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CC150 9.10
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/* CC150 9.10 */ | |
// stack of boxes | |
#include <iostream> | |
#include <vector> | |
using namespace std; | |
class Box { | |
public: | |
Box() : width(0), height(0), depth(0) {} | |
Box(int w, int h, int d) : width(w), height(h), depth(d) {} | |
int getWidth() { return width; } | |
int getHeight() { return height; } | |
int getDepth() { return depth; } | |
bool isSmallerThan(Box box2) { // strictly smaller | |
return width < box2.getWidth() && height < box2.getHeight() && depth < box2.getDepth(); | |
} | |
private: | |
int width, height, depth; | |
}; | |
// Recursion (DP) | |
int maxHeight(vector<Box> boxes, int index, vector<int> &heights) // find tallest stack with bottom 'index' | |
{ | |
if (index != -1 && heights[index] != 0) | |
return heights[index]; | |
int hmax = 0; | |
for (int i = 0; i != boxes.size(); ++i) { | |
if (index == -1 || boxes[i].isSmallerThan(boxes[index])) { // box i can be placed here | |
int h = maxHeight(boxes, i, heights); | |
if (h > hmax) hmax = h; | |
} | |
} | |
if (index == -1) // no bottom box, return hmax directly | |
return hmax; | |
else { // bottom box is index, add its heights to hmax | |
heights[index] = hmax + boxes[index].getHeight(); | |
return heights[index]; | |
} | |
} | |
int maxHeight(vector<Box> boxes) | |
{ | |
if (boxes.empty()) | |
return 0; | |
vector<int> heights(boxes.size(), 0); | |
return maxHeight(boxes, -1, heights); // index = -1 indicating no box is placed as bottom yet | |
} | |
int main() | |
{ | |
int n; | |
cout << "Number of boxes: "; | |
cin >> n; | |
vector<Box> boxes; | |
int width, height, depth; | |
cout << "Widths, heights, and depths of the boxes: " << endl; | |
for (int i = 0; i != n; ++i) { | |
cin >> width >> height >> depth; | |
boxes.push_back(Box(width, height, depth)); | |
} | |
cout << "Height of the tallest stack: " << maxHeight(boxes) << endl; | |
return 0; | |
} |
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