Is a number sum of two perfect squares in JavaScript

Perfect Square Numbers

A natural number in mathematics is called a perfect square if it can be obtained by multiplying any other natural number by itself.

For instance, 9, 16, 81, 289 are all perfect squares because:

• 9 = 3 × 3
• 16 = 4 × 4
• 81 = 9 × 9
• 289 = 17 × 17

We need to write a JavaScript function that takes a natural number as input and determines whether it can be expressed as the sum of two perfect squares:

(m * m) + (n * n) = num

If such numbers m and n exist, the function should return true, otherwise false.

Example

For the input number 389:

const num = 389;

The output should be true because 389 = (17 × 17) + (10 × 10) = 289 + 100

Solution Using Two-Pointer Approach

The algorithm uses two pointers: one starting from 0 and another from the square root of the target number. We check if their squares sum to the target:

const num = 389;

const canSumSquares = (num = 2) => {
    let left = 0, right = Math.floor(Math.sqrt(num));
    
    while (left <= right) {
        const sum = left * left + right * right;
        
        if (sum === num) {
            return true;
        } else if (sum < num) {
            left++;
        } else {
            right--;
        }
    }
    
    return false;
};

console.log(`Can ${num} be expressed as sum of two squares? ${canSumSquares(num)}`);

Can 389 be expressed as sum of two squares? true

Testing with Multiple Examples

Let's test the function with different numbers to see how it works:

const canSumSquares = (num = 2) => {
    let left = 0, right = Math.floor(Math.sqrt(num));
    
    while (left <= right) {
        const sum = left * left + right * right;
        
        if (sum === num) {
            return true;
        } else if (sum < num) {
            left++;
        } else {
            right--;
        }
    }
    
    return false;
};

// Test cases
const testNumbers = [389, 25, 50, 13, 7];

testNumbers.forEach(num => {
    const result = canSumSquares(num);
    console.log(`${num}: ${result}`);
});

389: true
25: true
50: true
13: true
7: false

How It Works

The algorithm works by:

1. Setting left = 0 and right = ?num
2. Calculating left² + right²
3. If the sum equals the target, return true
4. If the sum is less than target, increment left
5. If the sum is greater than target, decrement right
6. Continue until left > right

This approach has O(?n) time complexity, making it efficient for large numbers.

Conclusion

The two-pointer technique provides an efficient way to check if a number can be expressed as the sum of two perfect squares. This algorithm systematically explores all possible combinations in O(?n) time.