Box Stacking Problem

C++/Leetcode/boxstackingproblem.cpp

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+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+
+// Data structure to store a box (L × W × H)
+struct Box
+{
+    // enforce constraint: width is never more than length
+    int length, width, height;
+};
+
+// Function to generate rotations of all the boxes
+vector<Box> createAllRotations(vector<Box> const &boxes)
+{
+    // stores all rotations of each box
+    vector<Box> rotations;
+
+    // do for each box
+    for (const Box &box: boxes)
+    {
+        // push the original box: L × W × H
+        rotations.push_back(box);
+
+        // push the first rotation: max(L, H) × min(L, H) × W
+        rotations.push_back({ max(box.length, box.height),
+                        min(box.length, box.height),
+                        box.width });
+
+        // push the second rotation: max(W, H) × min(W, H) × L
+        rotations.push_back({ max(box.width, box.height),
+                        min(box.width, box.height),
+                        box.length });
+    }
+
+    return rotations;
+}
+
+// Create a stack of boxes that is as tall as possible
+int findMaxHeight(vector<Box> const &boxes)
+{
+    // generate rotations of each box
+    vector<Box> rotations = createAllRotations(boxes);
+
+    // sort the boxes in descending order of base area (L × W)
+    sort(rotations.begin(),
+        rotations.end(),
+        [](const Box &x, const Box &y) {
+            return x.length * x.width > y.length * y.width;
+        });
+
+    // `max_height[i]` stores the maximum possible height when the i'th box
+    // is on the top
+    vector<int> max_height(rotations.size());
+
+    // fill `max_height[]` in a bottom-up manner
+    for (int i = 0; i < rotations.size(); i++)
+    {
+        for (int j = 0; j < i; j++)
+        {
+            // dimensions of the lower box are each strictly larger than those
+            // of the higher box
+            if (rotations[i].length < rotations[j].length &&
+                    rotations[i].width < rotations[j].width) {
+                max_height[i] = max(max_height[i], max_height[j]);
+            }
+        }
+
+        max_height[i] += rotations[i].height;
+    }
+
+    // return the maximum value in `max_height[]`
+    return *max_element(max_height.begin(), max_height.end());
+}
+
+int main()
+{
+    // input boxes
+    vector<Box> boxes {
+        { 4, 2, 5 },
+        { 3, 1, 6 },
+        { 3, 2, 1 },
+        { 6, 3, 8 }
+    };
+
+    cout << "The maximum height is " << findMaxHeight(boxes);
+
+    return 0;
+}