全排列

Posted 2020-07-28 指尖起舞

交换两个数：

template<class T>
void exchange(T & f, T & s)
{
    T t = f;
    f = s;
    s = t;
};

递归方式——递归节：

void fullPermutation(int * fullArray, int start, int number, int & count)
{
    if(start >= number)
    {
        cout << count + 1 << "\t:" ;
        for(int i = 0;i < number; ++ i)
            cout << fullArray[i] << " ";
        cout << endl;
        count ++;
    }
    else
        for(int i = start; i < number; ++ i)
        {
            exchange(fullArray[start], fullArray[i]);
            fullPermutation(fullArray, start+1, number, count);
            exchange(fullArray[start], fullArray[i]);
        }
}

递归方式——精简：

int fullPermutation(int number)
{
    int * fullArray = new int[number];
    for (int i = 0;i < number;i ++)
        fullArray[i] = i + 1;
    int icount = 0;
    fullPermutation(fullArray, 0, number, icount);
    delete[] fullArray;
    return icount;
}

逆转数组：

void reverseArray(int * fullArray, int number)
{
    int i(0), j(number - 1);
    while (i < j)
        exchange(fullArray[i ++], fullArray[j --]);
}

找到传说中XY的索引坐标：

找到最后一个这样的xindex，使的fullArray[xindex] < fullArray[xindex + 1]；

xindex之后找到最后一个这样的yindex，使的fullArray[xindex] < fullArray[yindex]；

int findXY(int * fullArray, int number, int &xindex, int &yindex)
{
    xindex = -1;
    for (int i = 0; i < number - 1; ++ i)
    {
        if (fullArray[i] < fullArray[i + 1])
        {
            xindex = i;
            yindex = i + 1;
        }
        else if (xindex != -1 && fullArray[xindex] < fullArray[i + 1])
            yindex = i + 1;
    }
    return xindex;
}

非递归方式产生全排列：

void fullPermutation2(int * fullArray, int number, int & count){
    int xindex(-1);
    int yindex(-1);
    count = 1;
    cout << count << "\t:" ;
    for(int i = 0;i < number; i ++)
        cout << fullArray[i] << " ";
    cout << endl;
    while (-1 != findXY(fullArray,number, xindex, yindex))
    {
        exchange(fullArray[xindex], fullArray[yindex]);
        reverseArray(fullArray + xindex + 1, number - xindex -1);
        cout << ++ count << "\t:" ;
        for(int i = 0;i < number; i ++)
            cout << fullArray[i] << " ";
        cout << endl;
    }
}

非递归方式精简：

int fullPermutation2(int number)
{
    int * fullArray = new int[number];
    for (int i = 0;i < number;i ++)
        fullArray[i] = i + 1;
    int icount = 0;
    fullPermutation2(fullArray, number, icount);
    delete[] fullArray;
    return icount;
}

测试

#include <iostream>

using namespace std;


int main()
{
    int number;
    cout << "Number:" << endl;
    cin >> number;

    int firstmethod = fullPermutation(number);
    int secondmethod = fullPermutation2(number);

    cout << "the size of results int first method is \t" << firstmethod << endl;
    cout << "the size of results int second method is \t" << secondmethod << endl;

    system("pause");
    return 0;
}