hw5.1.js

// Array.sort(byVolume)
function byVolume (a, b) {
  va = a[0] + a[1] + a[2]
  vb = b[0] + b[1] + b[2]
  if (va > vb)
    return -1
  else if (vb > va)
    return 1
  return 0
}

// Answer the question
function maxNestedBoxes (boxes) {
  var size = boxes.length
    , i    = size - 1
    , memo = []

  memo[size] = 0

  function nextFeasible (i) {
    var box = boxes[i]
    for (; i < size; i++) {
      if (box[0] > boxes[i][0]
          && box[1] > boxes[i][1]
          && box[2] > boxes[i][2]) {
        return i
      }
    }
    return i
  }

  for(; i >= 0; i--) {
    memo[i] = Math.max(1 + memo[nextFeasible(i)],
                       memo[i + 1])
  }

  return memo
}

var test = [ [ 6, 6, 6 ], [ 1, 2, 3 ], [ 1, 1, 1 ] ]

test.sort(byVolume)

console.log(maxNestedBoxes(test))

var test2 = [ [ 3, 4, 1 ], [ 2, 2, 2 ], [ 2, 1, 1 ], [ 3, 3, 3 ] ]

test2.sort(byVolume)

console.log(maxNestedBoxes(test2))

var test3 = [ [ 7, 7, 7 ], [ 1, 1, 1 ], [ 1, 2, 3 ], [ 2, 3, 4 ], [ 3, 4, 5 ] ]

test3.sort(byVolume)

console.log(maxNestedBoxes(test3))