Merge pull request #610 from jashanwarraich/patch-3

Create 0-1Knapsack.cpp

Author: gantavyamalviya

Dynamic Programming/0-1Knapsack.cpp

@@ -0,0 +1,128 @@
+// Q173 https://www.codingninjas.com/codestudio/problems/1072980?topList=striver-sde-sheet-problems&utm_source=striver&utm_medium=website&leftPanelTab=0
+
+
+
+
+// Recursion
+// Time: O(2^n)
+// Space: O(n) 
+#include<bits/stdc++.h>
+int ks(vector<int> &val, vector<int> &wt, int ind, int W){
+    if(ind==0) {
+        if(wt[0]<=W) return val[0];
+        return 0;
+    }
+    int nt=ks(val,wt,ind-1,W);
+    int t=INT_MIN;
+    if(wt[ind]<=W)
+        t=val[ind]+ks(val,wt,ind-1,W-wt[ind]);
+    return max(t,nt);
+}
+
+int maxProfit(vector<int> &val, vector<int> &wt, int n, int W)
+{
+    return ks(val,wt,n-1,W);
+}
+
+
+// Memorisation
+// Time: O(N*m)
+// Space: O(N*M)+O(N) = auxiliary stack space+ dp
+#include<bits/stdc++.h>
+int ks(vector<int> &val, vector<int> &wt, int ind, int W,vector<vector<int>> &dp){
+    if(ind==0) {
+        if(wt[0]<=W) return val[0];
+        return 0;
+    }
+    if(dp[ind][W]!=-1) return dp[ind][W];
+    int nt=ks(val,wt,ind-1,W,dp);
+    int t=INT_MIN;
+    if(wt[ind]<=W)
+        t=val[ind]+ks(val,wt,ind-1,W-wt[ind],dp);
+    return dp[ind][W]=max(t,nt);
+}
+
+int maxProfit(vector<int> &val, vector<int> &wt, int n, int W)
+{    vector<vector<int>> dp(n,vector<int>(W+1,-1));
+    return ks(val,wt,n-1,W,dp);
+}
+
+
+
+
+
+// DP
+// Time: O(N*m)
+// Space: O(N*M)
+#include<bits/stdc++.h>
+int maxProfit(vector<int> &val, vector<int> &wt, int n, int W)
+{    vector<vector<int>> dp(n,vector<int>(W+1,0));
+    for(int cw=0;cw<W+1;cw++) dp[0][cw]=val[0];
+     for(int ind=1;ind<n;ind++){
+         for(int cw=0;cw<=W;cw++){
+             int nt=dp[ind-1][cw];   
+             int t=INT_MIN;
+             if(wt[ind]<=cw)
+                 t=val[ind]+dp[ind-1][cw-wt[ind]];
+             dp[ind][cw]=max(t,nt);
+         }
+         
+     }
+//      for(int ind=0;ind<n;ind++){
+//          for(int cw=0;cw<=W;cw++){
+//              cout<<dp[ind][cw]<<" ";
+//          }
+//          cout<<endl;
+//      }
+ 
+     return dp[n-1][W];
+ 
+}
+
+// TABULATION
+// Time: O(N*m)
+// Space: O(2*M)
+#include<bits/stdc++.h>
+int maxProfit(vector<int> &val, vector<int> &wt, int n, int W){
+    vector<int> p(W+1,0);
+    vector<int> c(W+1,0);
+    for(int cw=wt[0];cw<W+1;cw++) p[cw]=val[0];
+     for(int ind=1;ind<n;ind++){
+         for(int cw=0;cw<=W;cw++){
+             int nt=p[cw];   
+             int t=INT_MIN;
+             if(wt[ind]<=cw)
+                 t=val[ind]+p[cw-wt[ind]];
+             c[cw]=max(t,nt);
+         }
+         p=c;
+         
+     }
+     return p[W];
+ 
+}
+
+
+
+// SINGLE ARRAY TABULATION
+// Time: O(N*m)
+// Space: O(M)
+#include<bits/stdc++.h>
+int maxProfit(vector<int> &val, vector<int> &wt, int n, int W){
+    vector<int> p(W+1,0);
+//     vector<int> c(W+1,0);
+    for(int cw=wt[0];cw<W+1;cw++) p[cw]=val[0];
+     for(int ind=1;ind<n;ind++){
+         for(int cw=W;cw>=0;cw--){
+             int nt=p[cw];   
+             int t=INT_MIN;
+             if(wt[ind]<=cw)
+                 t=val[ind]+p[cw-wt[ind]];
+             p[cw]=max(t,nt);
+         }
+//          p=c;
+         
+     }
+     return p[W];
+ 
+}