feat: upgrade makeChanges to a more robust version
This commit is contained in:
Sérgio Salgado
parent
4c1be68f2a
commit
8a4f768957
1 changed files with 172 additions and 158 deletions
330
lib/bill-math.js
330
lib/bill-math.js
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@ -1,194 +1,193 @@
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const uuid = require('uuid')
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const _ = require('lodash/fp')
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const uuid = require('uuid')
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// Custom algorith for two cassettes. For three or more denominations, we'll need
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// to rethink this. Greedy algorithm fails to find *any* solution in some cases.
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// Dynamic programming may be too inefficient for large amounts.
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//
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// We can either require canononical denominations for 3+, or try to expand
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// this algorithm.
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exports.makeChange = function makeChange (cassettes, amount) {
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// Note: Everything here is converted to primitive numbers,
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// since they're all integers, well within JS number range,
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// and this is way more efficient in a tight loop.
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const MAX_AMOUNT_OF_SOLUTIONS = 10000
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const MAX_BRUTEFORCE_ITERATIONS = 10000000
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// Another note: While this greedy algorithm possibly works for all major denominations,
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// it still requires a fallback for cases where it might not provide any solution.
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// Example: Denominations: [3, 5, 10] | User inputs 4 times the [3] button, resulting in a 12 fiat tx
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// This algorithm resolves for 1 x [10], and can't resolve the remainder of 2
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return _.size(cassettes) > 2 ? makeChangeDynamic(cassettes, amount) : makeChangeDuo(cassettes, amount)
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function newSolution(cassettes, c0, c1, c2, c3, shouldFlip) {
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return [
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{
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provisioned: shouldFlip ? cassettes[0].count - c0 : c0,
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denomination: cassettes[0].denomination
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},
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{
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provisioned: shouldFlip ? cassettes[1].count - c1 : c1,
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denomination: cassettes[1].denomination
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},
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{
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provisioned: shouldFlip ? cassettes[2].count - c2 : c2,
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denomination: cassettes[2].denomination
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},
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{
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provisioned: shouldFlip ? cassettes[3].count - c3 : c3,
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denomination: cassettes[3].denomination
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}
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]
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}
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function makeChangeDuo (cassettes, amount) {
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function mergeCassettes(cassettes) {
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const map = {}
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_.forEach(it => {
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if (!map[it.denomination]) {
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map[it.denomination] = 0
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}
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map[it.denomination] += it.count
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}, cassettes)
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return _.map(it => ({ denomination: it, count: map[it] }), _.keys(map))
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}
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function unmergeCassettes(cassettes, output) {
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const map = {}
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_.forEach(it => {
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if (!map[it.denomination]) {
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map[it.denomination] = 0
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}
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map[it.denomination] += it.provisioned
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}, output)
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const response = []
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_.forEach(it => {
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const value = {
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denomination: it.denomination,
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id: uuid.v4()
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}
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const amountNeeded = map[it.denomination]
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if (!amountNeeded) {
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return response.push({ provisioned: 0, ...value })
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}
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if (amountNeeded < it.count) {
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map[it.denomination] = 0
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return response.push({ provisioned: amountNeeded, ...value })
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}
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map[it.denomination] -= it.count
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return response.push({ provisioned: it.count, ...value })
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}, cassettes)
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return response
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}
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function makeChangeDuo(cassettes, amount) {
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const small = cassettes[0]
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const large = cassettes[1]
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const largeDenom = large.denomination
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const smallDenom = small.denomination
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const largeBills = Math.min(large.count, Math.floor(amount / largeDenom))
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const amountNum = amount.toNumber()
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for (let i = largeBills; i >= 0; i--) {
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const remainder = amountNum - largeDenom * i
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if (remainder % smallDenom !== 0) continue
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const smallCount = remainder / smallDenom
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if (smallCount > small.count) continue
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return [
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{provisioned: smallCount, denomination: small.denomination, id: uuid.v4()},
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{provisioned: i, denomination: largeDenom, id: uuid.v4()}
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{
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provisioned: smallCount,
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denomination: small.denomination,
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id: uuid.v4()
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},
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{ provisioned: i, denomination: largeDenom, id: uuid.v4() }
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]
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}
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return null
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return []
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}
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function makeChangeDynamic (cassettes, amount) {
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while (_.size(cassettes) < 4) {
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cassettes.push({ denomination: 0, count: 0 })
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function makeChange(outCassettes, amount) {
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const available = _.reduce(
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(res, val) => res + val.count * val.denomination,
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0,
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outCassettes
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)
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if (available < amount) {
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console.log(`Tried to dispense more than was available for amount ${amount.toNumber()} with cassettes ${JSON.stringify(cassettes)}`)
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return null
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}
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const cassettes = mergeCassettes(outCassettes)
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const result =
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_.size(cassettes) >= 3
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? makeChangeDynamic(cassettes, amount, available)
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: makeChangeDuo(cassettes, amount)
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if (!result.length) return null
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return unmergeCassettes(outCassettes, result)
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}
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function makeChangeDynamicBruteForce(outCassettes, amount, available) {
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const solutions = []
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const amountNum = amount.toNumber()
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for (let i = 0; i * cassettes[0].denomination <= amountNum; i++) {
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for (
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let j = 0;
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i * cassettes[0].denomination + j * cassettes[1].denomination <=
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amountNum;
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j++
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) {
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if (cassettes[1].denomination === 0) break
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if (
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i * cassettes[0].denomination + j * cassettes[1].denomination ===
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amountNum &&
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i <= cassettes[0].count &&
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j <= cassettes[1].count &&
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i >= 0 &&
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j >= 0
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) {
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solutions.push([
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{
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provisioned: i,
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denomination: cassettes[0].denomination,
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id: uuid.v4()
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},
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{
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provisioned: j,
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denomination: cassettes[1].denomination,
