1 2 3 4 5 6 7 8 9 = 81 在1-9之間添加加減乘除號，使等式成立

/************************************************************************/
/* 1 2 3 4 5 6 7 8 9 = 81 在1-9之間添加加減乘除號，使等式成立。                                                                     */
/************************************************************************/
#include <iostream>
using namespace std;

bool stop = false;    //控制遍歷終止
int count_ = 0;        //計算結果數量
int count_loop = 0;    //計算循環次數

void trans(int* arr, int index)    //從右往左遞增遍歷
{
    if(index < 0)
        return;
    int temp = arr[index] / 4;
    if(temp <= 0)    //判斷是否需要進位
        return;
    arr[index] = arr[index] % 4;
    if(index == 0)    //判斷是否已經遍歷完
    {
        stop = true;
        return;
    }
    arr[index - 1] += temp;
    trans(arr, index - 1);
}

void show(int* symbol, int len)    //處理每次遍歷結果，並顯示正確項
{
    float number[9]= {1,2,3,4,5,6,7,8,9};
    int symbol_copy[9];
    for(int i = 0; i < 9; ++i)
    {
        symbol_copy[i] = symbol[i];
    }
    /*
    計算出帶乘除號的結果，將前面的項置為0，符號沿用前面的符號
    */
    for(int i = 0; i < len -1; i++)        //合並乘除項
    {
        if(symbol_copy[i] == 2 || symbol_copy[i] == 3)
        {
            if(symbol_copy[i] == 2)            //計算合並后的結果
            {
                number[i+1] = number[i] * number[i+1];
            }
            else if(symbol_copy[i] == 3)
            {
                number[i+1] = number[i] / number[i+1];
            }
            number[i] = 0;//合並后將前一個數置零

            if(i == 0)
                symbol_copy[i] = 0;
            else
                symbol_copy[i] = symbol_copy[i-1];    //乘除結果合並，符號替換成前面的符號
        }
    }

    float num = number[0];
    for(int i = 0; i < len - 1; ++i)    //計算結果
    {
        if(symbol_copy[i] == 0)
            num += number[i+1];
        else if(symbol_copy[i] == 1)
            num -= number[i+1];
    }

    if(num == 81)//打印正確等式
    {
        count_++;
        for(int i = 0; i < len -1; ++i)
        {
            cout<<i+1;
            if(symbol[i] == 0)
                cout<<"+";
            else if(symbol[i] == 1)
                cout<<"-";
            else if(symbol[i] == 2)
                cout<<"*";
            else if(symbol[i] == 3)
                cout<<"/";
        }
        cout<<"9=81"<<endl;
    }
}


int main()
{
    int  symbol[9] = {0};// [0:+ 1:- 2:* 3:/]
    int len = 9;
    while(!stop)
    {
        show(symbol, len);
        symbol[len-2]++;
        trans(symbol, len-2);
        count_loop++;
    }
    cout<<"有 "<<count_<<" 種可能"<<endl;
    cout<<"遍歷了"<<count_loop<<"次"<<endl;
    system("pause");
    return 0;
}