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C++ Program to Find Factorial of a Number Using Iteration

C++ Program To Find Power Without Using Multiplication(*) And Division(/) Operators

Last Updated : 17 Jan, 2023

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Method 1 (Using Nested Loops):
We can calculate power by using repeated addition.
For example to calculate 5^6.
1) First 5 times add 5, we get 25. (5^2)
2) Then 5 times add 25, we get 125. (5^3)
3) Then 5 times add 125, we get 625 (5^4)
4) Then 5 times add 625, we get 3125 (5^5)
5) Then 5 times add 3125, we get 15625 (5^6)

C++

// C++ code for power function  #include <bits/stdc++.h> using namespace std;  // Works only if a >= 0  // and b >= 0  int pow(int a, int b)  {      if (b == 0)          return 1;      int answer = a;      int increment = a;      int i, j;      for(i = 1; i < b; i++)      {          for(j = 1; j < a; j++)          {              answer += increment;          }          increment = answer;      }      return answer;  }   // Driver Code int main()  {      cout << pow(5, 3);      return 0;  }   // This code is contributed by rathbhupendra

Output :

Time Complexity: O(a * b)

Auxiliary Space: O(1)

Method 2 (Using Recursion)
Recursively add a to get the multiplication of two numbers. And recursively multiply to get a raise to the power b.

C++

// C++ program to implement  // the above approach #include<bits/stdc++.h> using namespace std;  // A recursive function  // to get x*y int multiply(int x, int y) {     if(y)         return (x + multiply(x,                  y - 1));     else         return 0; }  // A recursive function to get a^b // Works only if a >= 0 and b >= 0 int pow(int a, int b) {     if(b)         return multiply(a,                          pow(a, b - 1));     else         return 1; }   // Driver Code int main() {     cout << pow(5, 3);     getchar();     return 0; }  // This code is contributed by Akanksha Rai

Output :

Time Complexity: O(b)

Auxiliary Space: O(b)

Method 3 (Using bit masking)

we can a^n (let's say 3^5) as 3^4 * 3^0 * 3^1 = 3^, so we can represent 5 as its binary i.e. 101

C++

// C++ program to implement // the above approach #include <iostream> using namespace std;  // Function calculating power long long pow(int a, int n) {     int ans = 1;       while(n > 0)       {           // Calculate last bit(right most)            // bit of n           int last_bit = n&1;                      // if last bit is 1 then multiply            // ans and a           if(last_bit)           {             ans = ans*a;           }              // Make a equal to square of a as on        // every succeeding bit it got squared        // like a^0, a^1, a^2, a^4, a^8       a = a * a;       n = n >> 1;     }       return ans; }  // Driver code int main()  {     cout << pow(3, 5);     return 0; }

Time Complexity: O(log n)

Auxiliary Space: O(1)

C++ Program to Find Factorial of a Number Using Iteration

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Article Tags :

Divide and Conquer
Mathematical
C++ Programs
C++
DSA
C++ Basic Programs

Practice Tags :

CPP
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