JavaScript: Least number of perfect square that sums upto n

JavaScript Math: Exercise-106 with Solution

Fewest Perfect Squares Sum

Write a JavaScript program that accepts an integer (n) as input and calculates the lowest number of exact square numbers that sum to n.

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3.

Example:
Input: 12
Output: 3
Explanation: 12 = 3² + 1² + 1²
Input: 63
Output: 4
Explanation: 63 = 7² + 3² + 2² + 1².

Test Data:
(12) -> 3
(13) -> 2
(63) -> 4

Sample Solution:

JavaScript Code:

/**
 * Function to find the least number of perfect squares that sum up to a given number.
 * @param {number} n - The target number.
 * @returns {number} - The least number of perfect squares that sum up to the target number.
 */
function test(n) {
    // Array to store the least number of perfect squares for each number from 0 to n
    var maps = [];
    maps[0] = 0;
    maps[1] = 1;
    maps[2] = 2;
    maps[3] = 3;
    
    // Dynamic programming approach to calculate the least number of perfect squares
    for (var i = 3; i <= n; i++) {
        maps[i] = maps[i-1] + 1;
        for (var j = 1; j*j <= i; j++) {
            maps[i] = Math.min(maps[i], maps[i-j*j] + 1);
        }
    }
    
    return maps[n];
}

// Test cases
n = 12;
console.log("Number n = " + n);
console.log("Least number of perfect squares that sum up to n: " + test(n));
n = 13;
console.log("Number n = " + n);
console.log("Least number of perfect squares that sum up to n: " + test(n));
n = 63;
console.log("Number n = " + n);
console.log("Least number of perfect squares that sum up to n: " + test(n));

Output:

Number n = 12
Least number of perfect square that sums upto n: 3
Number n = 13
Least number of perfect square that sums upto n: 2
Number n = 63
Least number of perfect square that sums upto n: 4

Flowchart:

Live Demo:

See the Pen javascript-math-exercise-106 by w3resource (@w3resource) on CodePen.

For more Practice: Solve these Related Problems:

• Write a JavaScript function that calculates the minimum number of perfect squares that sum up to n using dynamic programming.
• Write a JavaScript function that employs a breadth-first search algorithm to determine the fewest perfect squares summing to n.
• Write a JavaScript function that recursively computes the minimal count with caching to avoid redundant calculations.
• Write a JavaScript function that validates input and returns an error if the number is negative before computing the result.

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