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id: uuid.v4()
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},
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{
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provisioned: 0,
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denomination: cassettes[2].denomination,
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id: uuid.v4()
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},
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{
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provisioned: 0,
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denomination: cassettes[3].denomination,
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id: uuid.v4()
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}
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])
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let x = 0
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const shouldFlip = amount > _.max(_.map(it => it.denomination * it.count, outCassettes))
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const amountNum = shouldFlip ? available - amount : amount
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const cassettes = shouldFlip ? _.reverse(outCassettes) : outCassettes
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const { denomination: denomination0, count: count0 } = cassettes[0]
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const { denomination: denomination1, count: count1 } = cassettes[1]
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const { denomination: denomination2, count: count2 } = cassettes[2]
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const { denomination: denomination3, count: count3 } = cassettes[3]
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const startTime = new Date().getTime()
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loop1: for (let i = 0; i <= count0; i++) {
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const firstSum = i * denomination0
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for (let j = 0; j <= count1; j++) {
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const secondSum = firstSum + j * denomination1
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if (secondSum > amountNum) break
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if (secondSum === amountNum) {
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solutions.push(newSolution(cassettes, i, j, 0, 0, shouldFlip))
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}
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for (
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let k = 0;
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i * cassettes[0].denomination +
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j * cassettes[1].denomination +
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k * cassettes[2].denomination <=
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amountNum;
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k++
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) {
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if (cassettes[2].denomination === 0) break
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if (
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i * cassettes[0].denomination +
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j * cassettes[1].denomination +
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k * cassettes[2].denomination ===
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amountNum &&
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i <= cassettes[0].count &&
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j <= cassettes[1].count &&
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k <= cassettes[2].count &&
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i >= 0 &&
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j >= 0 &&
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k >= 0
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) {
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solutions.push([
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{
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provisioned: i,
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denomination: cassettes[0].denomination,
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id: uuid.v4()
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},
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{
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provisioned: j,
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denomination: cassettes[1].denomination,
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id: uuid.v4()
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},
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{
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provisioned: k,
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denomination: cassettes[2].denomination,
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id: uuid.v4()
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},
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{
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provisioned: 0,
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denomination: cassettes[3].denomination,
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id: uuid.v4()
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}
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])
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for (let k = 0; k <= count2; k++) {
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const thirdSum = secondSum + k * denomination2
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if (thirdSum > amountNum) break
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if (denomination2 === 0) break
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if (thirdSum === amountNum) {
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solutions.push(newSolution(cassettes, i, j, k, 0, shouldFlip))
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}
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for (
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let l = 0;
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i * cassettes[0].denomination +
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j * cassettes[1].denomination +
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k * cassettes[2].denomination +
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l * cassettes[3].denomination <=
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amountNum;
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l++
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) {
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if (cassettes[3].denomination === 0) break
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if (
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i * cassettes[0].denomination +
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j * cassettes[1].denomination +
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k * cassettes[2].denomination +
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l * cassettes[3].denomination ===
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amountNum &&
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i <= cassettes[0].count &&
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j <= cassettes[1].count &&
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k <= cassettes[2].count &&
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l <= cassettes[3].count &&
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i >= 0 &&
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j >= 0 &&
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k >= 0 &&
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l >= 0
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) {
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solutions.push([
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{
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provisioned: i,
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denomination: cassettes[0].denomination,
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id: uuid.v4()
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},
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{
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provisioned: j,
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denomination: cassettes[1].denomination,
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id: uuid.v4()
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},
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{
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provisioned: k,
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denomination: cassettes[2].denomination,
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id: uuid.v4()
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},
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{
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provisioned: l,
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denomination: cassettes[3].denomination,
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id: uuid.v4()
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}
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])
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for (let l = 0; l <= count3; l++) {
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if ((x > MAX_AMOUNT_OF_SOLUTIONS && solutions.length >= 1) || x > MAX_BRUTEFORCE_ITERATIONS) break loop1
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x++
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const fourthSum = thirdSum + l * denomination3
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if (fourthSum > amountNum) break
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if (denomination3 === 0) break
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if (fourthSum === amountNum) {
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solutions.push(newSolution(cassettes, i, j, k, l, shouldFlip))
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}
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}
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}
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}
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}
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const endTime = new Date().getTime()
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console.log(`Exiting bruteforce after ${x} tries. Took ${endTime - startTime} ms`)
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return solutions
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}
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function makeChangeDynamic(cassettes, amount, available) {
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while (_.size(cassettes) < 4) {
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cassettes.push({ denomination: 0, count: 0 })
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}
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const amountNum = amount.toNumber()
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const solutions = makeChangeDynamicBruteForce(cassettes, amountNum, available)
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const sortedSolutions = _.sortBy(it => {
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const arr = []
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@ -206,5 +205,20 @@ function makeChangeDynamic (cassettes, amount) {
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_.head(sortedSolutions)
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)
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return cleanSolution
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const response = cleanSolution
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// Final sanity check
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let total = 0
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_.forEach(it => {
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total += it.provisioned * it.denomination
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}, response)
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if (total === amountNum) return response
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console.log(
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`Failed to find a solution for ${amountNum} with cassettes ${JSON.stringify(cassettes)}`
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)
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return []
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}
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module.exports = { makeChange }
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