Solution Powx,n

Problem Statement

Write a Recursive Approach to Calculate Power of Integer to N Pow(x,n).

Given an integer x and an integer n, write a recursive function to calculate the power of x to the nth power.

Example

Sr#	x	n	Output	Description
1	2	5	32	2 raised to the power of 5 equals 32.
2	3	4	81	3 raised to the power of 4 equals 81.
3	5	0	1	Any number raised to the power of 0 equals 1 (x^0 = 1).

Constraints:

-100.0 < x < 100.0
-2³¹ <= n <= 2³¹-1
n is an integer.
Either x is not zero or n > 0.
-10⁴ <= xⁿ <= 10⁴

Solution

To calculate the power of x to the nth power recursively, we can follow these steps:

If n is equal to 0, return 1 since any number raised to the power of 0 equals 1.
If n is less than 0, return 1 divided by the result of calculating x raised to the power of -n.
If n is greater than 0, recursively calculate x raised to the power of n/2. Store the result in a variable temp.
If n is even, return the square of temp (i.e., temp * temp).
If n is odd, return x multiplied by the square of temp (i.e., x * temp * temp).

This approach works by dividing the power n into smaller subproblems, reducing the number of recursive calls. By utilizing the property that x^(2k) is equal to (x^k)^2, we can optimize the computation and reduce the time complexity.

Code

Here is the code for this algorithm:

java

public class Solution {

  public static double calculatePower(double x, int n) {
    if (n == 0) {
      return 1;
    }
    if (n < 0) {
      return 1 / calculatePower(x, -n);
    }
    double temp = calculatePower(x, n / 2);
    if (n % 2 == 0) {
      return temp * temp;
    } else {
      return x * temp * temp;
    }
  }

  public static void main(String[] args) {
    // Example inputs
    double x1 = 2;
    int n1 = 5;
    double x2 = 3;
    int n2 = 4;
    double x3 = 5;
    int n3 = 0;

    // Calculate power and print results
    System.out.println(
      "Power of " +
      x1 +
      " to the power of " +
      n1 +
      " = " +
      calculatePower(x1, n1)
    );
    System.out.println(
      "Power of " +
      x2 +
      " to the power of " +
      n2 +
      " = " +
      calculatePower(x2, n2)
    );
    System.out.println(
      "Power of " +
      x3 +
      " to the power of " +
      n3 +
      " = " +
      calculatePower(x3, n3)
    );
  }
}

Time and Space Complexity

The time complexity of this algorithm is because we divide the problem size in half with each recursive call. The space complexity is as well because the maximum depth of the recursion is log n.

🤖 Don't fully get this? Learn it with Claude

Stuck on Solution Powx,n? Open Claude, copy a block below, and it'll teach you this exact concept — visually and interactively.

🪜 Hint ladder (no spoilers)

Progressively stronger hints — you still solve it.

I'm working on the problem **Solution Powx,n** (DSA). Give me a HINT LADDER: start with the tiniest nudge, then wait. Only reveal the next, stronger hint when I ask. Do NOT show the full solution unless I type 'show solution'. Keep me doing the thinking. If you're unsure or a claim isn't standard, say so and reason from first principles instead of guessing.

🎨 Explain the approach visually

See the technique, not just code.

Explain the optimal approach to **Solution Powx,n** with a VISUAL walkthrough: trace it on a small concrete example using ASCII art / a step-by-step diagram, narrate what changes each step, then give time & space complexity with a one-line derivation. If you're unsure or a claim isn't standard, say so and reason from first principles instead of guessing.

🔍 Review my solution

Catch bugs, edge cases, sub-optimality.

I'll paste my solution to **Solution Powx,n**. Review it for correctness, missed edge cases, and time/space complexity, then coach me toward the optimal — don't just rewrite it. Ask me to paste my code now. If you're unsure or a claim isn't standard, say so and reason from first principles instead of guessing.

🔁 Drill the pattern

Lock in recognition with look-alikes.

Give me 2 problems that use the SAME underlying pattern as **Solution Powx,n**. For each, let me attempt first, then review my answer and name the trigger signal that reveals the pattern. If you're unsure or a claim isn't standard, say so and reason from first principles instead of guessing.

📝 My notes

← Solution Split BST