用C++創建一個程序來計算所有可能的方程

Question

我有一個任務來創建一個C++程序來查找運算符的所有可能的數學公式。下面顯示了這個問題：

給定一組數字，例如{5,3,7,3和11}。用+， - ，*，/等運算符查找所有可能的數學公式，以便公式可以產生給定的答案。例如，5 + 7-3/3 = 11。

我需要一個想法如何開始與代碼。這是否像蠻力算法？我不知道如何交換操作員來創建可能的等式。我沒有要求完整的解決方案，只是一個想法如何開始編碼。

Answer 1

你可以這樣想。 +， - ，*，/可以分別作爲1,2,3,4。現在，如果你要嘗試所有不同大小的數組組合，你可以像這樣看待它。例如 。 4個數字。

1,1,1,1 1,1,1,2 1,1,1,3 1,1,1,4 

1,1,2,1 1,1,2,2 1,1,2,3 1,1,2,4 

等等等等。希望這可能有幫助！

Answer 2

我想說明這不是我最初的想法。我將在下面添加參考。請在下面找到C++代碼。這對我來說可能對你有一些幫助。

#include <iostream> 
#include<string> 
using namespace std; 

void cntdwn(double sum, double previous, string digits, double target, std::string expr) { 
    if (digits.length() == 0) { 
    if (sum + previous == target) { 
     std::cout<<expr << " = " << target; 
    } 
    } else { 
    for (int i = 1; i <= digits.length(); i++) { 
     double current = std::stod(digits.substr(0, i)); 
     string remaining = digits.substr(i); 
     cntdwn(sum + previous, current, remaining, target, expr + " + " + std::to_string(current)); 
     cntdwn(sum, previous * current, remaining, target, expr + " * " + std::to_string(current)); 
     cntdwn(sum, previous/current, remaining, target, expr + "/" + std::to_string(current)); 
     cntdwn(sum + previous, -current, remaining, target, expr + " - " + std::to_string(current)); 
    } 
    } 
} 

void f(string digits, double target) { 
    for (int i = 1; i <= digits.length(); i++) { 
    string current = digits.substr(0, i); 
    cntdwn(0, std::stod(current), digits.substr(i), target, current); 
    } 
} 

int main() { 
    // The digits go as concatenated string 
    f("5373",11); 
    return 0; 
} 

輸出：

5 * 3.000000 - 7.000000 + 3.000000 = 11 

參考：

Generate all combinations of mathematical expressions that add to target (Java homework/interview)

https://math.stackexchange.com/questions/459857/using-operators-and-4-4-4-4-digits-find-all-formulas-that-would-resolve

https://www.careercup.com/question?id=5735906000502784

附註

a) This code will not make any combinations for the digits. For example if we give (4,4,4,4) as numbers and 10 as target then it will not give any result as the solution in that case should be [(44-4)/4] {this example has been picked from second reference]. 

b) And this problem is a classic algorithmic problme popularly known as "Countdown Problem" picked from famous UK game.