#include <iostream> #include <vector> #include <cmath> #include <algorithm>

using namespace std;

const double epsilon = 1E-14; const double destination = 24;

const double CARD_VALUE_MIN = 1; const double CARD_VALUE_MAX = 13;

const char symbol_array[] = {'+','-','*','/'};

double max(const double a,const double b); bool approx_equal(const double a,const double b); double calc_each(const double a,const double b,const int method);

void insert_element(vector<double> &v,const int pos,const double value); bool print_formule(const vector<double> &v,const int formule_id,const int symb_a, const int symb_b,const int symb_c);

void calc_elements(const vector<double> &v); void calc_permutation(vector<double> queue,vector<double> to_permute); //只有对于没有重复的数组才能产生正确的全排列 void calc_permutation_standard(vector<double> queue);

int rcount = 0;

int main(int argc,char *argv[]) { if(argc < 5) { cout << "Calc point 24 verstion 0.1" << endl; cout << "Usage: " << argv[0] << " <card1> <card2> <card3> <card4> " << endl; return 1; } else { vector<double> card(4); vector<double> helper(1);

for(int i = 0; i < 4; i++) { card[i] = atof(argv[i+1]); if(card[i] < CARD_VALUE_MIN || card[i] > CARD_VALUE_MAX) { cout << "Invailed value of card!" << endl; return 1; } } /*if(card[0] == card[1] && card[0] == card[2] && card[0] == card[3]) calc_elements(card); else { calc_elements(card); calc_permutation(card,helper); }*/ calc_permutation_standard(card); cout << "The total result is " << rcount << endl; } return 0; }

double max(const double a,const double b) { return a > b ? a : b; }

bool approx_equal(const double a,const double b) { if(a == 0) return fabs(b) <= epsilon; if(b == 0) return fabs(a) <= epsilon;

return fabs(a - b) / max(fabs(a),fabs(b)) <= epsilon; }

double calc_each(const double a,const double b,const int method) { if(method == 0) return a + b; if(method == 1) return a - b; if(method == 2) return a * b; if(method == 3 && b != 0) return a / b; return -999; }

void insert_element(vector<double> &v,const int pos,const double value) { v.push_back(0);

for(int i = v.size() - 2; i >= pos; i--) v[i+1] = v[i]; v[pos] = value; }

bool print_formule(const vector<double> &v,const int formule_id,const int symb_a, const int symb_b,const int symb_c) { double r1,r2,result = 0;

if(formule_id == 0) { r1 = calc_each(v[0],v[1],symb_a); if(approx_equal(r1,-999)) return false; r2 = calc_each(r1,v[2],symb_b); if(approx_equal(r2,-999)) return false; result = calc_each(r2,v[3],symb_c); } else if(formule_id == 1) { r1 = calc_each(v[0],v[1],symb_a); if(approx_equal(r1,-999)) return false; r2 = calc_each(v[2],v[3],symb_b);//symb_c); if(approx_equal(r2,-999)) return false; result = calc_each(r1,r2,symb_c);//symb_b); } else if(formule_id == 2) { r1 = calc_each(v[1],v[2],symb_a);//symb_b); if(approx_equal(r1,-999)) return false; r2 = calc_each(v[0],r1,symb_b);//symb_a); if(approx_equal(r2,-999)) return false; result = calc_each(r2,v[3],symb_c); } else if(formule_id == 3) { r1 = calc_each(v[1],v[2],symb_a);//symb_b); if(approx_equal(r1,-999)) return false; r2 = calc_each(r1,v[3],symb_b);//symb_c); if(approx_equal(r2,-999)) return false; result = calc_each(v[0],r2,symb_c);//symb_a); } else if(formule_id == 4) { r1 = calc_each(v[2],v[3],symb_a);//symb_c); if(approx_equal(r1,-999)) return false; r2 = calc_each(v[1],r1,symb_b);//symb_b); if(approx_equal(r2,-999)) return false; result = calc_each(v[0],r2,symb_c);//symb_a); } if(approx_equal(result,-999)) return false;

if(approx_equal(result,destination)) { if(formule_id == 0) { cout << "((" << v[0] << symbol_array[symb_a] << v[1] << ")" << symbol_array[symb_b] << v[2] << ")" << symbol_array[symb_c] << v[3] << "=" << destination << endl; return true; } else if(formule_id == 1) { cout << "(" << v[0] << symbol_array[symb_a] << v[1] << ")" << symbol_array[symb_b] << "(" << v[2] << symbol_array[symb_c] << v[3] << ")=" << destination << endl; return true; } else if(formule_id == 2) { cout << "(" << v[0] << symbol_array[symb_a] << "(" << v[1] << symbol_array[symb_b] << v[2] << "))" << symbol_array[symb_c] << v[3] << "=" << destination << endl; return true; } else if(formule_id == 3) { cout << v[0] << symbol_array[symb_a] << "((" << v[1] << symbol_array[symb_b] << v[2] << ")" << symbol_array[symb_c] << v[3] << ")=" << destination << endl; return true; } else if(formule_id == 4) { cout << v[0] << symbol_array[symb_a] << "(" << v[1] << symbol_array[symb_b] << "(" << v[2] << symbol_array[symb_c] << v[3] << "))=" << destination << endl; return true; } } return false; }

void calc_elements(const vector<double> &v) { int i,j,k,l; for(l = 0; l < 5; l++) { for(i = 0; i < 4; i++) { for(j = 0; j < 4; j++) { for(k = 0; k < 4; k++) { if(print_formule(v,l,i,j,k)) { rcount++; } } } } } }

void calc_permutation(vector<double> queue,vector<double> to_permute) { if(queue.size() == 0) { to_permute.pop_back(); calc_elements(to_permute); } else { vector<double> mir_queue = queue; vector<double> mir_to_permute = to_permute; vector<double> bak_vector;

double back_value = mir_queue[mir_queue.size() - 1];

mir_queue.pop_back();

for(int i = 0; i < mir_to_permute.size(); i++) { bak_vector = mir_to_permute; insert_element(mir_to_permute,i,back_value); calc_permutation(mir_queue,mir_to_permute); mir_to_permute = bak_vector; } } }

void calc_permutation_standard(vector<double> queue) { sort(queue.begin(),queue.end()); calc_elements(queue);

while(next_permutation(queue.begin(),queue.end())) { calc_elements(queue); } }

首先我使用vc提供的标准算法库，穷举四个数所有肯能的排列，然后计算所有的肯能。。。

分析:

#1,#2,#3代表运算符,a,b,c,d代表运算数,对于表达式a #1 b #2 c #3 d根据运算顺序有如下六种可能.

1,运算顺序:#1,#2,#3 (( a #1 b) #2 c) #3 d

2,运算顺序:#1,#3,#2 ( a #1 b ) #2 ( c #3 d)

3,运算顺序:#2,#3,#1 a #1 (( b #2 c )　#3 d )

4,运算顺序:#2,#1,#3 (a #1 ( b #2 c　) ) #3 d

5运算顺序:#3,#1,#2 ( a #1 b ) #2 ( c #3 d )

6运算顺序:#3,#2,#1 a #1 ( b #2 ( c #3 d))

其中运算符对应关系有６４种

运算数对应关系２４种。 注意该函数void calc_permutation(vector<double> queue,vector<double> to_permute);我并未在main函数中用到，问题在于该函数对于输入的数种有重复情况时会漏解，至今无法解决。。。唉。。。 听牛虻这么说，你还在你刚念高一吧？我看过你在论坛上发的帖子，真的很不错，能有这样的水平，我当初还只懂点皮毛，好好学有前途啊。。