hw5.2.js

var T = [
  [ 1, 2, 3 ],
  [ 2, 2, 2 ],
  [ 3, 2, 1 ]
]

var symbols = [ 1, 2, 3 ]

function translateToProduct (k, i, ps) {
  // i says where to start partitioning
  // k says how many partitions
  var a = 0, b = 1, c = 2, d = 4
    , ab = k
  while (ab > 0) {
    if ( i % 2 == 1 ) {
      T [a] [ T [b] [c] ]
      T [ T [a] [b] ] [c]
    } else {
      T [ T [a] [b] ] [ T [c] [d] ]
      T [ T [a] [ T [b] [c] ] ] [d]
      T [a] [ T [ T [b] [c] ] [d] ]
    }
  }
  return t_pos
}

function canMakeProduct (ps, t) {
  var n     = ps.length
    , k_max = n / 2
    , memo  = []
    , i, k

  memo[n] = []
  for (i = 0; i < n; i ++) {
    memo[n].push(0)
    memo[i] = [ 0 ]
  }

  for (i = n - 1; i >= 0; i--) {
    for (k = 0; k < n; k ++) {
      var t_pos = translateToProduct(k, i, ps)
      if (t_pos == t) {
        memo[i][k] = 1
      } else {
        memo[i][k] = (memo[i + 1][k] || memo[i][k - 1]) ? 1 : 0
      }
    }
  }

  console.log(memo)

  return memo[0][n - 1]
}

canMakeProduct([ 1, 2, 3 ], 3)