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| 1 | +/** |
| 2 | + * @param {number[]} balls |
| 3 | + * @return {number} |
| 4 | + */ |
| 5 | +const getProbability = function (balls) { |
| 6 | + const k = balls.length |
| 7 | + const halfUsed = balls.reduce((acc, val) => acc + val, 0) / 2 |
| 8 | + const startArray = new Array(k) |
| 9 | + startArray.fill(0) |
| 10 | + const perm = function (b1, b2) { |
| 11 | + let p1, p2, s1, s2 |
| 12 | + s1 = b1.reduce((acc, val) => acc + val, 0) |
| 13 | + s2 = b2.reduce((acc, val) => acc + val, 0) |
| 14 | + const fact = function (n) { |
| 15 | + let f = 1 |
| 16 | + for (let i = 2; i <= n; i++) f *= i |
| 17 | + return f |
| 18 | + } |
| 19 | + p1 = fact(s1) |
| 20 | + p2 = fact(s2) |
| 21 | + b1.forEach((val) => { |
| 22 | + if (val > 1) p1 /= fact(val) |
| 23 | + }) |
| 24 | + b2.forEach((val) => { |
| 25 | + if (val > 1) p2 /= fact(val) |
| 26 | + }) |
| 27 | + return p1 * p2 |
| 28 | + } |
| 29 | + |
| 30 | + const getValidCombos = function (ballsUsed, colorNum = 0) { |
| 31 | + let box1Used = ballsUsed.reduce((acc, val) => acc + val, 0) |
| 32 | + let matches = { good: 0, total: 0 }, |
| 33 | + thisColorMax = halfUsed - box1Used |
| 34 | + if (colorNum === k - 1) { |
| 35 | + if (thisColorMax > balls[colorNum]) return { good: 0, total: 0 } |
| 36 | + ballsUsed[colorNum] = thisColorMax |
| 37 | + let ballsLeft = [] |
| 38 | + let colorsUsed = [0, 0] |
| 39 | + for (let i = 0; i < k; i++) { |
| 40 | + ballsLeft[i] = balls[i] - ballsUsed[i] |
| 41 | + if (ballsUsed[i] > 0) colorsUsed[0]++ |
| 42 | + if (ballsLeft[i] > 0) colorsUsed[1]++ |
| 43 | + } |
| 44 | + let permutations = perm(ballsUsed, ballsLeft, k) |
| 45 | + return { |
| 46 | + good: colorsUsed[1] === colorsUsed[0] ? permutations : 0, |
| 47 | + total: permutations, |
| 48 | + } |
| 49 | + } |
| 50 | + thisColorMax = Math.min(thisColorMax, balls[colorNum]) |
| 51 | + for (let i = 0; i <= thisColorMax; i++) { |
| 52 | + let match = getValidCombos([...ballsUsed], colorNum + 1) |
| 53 | + matches = { |
| 54 | + good: matches.good + match.good, |
| 55 | + total: matches.total + match.total, |
| 56 | + } |
| 57 | + ballsUsed[colorNum]++ |
| 58 | + } |
| 59 | + return matches |
| 60 | + } |
| 61 | + let res = getValidCombos(startArray) |
| 62 | + return res.good / res.total |
| 63 | +} |
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