Donada una matriu de dígits de longitud n > 1 dígits es troba dins del rang de 0 a 9. Realitzem una seqüència de tres operacions per sota fins que acabem amb tots els dígits.
- Seleccioneu els dos dígits inicials i afegiu (+)
- A continuació, es resta el dígit següent (-) del resultat del pas anterior.
- El resultat del pas anterior es multiplica ( X ) amb el següent dígit.
Realitzem la seqüència d'operacions anterior de manera lineal amb els dígits restants.
La tasca és trobar quantes permutacions de la matriu donada produeixen un resultat positiu després de les operacions anteriors.
Per exemple, considereu número d'entrada[] = {1 2 3 4 5}. Considerem una permutació 21345 per demostrar la seqüència d'operacions.
- Sumeu els dos primers dígits resultat = 2+1 = 3
- Resteu el següent dígit resultat=resultat-3= 3-3 = 0
- Multiplica el següent dígit resultat = resultat * 4 = 0 * 4 = 0
- Afegiu el següent dígit resultat = resultat+5 = 0+5 = 5
- resultat = 5 que és positiu, així que incrementeu el recompte en un
Exemples:
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 )
Preguntat a: Morgan Stanley
Primer generem totes les permutacions possibles d'una matriu de dígits donada i realitzem una seqüència determinada d'operacions seqüencialment a cada permutació i comprovem quin resultat de la permutació és positiu. El codi següent descriu la solució del problema fàcilment.
Nota: Podem generar totes les permutacions possibles utilitzant el mètode iteratiu vegeu això article o podem utilitzar la funció STL next_permutation() funció per generar-lo.
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>
Sortida:
4
Complexitat temporal: O(n*n!)
Espai auxiliar: O(1)
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