ספור תמורות שמייצרות תוצאה חיובית

בהינתן מערך של ספרות באורך n > 1 ספרות נמצא בטווח 0 עד 9. אנו מבצעים רצף של מתחת לשלוש פעולות עד שסיימנו עם כל הספרות
 

  1. בחר שתי ספרות התחלה והוסף (+)
  2. אז הספרה הבאה מופחתת (-) מהתוצאה של השלב שלמעלה. 
     
  3. התוצאה של השלב לעיל מוכפלת (X) עם הספרה הבאה.


אנו מבצעים את רצף הפעולות לעיל באופן ליניארי עם שאר הספרות. 
המשימה היא למצוא כמה תמורות של מערך נתון שמייצרות תוצאה חיובית לאחר הפעולות הנ"ל.
לדוגמה, שקול את מספר הקלט[] = {1 2 3 4 5}. הבה נבחן תמורה 21345 כדי להדגים רצף של פעולות. 

  1. הוסף תוצאת שתי הספרות הראשונות = 2+1 = 3
  2. הורידו תוצאה של הספרה הבאה=תוצאה-3= 3-3=0
  3. הכפל הספרה הבאה תוצאה=תוצאה*4= 0*4 = 0
  4. הוסף תוצאת הספרה הבאה = תוצאה+5 = 0+5 = 5
  5. תוצאה = 5 שזה חיובי אז הוסיפו את הספירה באחד


דוגמאות: 
 

Input : number[]='123' Output: 4 // here we have all permutations // 123 --> 1+2 -> 3-3 -> 0 // 132 --> 1+3 -> 4-2 -> 2 ( positive ) // 213 --> 2+1 -> 3-3 -> 0 // 231 --> 2+3 -> 5-1 -> 4 ( positive ) // 312 --> 3+1 -> 4-2 -> 2 ( positive ) // 321 --> 3+2 -> 5-1 -> 4 ( positive ) // total 4 permutations are giving positive result Input : number[]='112' Output: 2 // here we have all permutations possible // 112 --> 1+1 -> 2-2 -> 0 // 121 --> 1+2 -> 3-1 -> 2 ( positive ) // 211 --> 2+1 -> 3-1 -> 2 ( positive ) 


נשאל ב: מורגן סטנלי
 


תחילה אנו יוצרים את כל התמורות האפשריות של מערך ספרות נתון ומבצעים רצף נתון של פעולות ברצף על כל תמורה ובודקים איזו תוצאת תמורה חיובית. להלן הקוד מתאר פתרון בעיות בקלות.
הערה: אנו יכולים ליצור את כל התמורות האפשריות על ידי שימוש בשיטה איטרטיבית ראה זֶה מאמר או שנוכל להשתמש בפונקציית STL next_permutation() פונקציה כדי ליצור אותו. 
 

