task_operators_100.js

'use strict'

const assert = require('assert').strict

/**
 * Write a program that outputs all possibilities to put + or - or nothing
 * between the numbers 1, 2, ..., 9 (in this order) such that the result
 * equals 100. For example: 1 + 2 + 34 – 5 + 67 – 8 + 9 = 100.
 */

// Brute force solution: check all variants,
// print those that end up being equal to 100.

/**
 * @param {number[]}  numbers       Remaining numbers: [7, 8, 9]
 * @param {string}    resultString  Result in readable form: '1 + 23 - 4'
 * @param {number}    result        Result without the last operand
 * @param {number}    x             The last operand
 */
function put(numbers, resultString, result, x) {
    // Nothing to do
    if (numbers.length === 0) {
        // Found a solution
        if (result + x === 100) {
            console.log(`${resultString} == 100`)
            // Sanity check
            assert.strictEqual(eval(resultString), 100)
        }
        return
    }

    const n = numbers[0]

    // Put +
    put(numbers.slice(1), `${resultString} + ${n}`, result + x, n)

    // Put -
    put(numbers.slice(1), `${resultString} - ${n}`, result + x, -n)

    // Put nothing (concat)
    put(numbers.slice(1), `${resultString}${n}`, result, 10 * x + Math.sign(x) * n)
}

// We put 1 in there by default, since it always starts with 1.
put([2, 3, 4, 5, 6, 7, 8, 9], '1', 0, 1)