Maximum height by stacking Cuboids

Box stacking problem max height of stack possible (can be rotated). All the dimensions of the box beneath should be greater than the one stacked above it.

Javascript

const maxHeight = (cuboids) => {
  // Sort each cuboid dimensions.
  for (const cuboid of cuboids) {
    cuboid.sort((a, b) => a - b);
  }
  
  // Sort the cuboids from largest to smallest order.
  cuboids.sort((a, b) => {
    if (a[0] != b[0]) {
      return b[0] - a[0];
    }
    if (a[1] != b[1]) {
      return b[1] - a[1];
    }
    return b[2] - a[2];
  });
  
  // dp[i] means max height upto cuboid 'i' (row i).
  const dp = Array(cuboids.length);
  
  for (let i = 0; i < cuboids.length; i++) {
    // We choose the largest side of cuboid to be height to maximize it.
    dp[i] = cuboids[i][2];
    for (let j = 0; j < i; j++) {
      if (cuboids[j][0] >= cuboids[i][0] && cuboids[j][1] >= cuboids[i][1] && cuboids[j][2] >= cuboids[i][2]) {
        dp[i] = Math.max(dp[i], dp[j] + cuboids[i][2]);
      }
    }
  }
  
  return Math.max(...dp);
}

console.log(maxHeight([
  [1, 1, 1 ],
  [2, 3, 10],
  [2, 4, 1 ],
]));
// 15

Demo