fix(curriculum): replace flaky solution (#54616)
Krzysztof G
GitHub
parent
e70ef2a03f
commit
26ea6d30c9
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@ -172,97 +172,145 @@ monopolyOdds(8);
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# --solutions--
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```js
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function monopolyOdds(n) {
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function chanceCard(position, chanceCardPosition) {
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chanceCardPosition = (chanceCardPosition + 1) % 16;
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if (chanceCardPosition < 6) {
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position = chanceCardsMoves[chanceCardPosition];
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} else if (chanceCardPosition === 6 || chanceCardPosition === 7) {
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position = nextMovesFromR[position];
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} else if (chanceCardPosition === 8) {
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position = nextMovesFromU[position];
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} else if (chanceCardPosition === 9) {
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position -= 3;
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const GO = 0;
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const JAIL = 10;
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const GO_TO_JAIL = 30;
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const C1 = 11;
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const E3 = 24;
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const H2 = 39;
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const R1 = 5;
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const R2 = 15;
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const R3 = 25;
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const U1 = 12;
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const U2 = 28;
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const SPECIAL_CARDS = 16;
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const GAME_SQUARES = 40;
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const CC1 = 2;
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const CC2 = 17;
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const CC3 = 33;
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const CHESTS = [CC1, CC2, CC3];
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const chestCardsMoves = [GO, JAIL];
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const CH1 = 7;
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const CH2 = 22;
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const CH3 = 36;
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const CHANCES = [CH1, CH2, CH3];
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const chanceCardsMoves = [GO, JAIL, C1, E3, H2, R1];
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const chanceToRailroad = { [CH1]: R2, [CH2]: R3, [CH3]: R1 };
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const chanceToUtility = { [CH1]: U1, [CH2]: U2, [CH3]: U1 };
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function multiplyMatrix(matrix1, matrix2) {
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const multiplied = [];
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for (let row = 0; row < matrix1.length; row++) {
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const newRow = [];
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for (let col = 0; col < matrix1[row].length; col++) {
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let newCell = 0;
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for (let i = 0; i < matrix1[row].length; i++) {
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const value1 = matrix1[row][i];
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const value2 = matrix2[i][col];
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newCell += value1 * value2;
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}
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newRow.push(newCell);
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}
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return [position, chanceCardPosition];
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multiplied.push(newRow);
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}
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return multiplied;
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}
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function chestCard(position, chestPosition) {
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chestPosition = (chestPosition + 1) % 16;
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if (chestPosition < 2) {
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position = chestCardsMoves[chestPosition];
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function normalizeRow(row) {
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const sum = row.reduce((total, value) => total + value, 0);
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if (sum > 0) {
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for (let j = 0; j < row.length; j++) {
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const value = row[j];
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row[j] = value / sum;
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}
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return [position, chestPosition];
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}
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}
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function isChest(position) {
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return position === 2 || position === 17 || position === 33;
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}
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function sortByProbability(board) {
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return board
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.map((probability, squareNo) => [squareNo, probability])
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.sort((a, b) => a[1] - b[1])
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}
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function isChance(position) {
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return position === 7 || position === 22 || position === 36;
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}
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function getTopThree(board) {
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return sortByProbability(board)
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.slice(-3)
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.reverse()
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.map(([squareNo, _]) => squareNo.toString().padStart(2, '0')
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)
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.join('');
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}
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function isJail(position) {
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return position === 30;
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}
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function didConverge(matrix1, matrix2, precision) {
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return matrix1.every((row, rowNo) => row.every((value1, colNo) => Math.abs(value1 - matrix2[rowNo][colNo]) <= precision))
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}
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function roll(dice) {
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return Math.floor(Math.random() * dice) + 1;
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}
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function monopolyOdds(diceSides) {
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// Based on https://github.com/ByteThisCoding/project-euler/blob/master/problems/0084/0084.ts
