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Преброј пермутације које дају позитиван резултат

Дат низ цифара дужине н > 1 цифара се налази у опсегу од 0 до 9. Изводимо низ испод три операције док не завршимо са свим цифрама
 

  1. Изаберите почетне две цифре и додајте (+)
  2. Затим се следећа цифра одузима (-) од резултата претходног корака. 
     
  3. Резултат претходног корака се множи ( Кс ) са следећом цифром.


Горњи низ операција изводимо линеарно са преосталим цифрама. 
Задатак је пронаћи колико пермутација датог низа даје позитиван резултат након горе наведених операција.
На пример, размотрите улазни број[] = {1 2 3 4 5}. Хајде да размотримо пермутацију 21345 да бисмо демонстрирали редослед операција. 



  1. Додајте прве две цифре резултат = 2+1 = 3
  2. Одузми следећу цифру резултат=резултат-3= 3-3 = 0
  3. Помножите следећу цифру резултат=резултат*4= 0*4 = 0
  4. Додајте следећу цифру резултат = резултат+5 = 0+5 = 5
  5. резултат = 5 што је позитивно, тако да се повећавање рачуна за један


Примери: 
 

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 )


Упитан у: Морган Станлеи
 


Прво генеришемо све могуће пермутације датог низа цифара и изводимо дати низ операција секвенцијално на свакој пермутацији и проверавамо који је резултат пермутације позитиван. Код у наставку лако описује решење проблема.
Напомена : Можемо генерисати све могуће пермутације било коришћењем итеративне методе, види ово чланак или можемо користити СТЛ функцију следећа_пермутација() функцију да га генерише. 
 



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> 

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