✨findSolution()

JS ⟩ value ⟩ function ⟩ recursive ⟩ findSolution()

by starting from 1 and repeatedly either + 5 or * 3, an infinite set of numbers can be produced. given a number, tries to find a solution of such additions and multiplications that produces that number.

💾 程式

• replit ⟩ findSolution(x)

// start from n = 1, then
// • n + 5
// • n * 3
function findSolution(target) {

    // check if n === target (recursive function)
    function checkNode(n = 1, expr = '1') {

        // base cases
        if (n === target) return expr;  // target found
        if (n > target) return null;    // no solution

        // recursive cases (two branches)
        return (
            checkNode(n + 5, `(${expr} + 5)`) ||
            checkNode(n * 3, `(${expr} * 3)`)
        )

    }

    // check from n = 1
    return checkNode();
}

💈範例：

findSolution(26),    // (((((1 + 5) + 5) + 5) + 5) + 5)
findSolution(23),    // (((1 + 5) * 3) + 5)
findSolution(82),    // ((((((1 * 3) + 5) * 3) * 3) + 5) + 5)

📗 參考

• Eloquent JavaScript ⟩ Recursion

📘 手冊

• Recursion