Multiplication by credentials using recursion

Question

I am looking for a way to code a program that will multiply an integer by an exponent using only a recursion loop. I have a very limited understanding of recursion, but I was able to code something to give factorial:

int fac2(int n)
{
    if (n == 1){
        return 1;
    } else {
        return n*fac2(n-1);
    }
}

I have a way to find power already, but it uses a loop for:

int my_power(int x, int e)
{
    int i, total;
    total = 1;
    for (i = 1; i <= e; i++){
    total *= x;
    }
    return total;
}

How to replace this for loop with recursion?

Answer 1

This function will be, as far as I know, for any probable case (someone installed "asdfj", since x or e hardly works).

#include <stdio.h>

double my_power(int x, int e)
{
    if (x == 0)
    {
        return 0;
    }
    if (e == 0)
    {
        return 1;
    }
    if (e > 0)
    {
        return x * my_power(x, e-1);
    }
    if (e < 0)
    {
        return 1/(x*my_power(x, -e-1));
    }
}

Answer 2

int my_power (int x, int e) {
  if (e == 0) return 1;

  return x * my_power(x, e-1);
}

Answer 3

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Answer 4

Dave Anderson , :

1) x is 0 
2) e is negative.

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: , , :

int main(void)
{
    // n = 0 special case
    test(0, 0, 1);
    test(4, 0, 1);
    test(-5, 0, 1);

    // x = 0 special case
    test(0, 0, 1);
    test(0, 2, 0);

    // normal use
    test(4, 1, 4);
    test(4, -1, 0.25);
    test(-4, 3, -64);
    test(8, 2, 64);
    test(2, 3, 8);
    test(2, -3, 0.125);
    test(2, -5, 0.03125);

    // Invalid input tests
    std::cout << std::endl << "Invalid input tests" << std::endl;
    test (0, -2, NULL);
    test(0, -4, NULL);


    // Negative Tests
    std::cout << std::endl << "Negative tests (expect failure)" << std::endl;
    test(4, 0, 4);
    test(2, 1, 1);
    test(2, -5, 0.0313);

    return 0;
}

double power(int x, int n)
{
    // check for invalid input
    if (n == 0)
    {
        return 1;
    }

    if (n > 0)
    {
        return x * power(x, n - 1);
    }
    else if (n < 0)
    {
        return 1 / (x * power(x, -n - 1));
    }
}

bool test(int x, int n, double expected)
{
    if (x == 0 && n < 0)
    {
        std::cout << "Testing " << x << "^" << n << ", result = 'Invalid input'." <<  std::endl;
        return false;
    }

    double result = power(x, n);
    std::cout << "Testing " << x << "^" << n << ", result = " << result << ". Expected " << expected << " - test " << ((result == expected) ? "PASSED" : "FAILED") <<  std::endl;
    return true;
}

:

Testing 0^0, result = 1. Expected 1 - test PASSED
Testing 4^0, result = 1. Expected 1 - test PASSED
Testing -5^0, result = 1. Expected 1 - test PASSED
Testing 0^0, result = 1. Expected 1 - test PASSED
Testing 0^2, result = 0. Expected 0 - test PASSED
Testing 4^1, result = 4. Expected 4 - test PASSED
Testing 4^-1, result = 0.25. Expected 0.25 - test PASSED
Testing -4^3, result = -64. Expected -64 - test PASSED
Testing 8^2, result = 64. Expected 64 - test PASSED
Testing 2^3, result = 8. Expected 8 - test PASSED
Testing 2^-3, result = 0.125. Expected 0.125 - test PASSED
Testing 2^-5, result = 0.03125. Expected 0.03125 - test PASSED

Invalid input tests
Testing 0^-2, result = 'Invalid input'.
Testing 0^-4, result = 'Invalid input'.

Negative tests (expect failure)
Testing 4^0, result = 1. Expected 4 - test FAILED
Testing 2^1, result = 2. Expected 1 - test FAILED
Testing 2^-5, result = 0.03125. Expected 0.0313 - test FAILED

Answer 5

, , , :

• x ⁿ= (x ^n/2) ² n
• x ⁿ= x * (x ^⊦n/2⫞) ² n
• x ¹= x
• x ⁰= 1

"⊦n/2⫞" n/2 ( , n/2 C, n - ).

,

• != n * (n - 1)!, n > 0
• 0!= 1

, .

Answer 6

:

FUNCTION mypower(number, exponent)
    IF exponent == 0 THEN:
        RETURN 1
    ELSE IF exponent > 0 THEN:
        RETURN number * mypower(number, exponent - 1)
    ELSE:
        RETURN 1 / mypower(number, -(exponent))

, double.

:

double mypower(int n, int e) {
    if (e == 0)
        return 1;
    else if (e > 0)
        return n * mypower(n, e - 1);
    else
        return 1 / mypower(n, -e);
}

Answer 7

, C-land, , .

, . , . , a "loop" ( ):

for (i, n, f, a) = 
  if (i > n) {
    return a
  } else {
    return for (i+1, n, f, f(a, i))
  }

(a, , "", "" )

, , - , , " ". , C ( , ), , .

for, :

mult(a,b) = a*b
fac(n) = for (1, n, mult, 1)

, i .

(, , ) - , , . e -> ... , ... - (, x -> x+1) (a,b) . C , , , fac :

fac(n) = for (1, n, (a,i) -> a*i, 1)

pow :

pow(x, e) = for(1, e, (a,i) -> a*x, 1) 

for , pow.

, ( ), .