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  1. #include <iostream>
  2.  
  3. using namespace std;
  4.  
  5. struct FRACTION
  6. {
  7.     int num;
  8.     int den;
  9. };
  10.  
  11. bool haveCommonDigit(int num1, int num2)
  12. {
  13.     int x1 = num1 % 10;
  14.     int y1 = num1 / 10;
  15.     int x2 = num2 % 10;
  16.     int y2 = num2 / 10;
  17.  
  18.     return (x1 == x2 || x1 == y2 || y1 == x2 || y1 == y2);
  19. }
  20.  
  21. bool arePalindromesOfEachOther(int num1, int num2)
  22. {
  23.     int x1 = num1 % 10;
  24.     int y1 = num1 / 10;
  25.     int x2 = num2 % 10;
  26.     int y2 = num2 / 10;
  27.  
  28.     return (x1 == y2 && x2 == y1);
  29. }
  30.  
  31. int gcd(int num1, int num2)
  32. {
  33.     if (num2 == 0)
  34.         return num1;
  35.     else
  36.         return gcd(num2, num1 % num2);
  37. }
  38.  
  39. FRACTION cancelCommonDigits(int num1, int num2)
  40. {
  41.     int x1 = num1 % 10;
  42.     int y1 = num1 / 10;
  43.     int x2 = num2 % 10;
  44.     int y2 = num2 / 10;
  45.  
  46.     int simple1 = num1;
  47.     int simple2 = num2;
  48.  
  49.     if (x1 == x2)
  50.     {
  51.         simple1 = num1 / 10;
  52.         simple2 = num2 / 10;
  53.     }
  54.     else if (x1 == y2)
  55.     {
  56.         simple1 = num1 / 10;
  57.         simple2 = num2 % 10;
  58.     }
  59.     else if (y1 == x2)
  60.     {
  61.         simple1 = num1 % 10;
  62.         simple2 = num2 / 10;
  63.     }
  64.     else if (y1 == y2)
  65.     {
  66.         simple1 = num1 % 10;
  67.         simple2 = num2 % 10;
  68.     }
  69.  
  70.     int common_divisor = gcd(num1, num2);
  71.     int common_divisor_simple = gcd(simple1, simple2);
  72.     if (num1 / common_divisor == simple1 / common_divisor_simple && num2 / common_divisor == simple2 / common_divisor_simple)
  73.     {
  74.         cout << num1 << "/" << num2 << " = " << simple1 << "/" << simple2 << endl;
  75.  
  76.         FRACTION ret = {simple1, simple2};
  77.         return ret;
  78.     }
  79.     else
  80.     {
  81.         FRACTION ret = {};
  82.         return ret;
  83.     }
  84. }
  85.  
  86. int main()
  87. {
  88.     FRACTION fractions[4] = {};
  89.     int fractions_index = 0;
  90.  
  91.     for (int i = 11; i < 100; i++)
  92.     {
  93.         for (int j = 11; j < 100; j++)
  94.         {
  95.             /*  can't be factors of 10
  96.                 must be less than 1 in value
  97.                 must have a common digit
  98.                 can't be palindromes of each other (if we cancel just one digit, after simplifying we get 1, which isn't allowed)
  99.              */
  100.             if ((i % 10 != 0 && j % 10 != 0) && (i % j > 0 && i / j == 0) && haveCommonDigit(i, j) && !arePalindromesOfEachOther(i, j))
  101.             {
  102.                 FRACTION frac = cancelCommonDigits(i, j);
  103.                 if (frac.den != 0)
  104.                 {
  105.                     fractions[fractions_index] = frac;
  106.                     fractions_index++;
  107.                 }
  108.             }
  109.         }
  110.     }
  111.  
  112.     int numerator = 1;
  113.     int denominator = 1;
  114.     int common_divisor;
  115.  
  116.     for (int i = 0; i < 4; i++)
  117.     {
  118.         numerator *= fractions[i].num;
  119.         denominator *= fractions[i].den;
  120.     }
  121.  
  122.     common_divisor = gcd(numerator, denominator);
  123.     cout << denominator / common_divisor;
  124.  
  125.     return 0;
  126. }
  127.  
Success #stdin #stdout 0.02s 2724KB
comments (?)
stdin 
Standard input is empty
stdout 
16/64 = 1/4
19/95 = 1/5
26/65 = 2/5
49/98 = 4/8
100
https://ideone.com/SCdHN4
language:
C++ (gcc 8.3)
created:
11 years ago
visibility:
secret

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