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Suskaičiuokite permutacijas, kurios duoda teigiamą rezultatą

Duotas skaitmenų masyvas, kurio ilgis n > 1 skaitmuo, yra intervale nuo 0 iki 9. Atliekame žemiau trijų operacijų seką, kol baigsime su visais skaitmenimis
 

  1. Pasirinkite pradinius du skaitmenis ir pridėkite (+)
  2. Tada kitas skaitmuo atimamas ( - ) iš aukščiau pateikto veiksmo rezultato. 
     
  3. Pirmiau pateikto veiksmo rezultatas padauginamas ( X ) iš kito skaitmens.


Aukščiau nurodytą operacijų seką atliekame tiesiškai su likusiais skaitmenimis. 
Užduotis yra rasti, kiek permutacijų duotame masyve duoda teigiamą rezultatą po aukščiau nurodytų operacijų.
Pavyzdžiui, apsvarstykite įvestą numerį [] = {1 2 3 4 5}. Panagrinėkime permutaciją 21345, kad parodytume operacijų seką. 



  1. Pridėkite pirmuosius du skaitmenis = 2 + 1 = 3
  2. Atimkite kitą skaitmenį rezultatas = rezultatas-3 = 3-3 = 0
  3. Padauginkite kitą skaitmenį rezultatas = rezultatas * 4 = 0 * 4 = 0
  4. Pridėkite kitą skaitmenį rezultatas = rezultatas + 5 = 0 + 5 = 5
  5. rezultatas = 5, kuris yra teigiamas, todėl skaičiuokite vienetu


Pavyzdžiai: 
 

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 )


Paklausė: Morganas Stenlis
 


Pirmiausia sugeneruojame visas galimas duoto skaitmenų masyvo permutacijas ir nuosekliai atliekame nurodytą operacijų seką kiekvienai permutacijai ir patikriname, kurios permutacijos rezultatas yra teigiamas. Žemiau pateiktas kodas lengvai apibūdina problemos sprendimą.
Pastaba: Galime sugeneruoti visas įmanomas permutacijas naudodami iteracinį metodą, žr tai straipsnis arba galime naudoti STL funkciją next_permutation() funkcija jį generuoti. 
 



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> 

Išvestis:  

4

Laiko sudėtingumas: O(n*n!)

Pagalbinė erdvė: O(1)
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