求第N个排列数

设序列为N个M位数的基本数字组成的排列数(N<=M)

假设序列是有序的,求第n个排列数(以0开始索引,0<=n<N!)

 

void GetNofP(char const * const in,char* out,int const size,unsigned long long N)
//in必须为递增的序列,size为in的大小
//out为结果序列,out的大小必须大于size
//0<=N<size!

{
    strcpy(out,in);
    vector<unsigned long long > info(size);
int pos = size -1;
    info[pos] = 1;
int i =1;
    --pos;
while(pos>=0)
    {
        info[pos] = info[pos+1]*i;
        ++i;
        --pos;
    }
for(int i = 0;N!=0&&i<size;++i)
    {
        unsigned long cur =(unsigned  long) (N/info[i]);
if(cur==0)
continue;        
int newPos = i+cur;
int curVal =out[i];
out[i] = out[newPos];        
        --newPos;
while(newPos>i)
        {
out[newPos+1]=out[newPos];
            --newPos;
        }
out[i+1] = curVal;
        N = N%info[i];
    } 
}

测试代码

int main(int argc, char* argv[])
{
char arr[] = "1234";
char out[sizeof(arr)];
    unsigned long long sum =0;
int size =sizeof(arr)/sizeof(arr[0]) -1;
    sum=1;
for(int i=1;i<=size;++i)
    {
        sum*=i;
    }
int beg = GetTickCount();
for(unsigned long long i=0;i<sum;++i)
    {        
        GetNofP(arr,out,size,i);
        cout<<out<<endl;
    }    
int end = GetTickCount();
    cout<<(end - beg)<<endl;
    cout<<sum<<endl;

return 0;
}

1234
1243
1324
1342
1423
1432
2134
2143
2314
2341
2413
2431
3124
3142
3214
3241
3412
3421
4123
4132
4213
4231
4312
4321
0
24
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