C++
   // C++ program to find count of permutations that produce   // positive result.   #include       using     namespace     std  ;   // function to find all permutation after executing given   // sequence of operations and whose result value is positive   // result > 0 ) number[] is array of digits of length of n   int     countPositivePermutations  (  int     number  []     int     n  )   {      // First sort the array so that we get all permutations      // one by one using next_permutation.      sort  (  number       number  +  n  );      // Initialize result (count of permutations with positive      // result)      int     count     =     0  ;      // Iterate for all permutation possible and do operation      // sequentially in each permutation      do      {      // Stores result for current permutation. First we      // have to select first two digits and add them      int     curr_result     =     number  [  0  ]     +     number  [  1  ];      // flag that tells what operation we are going to      // perform      // operation = 0 ---> addition operation ( + )      // operation = 1 ---> subtraction operation ( - )      // operation = 0 ---> multiplication operation ( X )      // first sort the array of digits to generate all      // permutation in sorted manner      int     operation     =     1  ;      // traverse all digits      for     (  int     i  =  2  ;     i   <  n  ;     i  ++  )      {      // sequentially perform +  -  X operation      switch     (  operation  )      {      case     0  :      curr_result     +=     number  [  i  ];      break  ;      case     1  :      curr_result     -=     number  [  i  ];      break  ;      case     2  :      curr_result     *=     number  [  i  ];      break  ;      }      // next operation (decides case of switch)      operation     =     (  operation     +     1  )     %     3  ;      }      // result is positive then increment count by one      if     (  curr_result     >     0  )      count  ++  ;      // generate next greater permutation until it is      // possible      }     while  (  next_permutation  (  number       number  +  n  ));      return     count  ;   }   // Driver program to test the case   int     main  ()   {      int     number  []     =     {  1       2       3  };      int     n     =     sizeof  (  number  )  /  sizeof  (  number  [  0  ]);      cout      < <     countPositivePermutations  (  number       n  );      return     0  ;   }   
Java
   // Java program to find count of permutations    // that produce positive result.    import     java.util.*  ;   class   GFG      {   // function to find all permutation after    // executing given sequence of operations    // and whose result value is positive result > 0 )    // number[] is array of digits of length of n    static     int     countPositivePermutations  (  int     number  []           int     n  )      {         // First sort the array so that we get       // all permutations one by one using      // next_permutation.       Arrays  .  sort  (  number  );         // Initialize result (count of permutations       // with positive result)       int     count     =     0  ;         // Iterate for all permutation possible and       // do operation sequentially in each permutation       do      {         // Stores result for current permutation.       // First we have to select first two digits      // and add them       int     curr_result     =     number  [  0  ]     +     number  [  1  ]  ;         // flag that tells what operation we are going to       // perform       // operation = 0 ---> addition operation ( + )       // operation = 1 ---> subtraction operation ( - )       // operation = 0 ---> multiplication operation ( X )       // first sort the array of digits to generate all       // permutation in sorted manner       int     operation     =     1  ;         // traverse all digits       for     (  int     i     =     2  ;     i      <     n  ;     i  ++  )         {         // sequentially perform +  -  X operation       switch     (  operation  )         {         case     0  :         curr_result     +=     number  [  i  ]  ;         break  ;         case     1  :         curr_result     -=     number  [  i  ]  ;         break  ;         case     2  :         curr_result     *=     number  [  i  ]  ;         break  ;         }         // next operation (decides case of switch)       operation     =     (  operation     +     1  )     %     3  ;         }         // result is positive then increment count by one       if     (  curr_result     >     0  )         count  ++  ;         // generate next greater permutation until       // it is possible       }     while  (  next_permutation  (  number  ));         return     count  ;      }      static     boolean     next_permutation  (  int  []     p  )   {      for     (  int     a     =     p  .  length     -     2  ;     a     >=     0  ;     --  a  )      if     (  p  [  a  ]      <     p  [  a     +     1  ]  )      for     (  int     b     =     p  .  