g1601_1700.s1691_maximum_height_by_stacking_cuboids.Solution Maven / Gradle / Ivy

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package g1601_1700.s1691_maximum_height_by_stacking_cuboids;

// #Hard #Array #Dynamic_Programming #Sorting #2022_04_15_Time_6_ms_(83.07%)_Space_42_MB_(80.25%)

import java.util.Arrays;

/**
 * 1691 - Maximum Height by Stacking Cuboids\.
 *
 * Hard
 *
 * Given `n` `cuboids` where the dimensions of the i^th cuboid is cuboids[i] = [width_i, length_i, height_i] ( **0-indexed** ). Choose a **subset** of `cuboids` and place them on each other.
 *
 * You can place cuboid `i` on cuboid `j` if width_i <= width_j and length_i <= length_j and height_i <= height_j. You can rearrange any cuboid's dimensions by rotating it to put it on another cuboid.
 *
 * Return _the **maximum height** of the stacked_ `cuboids`.
 *
 * **Example 1:**
 *
 * **![](https://assets.leetcode.com/uploads/2019/10/21/image.jpg)**
 *
 * **Input:** cuboids = \[\[50,45,20],[95,37,53],[45,23,12]]
 *
 * **Output:** 190
 *
 * **Explanation:**
 *
 * Cuboid 1 is placed on the bottom with the 53x37 side facing down with height 95.
 *
 * Cuboid 0 is placed next with the 45x20 side facing down with height 50.
 *
 * Cuboid 2 is placed next with the 23x12 side facing down with height 45.
 *
 * The total height is 95 + 50 + 45 = 190.
 *
 * **Example 2:**
 *
 * **Input:** cuboids = \[\[38,25,45],[76,35,3]]
 *
 * **Output:** 76
 *
 * **Explanation:**
 *
 * You can't place any of the cuboids on the other.
 *
 * We choose cuboid 1 and rotate it so that the 35x3 side is facing down and its height is 76.
 *
 * **Example 3:**
 *
 * **Input:** cuboids = \[\[7,11,17],[7,17,11],[11,7,17],[11,17,7],[17,7,11],[17,11,7]]
 *
 * **Output:** 102
 *
 * **Explanation:**
 *
 * After rearranging the cuboids, you can see that all cuboids have the same dimension.
 *
 * You can place the 11x7 side down on all cuboids so their heights are 17.
 *
 * The maximum height of stacked cuboids is 6 \* 17 = 102.
 *
 * **Constraints:**
 *
 * *   `n == cuboids.length`
 * *   `1 <= n <= 100`
 * *   1 <= width_i, length_i, height_i <= 100
**/
public class Solution {
    public int maxHeight(int[][] arr) {
        for (int[] a : arr) {
            Arrays.sort(a);
        }
        Arrays.sort(
                arr,
                (a, b) -> {
                    if (a[0] != b[0]) {
                        return a[0] - b[0];
                    } else if (a[1] != b[1]) {
                        return a[1] - b[1];
                    }
                    return a[2] - b[2];
                });
        int ans = 0;
        int[] dp = new int[arr.length];
        for (int i = 0; i < arr.length; i++) {
            dp[i] = arr[i][2];
            for (int j = 0; j < i; j++) {
                if (arr[i][0] >= arr[j][0] && arr[i][1] >= arr[j][1] && arr[i][2] >= arr[j][2]) {
                    dp[i] = Math.max(dp[i], arr[i][2] + dp[j]);
                }
            }
            ans = Math.max(ans, dp[i]);
        }
        return ans;
    }
}