bool *flag, char *buf, long long int *factor, int &used, long long int &count, int &b0, int &b1, int &b2, int &b3)

{

if (pos == 8)

{

if ((buf[buf[b0]]*b0 + buf[buf[b1]]*b1 + buf[buf[b2]]*b2 + buf[buf[b3]]*b3) % n == k)

{

count += factor[n-used];

}

return;

}

for (int i = 0; i < n; i++)

{

bool newAssigned = false;

if (pos == 0)

{

buf[b0] = i;

flag[i] = true;

used = 1;

parse(n, k, pos+1, flag, buf, factor, used, count, b0, b1, b2, b3);

buf[b0] = -1;

flag[i] = false;

used--;

}

else if (pos == 1)

{

if (buf[buf[b0]] == -1)

{

if (flag[i])

{

continue;

}

buf[buf[b0]] = i;

flag[i] = true;

used++;

newAssigned = true;

}

parse(n, k, pos+1, flag, buf, factor, used, count, b0, b1, b2, b3);

if (newAssigned)

{

buf[buf[b0]] = -1;

flag[i] = false;

used--;

}

else

{

break;

}

}

else if (pos == 2)

{

if (buf[b1] == -1)

{

if (flag[i])

{

continue;

}

buf[b1] = i;

flag[i] = true;

used++;

newAssigned = true;

}

parse(n, k, pos+1, flag, buf, factor, used, count, b0, b1, b2, b3);

if (newAssigned)

{

buf[b1] = -1;

flag[i] = false;

used--;

}

else

{

break;

}

}

else if (pos == 3)

{

if (buf[buf[b1]] == -1)

{

if (flag[i])

{

continue;

}

buf[buf[b1]] = i;

flag[i] = true;

used++;

newAssigned = true;

}

parse(n, k, pos+1, flag, buf, factor, used, count, b0, b1, b2, b3);

if (newAssigned)

{

buf[buf[b1]] = -1;

flag[i] = false;

used--;

}

else

{

break;

}

}

else if (pos == 4)

{

if (buf[b2] == -1)

{

if (flag[i])

{

continue;

}

buf[b2] = i;

flag[i] = true;

used++;

newAssigned = true;

}

parse(n, k, pos+1, flag, buf, factor, used, count, b0, b1, b2, b3);

if (newAssigned)

{

buf[b2] = -1;

flag[i] = false;

used--;

}

else

{

break;

}

}

else if (pos == 5)

{

if (buf[buf[b2]] == -1)

{

if (flag[i])

{

continue;

}

buf[buf[b2]] = i;

flag[i] = true;

used++;

newAssigned = true;

}

parse(n, k, pos+1, flag, buf, factor, used, count, b0, b1, b2, b3);

if (newAssigned)

{

buf[buf[b2]] = -1;

flag[i] = false;

used--;

}

else

{

break;

}

}

else if (pos == 6)

{

if (buf[b3] == -1)

{

if (flag[i])

{

continue;

}

buf[b3] = i;

flag[i] = true;

used++;

newAssigned = true;

}

parse(n, k, pos+1, flag, buf, factor, used, count, b0, b1, b2, b3);

if (newAssigned)

{

buf[b3] = -1;

flag[i] = false;

used--;

}

else

{

break;

}

}

else if (pos == 7)

{

if (buf[buf[b3]] == -1)

{

if (flag[i])

{

continue;

}

buf[buf[b3]] = i;

flag[i] = true;

used++;

newAssigned = true;

}

parse(n, k, pos+1, flag, buf, factor, used, count, b0, b1, b2, b3);

if (newAssigned)

{

buf[buf[b3]] = -1;

flag[i] = false;

used--;

}

else

{

break;

}

}

}

}

static int howmany (int N,int K,int B0,int B1,int B2,int B3)

{

bool flag[11];

char buf[11];

for (int i = 0; i < N; i++)

{

flag[i] = false;

buf[i] = -1;

}

long long int factor[12];

factor[0] = 1;

for (int i = 1; i < 12; i++)

{

factor[i] = factor[i-1] * i;

}

int used = 0;

long long int count = 0;

parse(N, K, 0, flag, buf, factor, used, count, B0, B1, B2, B3);

return count;

}

};

//start 提示：自动阅卷起始唯一标识，请勿删除或增加。

int main()

{

cout<<Test::howmany(11,6,5,9,8,7)<<endl;

}

//end //提示：自动阅卷结束唯一标识，请勿删除或增加。