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Multiplication de deux nombres avec opérateur de décalage

Pour deux nombres n et m donnés, vous devez trouver n*m sans utiliser d’opérateur de multiplication. 
Exemples :  

Input: n = 25  m = 13 Output: 325 Input: n = 50  m = 16 Output: 800

Méthode 1
Nous pouvons résoudre ce problème avec l'opérateur de quart de travail. L’idée repose sur le fait que chaque nombre peut être représenté sous forme binaire. Et la multiplication avec un nombre équivaut à la multiplication avec des puissances de 2. Les puissances de 2 peuvent être obtenues en utilisant l'opérateur de décalage vers la gauche.
Vérifiez chaque bit défini dans la représentation binaire de m et pour chaque bit défini, décalage à gauche n fois, où compte si la valeur de position du bit défini de m et ajoutez cette valeur pour répondre.
 

C++
// CPP program to find multiplication // of two number without use of // multiplication operator #include   using namespace std; // Function for multiplication int multiply(int n int m) {   int ans = 0 count = 0;  while (m)  {  // check for set bit and left   // shift n count times  if (m % 2 == 1)   ans += n << count;  // increment of place value (count)  count++;  m /= 2;  }  return ans; } // Driver code int main() {  int n = 20  m = 13;  cout << multiply(n m);  return 0; } 
Java
// Java program to find multiplication // of two number without use of // multiplication operator class GFG {    // Function for multiplication  static int multiply(int n int m)  {   int ans = 0 count = 0;  while (m > 0)  {  // check for set bit and left   // shift n count times  if (m % 2 == 1)   ans += n << count;    // increment of place   // value (count)  count++;  m /= 2;  }    return ans;  }    // Driver code  public static void main (String[] args)  {  int n = 20 m = 13;    System.out.print( multiply(n m) );  } } // This code is contributed by Anant Agarwal. 
Python3
# python 3 program to find multiplication # of two number without use of # multiplication operator # Function for multiplication def multiply(n m): ans = 0 count = 0 while (m): # check for set bit and left  # shift n count times if (m % 2 == 1): ans += n << count # increment of place value (count) count += 1 m = int(m/2) return ans # Driver code if __name__ == '__main__': n = 20 m = 13 print(multiply(n m)) # This code is contributed by # Ssanjit_Prasad 
C#
// C# program to find multiplication // of two number without use of // multiplication operator using System; class GFG {    // Function for multiplication  static int multiply(int n int m)  {   int ans = 0 count = 0;  while (m > 0)  {  // check for set bit and left   // shift n count times  if (m % 2 == 1)   ans += n << count;    // increment of place   // value (count)  count++;  m /= 2;  }    return ans;  }    // Driver Code  public static void Main ()  {  int n = 20 m = 13;    Console.WriteLine( multiply(n m) );  } } // This code is contributed by vt_m. 
PHP
 // PHP program to find multiplication // of two number without use of // multiplication operator // Function for multiplication function multiply( $n $m) { $ans = 0; $count = 0; while ($m) { // check for set bit and left  // shift n count times if ($m % 2 == 1) $ans += $n << $count; // increment of place value (count) $count++; $m /= 2; } return $ans; } // Driver code $n = 20 ; $m = 13; echo multiply($n $m); // This code is contributed by anuj_67. ?> 
JavaScript
<script> // JavaScript program to find multiplication  // of two number without use of  // multiplication operator  // Function for multiplication  function multiply(n m)  {   let ans = 0 count = 0;   while (m)   {   // check for set bit and left   // shift n count times   if (m % 2 == 1)   ans += n << count;   // increment of place value (count)   count++;   m = Math.floor(m / 2);   }   return ans;  }  // Driver code   let n = 20  m = 13;   document.write(multiply(n m));    // This code is contributed by Surbhi Tyagi. </script> 

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260


Complexité temporelle : O (log n)



Espace auxiliaire : O(1)

comment convertir une chaîne en entier en Java

Méthode 2

Nous pouvons utiliser l'opérateur shift dans les boucles.

C++
#include    using namespace std;   int multiply(int n int m){  bool isNegative = false;  if (n < 0 && m < 0) {  n = -n m = -m;  }  if (n < 0) {  n = -n isNegative = true;  }  if (m < 0) {  m = -m isNegative = true;  }   int result = 0;  while (m){  if (m & 1) {  result += n;  }  // multiply a by 2  n = n << 1;  // divide b by 2  m = m >> 1;  }  return (isNegative) ? -result : result; }   int main() {  int n = 20  m = 13;  cout << multiply(n m);  return 0; } 
Java
// Java program for the above approach import java.io.*; class GFG {    public static int multiply(int n int m){  boolean isNegative = false;  if (n < 0 && m < 0) {  n = -n;  m = -m;  }  if (n < 0) {  n = -n;  isNegative = true;  }  if (m < 0) {  m = -m;  isNegative = true;  }  int result = 0;  while (m>0){  if ((m & 1)!=0) {  result += n;  }  // multiply a by 2  n = n << 1;  // divide b by 2  m = m >> 1;  }  return (isNegative) ? -result : result; }  public static void main (String[] args) {  int n = 20  m = 13;  System.out.println(multiply(n m));  } } // This code is contributed by Pushpesh Raj. 
Python3
def multiply(n m): is_negative = False if n < 0 and m < 0: n m = -n -m if n < 0: n is_negative = -n True if m < 0: m is_negative = -m True result = 0 while m: if m & 1: result += n # multiply a by 2 n = n << 1 # divide b by 2 m = m >> 1 return -result if is_negative else result n = 20 m = 13 print(multiply(n m)) 
C#
// C# program for the above approach using System; class GFG {    public static int multiply(int n int m){  bool isNegative = false;  if (n < 0 && m < 0) {  n = -n;  m = -m;  }  if (n < 0) {  n = -n;  isNegative = true;  }  if (m < 0) {  m = -m;  isNegative = true;  }  int result = 0;  while (m>0){  if ((m & 1)!=0) {  result += n;  }  // multiply a by 2  n = n << 1;  // divide b by 2  m = m >> 1;  }  return (isNegative) ? -result : result; }  public static void Main () {  int n = 20  m = 13;  Console.WriteLine(multiply(n m));  } } // This code is contributed by Utkarsh 
JavaScript
function multiply(n m) {  let isNegative = false;  if (n < 0 && m < 0) {  n = -n m = -m;  }  if (n < 0) {  n = -n isNegative = true;  }  if (m < 0) {  m = -m isNegative = true;  }  let result = 0;  while (m) {  if (m & 1) {  result += n;  }  // multiply a by 2  n = n << 1;  // divide b by 2  m = m >> 1;  }  return (isNegative) ? -result : result; } console.log(multiply(20 13)); 

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260

Complexité temporelle : O(log(m))

chaîne comparer java

Espace auxiliaire : O(1)

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