Create Box Stacking Problem.cpp

algorithms/dynamic-programming/Box Stacking Problem.cpp

@@ -0,0 +1,54 @@
+#include<bits/stdc++.h>
+using namespace std;
+bool canPlaceBoxes(vector<int>b1,vector<int>b2){
+    if(b1[0]>b2[0]&&b1[1]>b2[1]&&b1[2]>b2[2])
+        return true;
+    return false;
+}
+bool BoxCompare(vector<int>b1, vector<int>b2){
+    return b1[2]>b2[2];
+}
+int box_stacking(vector<vector<int>>&boxes){
+    //sorting the boxes based on their heights
+    //creating a custom compare function 
+    sort(boxes.begin(),boxes.end(),BoxCompare);
+    int n=boxes.size();
+    vector<int>dp(n+1,0);
+    //filling dp array with the heights
+    for(int i=0;i<n;i++){
+        dp[i]=boxes[i][2];
+    }
+    //bottom up approach
+    for(int i=0;i<n;i++){
+        for(int j=0;j<i;j++){
+            //canPlaceBoxes function checks whether h`<h , w`<w and d`<d
+            if(canPlaceBoxes(boxes[j],boxes[i])){
+                int current_height=boxes[i][2];
+                //taking jth box as the bottom, checking whether the height is maximum
+                //if this is true we stack the previous max height boxes over this
+                // this is the step where we need to use the previous results to get the current result
+                if(dp[j]+current_height>dp[i]){
+                    dp[i]=dp[j]+current_height;
+                }
+            }
+        }
+    }
+    int max_height=INT_MIN;
+    for(int i=0;i<n;i++){
+        max_height=max(max_height,dp[i]);
+    }
+    return max_height;
+}
+int main(){
+    vector<vector<int>> boxes={
+        {2,1,2},
+        {3,2,3},
+        {2,2,8},
+        {2,3,4},
+        {2,2,1},
+        {4,4,5},
+    };
+    //ans should be 10
+    int height=box_stacking(boxes);
+    cout<<"Max Height"<<" "<<height<<endl;
+}