/src/main/java/org/rajivprab/sandbox/cuboid_stacking/CuboidStacking.java

package org.rajivprab.sandbox.cuboid_stacking;

import com.google.common.collect.Lists;

import java.util.*;
import java.util.stream.Collectors;

/**
 * https://leetcode.com/problems/maximum-height-by-stacking-cuboids/
 *
 * Given n cuboids where the dimensions of the ith cuboid is cuboids[i] = [widthi, lengthi, heighti] (0-indexed).
 * Choose a subset of cuboids and place them on each other.
 *
 * You can place cuboid i on cuboid j if widthi <= widthj and lengthi <= lengthj and heighti <= heightj. You can
 * rearrange any cuboid's dimensions by rotating it to put it on another cuboid.
 *
 * Return the maximum height of the stacked cuboids.
 *
 * ---------------------
 *
 * Solution used:
 * https://leetcode.com/problems/maximum-height-by-stacking-cuboids/discuss/970293/JavaC%2B%2BPython-DP-Prove-with-Explanation
 */
class CuboidStacking {
    static int getMaxHeight(List<List<Integer>> cuboids) {
        List<Cuboid> sortedCuboids = cuboids.stream().map(Cuboid::getOrientedCuboid).collect(Collectors.toList());
        Collections.sort(sortedCuboids, Comparator.comparingInt(o -> o.height));
        return getMaxHeightSorted(sortedCuboids);
    }

    private static int getMaxHeightSorted(List<Cuboid> cuboids) {
        int[] maxHeightWhenUsedAsBase = new int[cuboids.size()];
        for (int baseIndex=0; baseIndex<cuboids.size(); baseIndex++) {
            Cuboid base = cuboids.get(baseIndex);
            maxHeightWhenUsedAsBase[baseIndex] = base.height;
            for (int secondIndex=0; secondIndex<baseIndex; secondIndex++) {
                Cuboid second = cuboids.get(secondIndex);
                if (second.canStackOnTopOf(base)) {
                    int height = base.height + maxHeightWhenUsedAsBase[secondIndex];
                    maxHeightWhenUsedAsBase[baseIndex] = Math.max(maxHeightWhenUsedAsBase[baseIndex], height);
                }
            }
        }
        return Arrays.stream(maxHeightWhenUsedAsBase).max().getAsInt();
    }
}