length     -     1  ;;     --  b  )      if     (  p  [  b  ]     >     p  [  a  ]  )         {      int     t     =     p  [  a  ]  ;      p  [  a  ]     =     p  [  b  ]  ;      p  [  b  ]     =     t  ;      for     (  ++  a       b     =     p  .  length     -     1  ;     a      <     b  ;     ++  a       --  b  )         {      t     =     p  [  a  ]  ;      p  [  a  ]     =     p  [  b  ]  ;      p  [  b  ]     =     t  ;      }      return     true  ;      }      return     false  ;   }   // Driver Code   public     static     void     main  (  String  []     args  )   {      int     number  []     =     {  1       2       3  };         int     n     =     number  .  length  ;         System  .  out  .  println  (  countPositivePermutations  (  number       n  ));      }   }      // This code is contributed by PrinciRaj1992   
Python3
   # Python3 program to find count of permutations    # that produce positive result.    # function to find all permutation after    # executing given sequence of operations    # and whose result value is positive result > 0 )    # number[] is array of digits of length of n    def   countPositivePermutations  (  number     n  ):   # First sort the array so that we get    # all permutations one by one using   # next_permutation.    number  .  sort  ()   # Initialize result (count of permutations    # with positive result)    count   =   0  ;   # Iterate for all permutation possible and    # do operation sequentially in each permutation    while   True  :   # Stores result for current permutation.    # First we have to select first two digits   # and add them    curr_result   =   number  [  0  ]   +   number  [  1  ];   # flag that tells what operation we are going to    # perform    # operation = 0 ---> addition operation ( + )    # operation = 1 ---> subtraction operation ( - )    # operation = 0 ---> multiplication operation ( X )    # first sort the array of digits to generate all    # permutation in sorted manner    operation   =   1  ;   # traverse all digits    for   i   in   range  (  2     n  ):   # sequentially perform +  -  X operation    if   operation   ==   0  :   curr_result   +=   number  [  i  ];   else   if   operation   ==   1  :   curr_result   -=   number  [  i  ];   else   if   operation   ==   2  :   curr_result   *=   number  [  i  ];   # next operation (decides case of switch)    operation   =   (  operation   +   1  )   %   3  ;   # result is positive then increment count by one    if   (  curr_result   >   0  ):   count   +=   1   # generate next greater permutation until    # it is possible    if  (  not   next_permutation  (  number  )):   break   return   count  ;   def   next_permutation  (  p  ):   for   a   in   range  (  len  (  p  )  -  2     -  1     -  1  ):   if   (  p  [  a  ]    <   p  [  a   +   1  ]):   for   b   in   range  (  len  (  p  )  -  1     -  1000000000     -  1  ):   if   (  p  [  b  ]   >   p  [  a  ]):   t   =   p  [  a  ];   p  [  a  ]   =   p  [  b  ];   p  [  b  ]   =   t  ;   a   +=   1   b   =   len  (  p  )   -   1   while  (  a    <   b  ):   t   =   p  [  a  ];   p  [  a  ]   =   p  [  b  ];   p  [  b  ]   =   t  ;   a   +=   1   b   -=   1   return   True  ;   return   False  ;   # Driver Code   if   __name__   ==  '__main__'  :   number   =   [  1     2     3  ]   n   =   len  (  number  )   print  (  countPositivePermutations  (  number     n  ));   # This code is contributed by rutvik_56.   
C#
   // C# program to find count of permutations    // that produce positive result.    using     System  ;   class     GFG   {       // function to find all permutation after    // executing given sequence of operations    // and whose result value is positive result > 0 )    // number[] is array of digits of length of n    static     int     countPositivePermutations  (  int     []  number           int     n  )      {         // First sort the array so that we get       // all permutations one by one using      // next_permutation.       Array  .  Sort  (  number  );         // Initialize result (count of permutations       // with positive result)       int     count     =     0  ;         // Iterate for all permutation possible and       // do operation sequentially in each permutation       do      {         // Stores result for current permutation.       // First we have to select first two digits      // and add them       int     curr_result     =     number  [  0  ]     +     number  [  1  ];         // flag that tells what operation we are going to       // perform       // operation = 0 ---> addition operation ( + )       // operation = 1 ---> subtraction operation ( - )       // operation = 0 ---> multiplication operation ( X )       // first sort the array of digits to generate all       // permutation in sorted manner       int     operation     =     1  ;         // traverse all digits       for     (  int     i     =     2  ;     i      <     n  ;     i  ++  )         {         // sequentially perform +  -  X operation       switch     (  operation  )         {         case     0  :         curr_result     +=     number  [  i  ];         break  ;         case     1  :         curr_result     -=     number  [  i  ];         break  ;         case     2  :         curr_result     *=     number  [  i  ];         break  ;         }         // next operation (decides case of switch)       operation     =     (  operation     +     1  )     %     3  ;         }         // result is positive then increment count by one       if     (  curr_result     >     0  )         count  ++  ;         // generate next greater permutation until       // it is possible       }     while  (  next_permutation  (  number  ));         return     count  ;      }      static     bool     next_permutation  (  int  []     p  )   {      for     (  int     a     =     p  .  Length     -     2  ;     a     >=     0  ;     --  a  )      if     (  p  [  a  ]      <     p  [  a     +     1  ])      for     (  int     b     =     p  .  Length     -     1  ;;     --  b  )      if     (  p  [  b  ]     >     p  [  a  ])         {      int     t     =     p  [  a  ];      p  [  a  ]     =     p  [  b  ];      p  [  b  ]     =     t  ;      for     (  ++  a       b     =     p  .  Length     -     1  ;         a      <     b  ;     ++  a       --  b  )         {      t     =     p  [  a  ];      p  [  a  ]     =     p  [  b  ];      p  [  b  ]     =     t  ;      }      return     true  ;      }      return     false  ;   }   // Driver Code   static     public     void     Main     ()   {      int     []  number     =     {  1       2       3  };         int     n     =     number  .  Length  ;         Console  .  Write  (  countPositivePermutations  (  number       n  ));      }   }      // This code is contributed by ajit..   
JavaScript
    <  script  >      // Javascript program to find count of permutations      // that produce positive result.          // function to find all permutation after      // executing given sequence of operations      // and whose result value is positive result > 0 )      // number[] is array of digits of length of n      function     countPositivePermutations  (  number       n  )      {      // First sort the array so that we get      // all permutations one by one using      // next_permutation.      number  .  sort  (  function  (  a       b  ){  return     a     -     b  });      // Initialize result (count of permutations      // with positive result)      let     count     =     0  ;      // Iterate for all permutation possible and      // do operation sequentially in each permutation      do      {      // Stores result for current permutation.      // First we have to select first two digits      // and add them      let     curr_result     =     number  [  0  ]     +     number  [  1  ];      // flag that tells what operation we are going to      // perform      // operation = 0 ---> addition operation ( + )      // operation = 1 ---> subtraction operation ( - )      // operation = 0 ---> multiplication operation ( X )      // first sort the array of digits to generate all      // permutation in sorted manner      let     operation     =     1  ;      // traverse all digits      for     (  let     i     =     2  ;     i      <     n  ;     i  ++  )      {      // sequentially perform +  -  X operation      switch     (  operation  )      {      case     0  :      curr_result     +=     number  [  i  ];      break  ;      case     1  :      curr_result     -=     number  [  i  ];      break  ;      case     2  :      curr_result     *=     number  [  i  ];      break  ;      }      // next operation (decides case of switch)      operation     =     (  operation     +     1  )     %     3  ;      }      // result is positive then increment count by one      if     (  curr_result     >     0  )      count  ++  ;      // generate next greater permutation until      // it is possible      }     while  (  next_permutation  (  number  ));      return     count  ;      }      function     next_permutation  (  p  )      {      for     (  let     a     =     p  .  length     -     2  ;     a     >=     0  ;     --  a  )      if     (  p  [  a  ]      <     p  [  a     +     1  ])      for     (  let     b     =     p  .  length     -     1  ;;     --  b  )      if     (  p  [  b  ]     >     p  [  a  ])      {      let     t     =     p  [  a  ];      p  [  a  ]     =     p  [  b  ];      p  [  b  ]     =     t  ;      for     (  ++  a       b     =     p  .  length     -     1  ;      a      <     b  ;     ++  a       --  b  )      {      t     =     p  [  a  ];      p  [  a  ]     =     p  [  b  ];      p  [  b  ]     =     t  ;      }      return     true  ;      }      return     false  ;      }          let     number     =     [  1       2       3  ];      let     n     =     number  .  length  ;      document  .  write  (  countPositivePermutations  (  number       n  ));        <  /script>   

תְפוּקָה:  

4 

מורכבות זמן: O(n*n!)

מרחב עזר: O(1)
אם יש לך פתרון טוב יותר ומוטב לבעיה זו, אנא שתף ​​בתגובות.