Merge pull request #101 from sourav-naskar/main

added Rod Cutting DP problem

Author: gantavyamalviya

Dynamic Programming/Rod-Cutting.cpp

@@ -0,0 +1,76 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int cutRodUtil(vector<int>& price, int ind, int N, vector<vector<int>>& dp){
+
+    if(ind == 0){
+        return N*price[0];
+    }
+    
+    if(dp[ind][N]!=-1)
+        return dp[ind][N];
+        
+    int notTaken = 0 + cutRodUtil(price,ind-1,N,dp);
+    
+    int taken = INT_MIN;
+    int rodLength = ind+1;
+    if(rodLength <= N)
+        taken = price[ind] + cutRodUtil(price,ind,N-rodLength,dp);
+        
+    return dp[ind][N] = max(notTaken,taken);
+}
+
+
+int cutRod(vector<int>& price,int N) {
+
+    vector<int> cur (N+1,0);
+    
+    for(int i=0; i<=N; i++){
+        cur[i] = i*price[0];
+    }
+    
+    for(int ind=1; ind<N; ind++){
+        for(int length =0; length<=N; length++){
+        
+             int notTaken = 0 + cur[length];
+    
+             int taken = INT_MIN;
+             int rodLength = ind+1;
+             if(rodLength <= length)
+                taken = price[ind] + cur[length-rodLength];
+        
+             cur[length] = max(notTaken,taken);   
+        }
+    }
+    
+    return cur[N];
+}
+
+
+
+int main() {
+
+  vector<int> price = {2,5,7,8,10};
+  
+  int n = price.size();
+                                 
+  cout<<"The Maximum price generated is "<<cutRod(price,n);
+}
+
+/*
+Output:
+
+The Maximum price generated is 12
+
+Time Complexity: O(N*N)
+
+Reason: There are two nested loops.
+
+Space Complexity: O(N)
+
+Reason: We are using an external array of size ‘N+1’ to store only one row.
+
+*/
+
+// contributed by Sourav Naskar