Hypergeometric Distribution Sequence

hyperGeoDistriSeq.js

'use strict'

function fact(n) {
  if (n > 1) return n * fact(n - 1)
  else return 1
}

function combination(n, m) {
  /* C(n, m) = n * (n-1) * ... * (n-m+1) / m! */
  if (!(n >= m)) console.error(new Error("m must be smaller than n"))
  var res = 1
  for (var i = 0; i < m; i++) {
    res *= n - i
  }
  res /= fact(m)
  return res
}

/**
* @param N
* the number of all products
* @param M
* the number of shobby products
* @param n
* the number of products you draw
*/
function hyperGeoDistriSeq(N, M, n) {
  /* P(X=k) = C(M, k) * C(N-M, n-k) / C(n, N) */
  var res = {}
  const C = combination
  var denominator = C(N, n)
  for (var k = 0; k <= Math.min(n, M); k++) {
    res[k] = C(M, k) * C(N-M, n-k) / denominator
  }
  return res
}


/**
* DEMO
*/
(function () {
  const H = hyperGeoDistriSeq
  const rl = require('readline').createInterface({
    input: process.stdin,
    output: process.stdout
  })
  rl.question('How many products are there? ', (N) => {
    rl.question('How many products are defective? ', (M) => {
      rl.question('How many products will you choose? ', (n) => {
        const distri = H(N, M, n)
        var X = ''
        var P = ''
        for (var i in distri) {
          var x = i.toString()
          var p = distri[i].toString()
          if (x.length > p.length) {
            p += ' '.repeat(x.length - p.length)
          } else if (x.length < p.length) {
            x += ' '.repeat(p.length - x.length)
          }
          X += ' ' + x + ' |'
          P += ' ' + p + ' |'
        }
        console.log(`
X ~ H(N=${N}, M=${M}, n=${n})

| X |${X}
${'-'.repeat(`| X |${X}`.length)}
| P |${P}`)
        rl.close();
      })
    })
  })
})()