Power Calculator - Problem

Calculate the result of raising a base to an exponent using a loop (no built-in power function). Your solution must handle both positive and negative exponents.

For positive exponents, multiply the base by itself exponent times. For negative exponents, calculate the positive power first, then return 1.0 / result.

Note: Return the result as a floating-point number to handle negative exponents properly.

Input & Output

Example 1 — Positive Exponent

$ Input: base = 2, exponent = 3

› Output: 8.0

💡 Note: 2^3 = 2 × 2 × 2 = 8

Example 2 — Negative Exponent

$ Input: base = 2, exponent = -3

› Output: 0.125

💡 Note: 2^(-3) = 1/(2^3) = 1/8 = 0.125

Example 3 — Zero Exponent

$ Input: base = 5, exponent = 0

› Output: 1.0

💡 Note: Any number raised to power 0 equals 1

Constraints

-100 ≤ base ≤ 100
-30 ≤ exponent ≤ 30
base ≠ 0 when exponent < 0

Visualization

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Asked in

M Microsoft 15 A Apple 12 F Facebook 8

The key insight is to use a loop to multiply the base by itself exponent times, handling negative exponents by taking the reciprocal. The basic approach runs in O(n) time, while exponentiation by squaring optimizes to O(log n).

Common Approaches

✓ Exponentiation by Squaring

⏱️ Time: O(log n) Space: O(log n)

Instead of multiplying n times, use the property that x^n = (x^(n/2))^2. This reduces the number of operations from O(n) to O(log n).

Iterative Multiplication

⏱️ Time: O(n) Space: O(1)

Start with result = 1, then multiply by base exactly |exponent| times using a loop. Handle negative exponents by taking reciprocal of the positive result.

Exponentiation by Squaring — Algorithm Steps

If exponent is 0, return 1
If exponent is even, calculate base^(exp/2) and square it
If exponent is odd, multiply base with base^(exp-1)
Handle negative exponents by taking reciprocal

Visualization

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Step-by-Step Walkthrough

Divide

Split exponent in half

Conquer

Calculate base^(exp/2) recursively

Combine

Square the result, handle odd exponents

Code -

solution.c — C

#include <stdio.h>

double powerHelper(int base, int exp) {
    if (exp == 0) return 1.0;
    if (exp == 1) return (double)base;
    
    if (exp % 2 == 0) {
        double half = powerHelper(base, exp / 2);
        return half * half;
    } else {
        return base * powerHelper(base, exp - 1);
    }
}

double solution(int base, int exponent) {
    if (exponent < 0) {
        return 1.0 / powerHelper(base, -exponent);
    }
    return powerHelper(base, exponent);
}

int main() {
    int base, exponent;
    scanf("%d", &base);
    scanf("%d", &exponent);
    
    double result = solution(base, exponent);
    printf("%f\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(log n)

Each recursive call halves the exponent, so depth is log(exponent)

⚡ Linearithmic

Space Complexity

O(log n)

Recursion stack depth is log(exponent) for the recursive calls

⚡ Linearithmic Space

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Power Calculator - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Exponentiation by Squaring — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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