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function getTopThree(board) {
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return sortByVisits(board)
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.slice(0, 3)
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.map(elem => elem[0].toString().padStart(2, '0'))
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.join('');
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}
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function sortByVisits(board) {
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return board
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.map((element, index) => [index, element])
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.sort((a, b) => a[1] - b[1])
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.reverse();
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}
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const rounds = 2000000;
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const chestCardsMoves = [0, 10];
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const chanceCardsMoves = [0, 10, 11, 24, 39, 5];
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const nextMovesFromR = { 7: 15, 22: 25, 36: 5 };
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const nextMovesFromU = { 7: 12, 36: 12, 22: 28 };
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const board = new Array(40).fill(0);
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let doubleCount = 0;
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let curPosition = 0;
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let curChestCard = 0;
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let curChanceCard = 0;
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for (let i = 0; i < rounds; i++) {
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const dice1 = roll(n);
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const dice2 = roll(n);
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if (dice1 === dice2) {
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doubleCount++;
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} else {
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doubleCount = 0;
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const timesRolled = new Array(diceSides * 2 + 1).fill(0);
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for (let dice1 = 1; dice1 <= diceSides; dice1++) {
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for (let dice2 = 1; dice2 <= diceSides; dice2++) {
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timesRolled[dice1 + dice2]++;
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}
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}
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if (doubleCount > 2) {
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curPosition = 10;
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doubleCount = 0;
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} else {
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curPosition = (curPosition + dice1 + dice2) % 40;
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// Transitions matrix contain probabilities of reaching each square (row values)
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// from each starting square (row no.).
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let transitions = [];
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for (let startSquare = 0; startSquare < GAME_SQUARES; startSquare++) {
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const row = new Array(GAME_SQUARES).fill(0);
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for (let rollResult = 2; rollResult <= diceSides * 2; rollResult++) {
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const rollChance = timesRolled[rollResult]
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const position = (startSquare + rollResult) % GAME_SQUARES;
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if (isChance(curPosition)) {
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[curPosition, curChanceCard] = chanceCard(curPosition, curChanceCard);
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} else if (isChest(curPosition)) {
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[curPosition, curChestCard] = chestCard(curPosition, curChestCard);
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} else if (isJail(curPosition)) {
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curPosition = 10;
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if (CHANCES.includes(position)) {
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// Chance cards ordering movement.
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for (let i = 0; i < chanceCardsMoves.length; i++) {
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const nextSquare = chanceCardsMoves[i];
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row[nextSquare] += rollChance / SPECIAL_CARDS;
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}
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row[chanceToRailroad[position]] += 2 * rollChance / SPECIAL_CARDS;
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row[chanceToUtility[position]] += rollChance / SPECIAL_CARDS;
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row[position - 3] += rollChance / SPECIAL_CARDS;
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// Rest non-moving Chance cards.
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row[position] += (SPECIAL_CARDS - chanceCardsMoves.length) * rollChance / SPECIAL_CARDS;
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} else if (CHESTS.includes(position)) {
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// Community Chest cards ordering movement.
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for (let i = 0; i < chestCardsMoves.length; i++) {
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const nextSquare = chestCardsMoves[i];
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row[nextSquare] += rollChance / SPECIAL_CARDS;
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}
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// Rest non-moving Community Chest cards.
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row[position] += (SPECIAL_CARDS - chestCardsMoves.length) * rollChance / SPECIAL_CARDS
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} else if (position === GO_TO_JAIL) {
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row[JAIL] += rollChance;
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} else {
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row[position] += rollChance;
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}
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}
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board[curPosition]++;
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normalizeRow(row)
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transitions.push(row);
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}
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return getTopThree(board);
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const precision = 0.000001;
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for (let i = 0; i < GAME_SQUARES; i++) {
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const next = multiplyMatrix(transitions, transitions);
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if (didConverge(transitions, next, precision)) {
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break;
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}
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transitions = next;
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}
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// All rows converge to the same values.
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return getTopThree(transitions[0]);
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}
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```
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