knapsack updated

Author: zarif98sjs

Dynamic Programming/15 0-1 Knapsack.cpp

@@ -1,15 +1,21 @@
 
 /**
 
-Problem : 0-1 Knapsack
+F(i,W) = max( include ith item , exclude ith item )
 
-In 0-1 Knapsack problem, we are given a set of items, each with a weight and a value and
-we need to determine the number of each item to include in a collection so that
-the total weight is less than or equal to a given limit and the total value is as large as possible.
+Here ,
+include ith item = F(i+1,W+w[i]) + v[i]
+exclude ith item = F(i+1,W)
+
+Base case:
+
+F(i,W>MAX_WEIGHT)     = INT_MIN
+F(i>n,W<=MAX_WIGHT)   = 0
+F(i>n,W>MAX_WIGHT)    = INT_MIN
 
 **/
 
-/**Which of the favors of your Lord will you deny ?**/
+/** Which of the favors of your Lord will you deny ? **/
 
 #include<bits/stdc++.h>
 using namespace std;
@@ -20,116 +26,152 @@ using namespace std;
 #define MP make_pair
 #define F first
 #define S second
-#define INF INT_MAX
 
 #define ALL(x) (x).begin(), (x).end()
 #define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
+#define READ        freopen("alu.txt", "r", stdin)
+#define WRITE       freopen("vorta.txt", "w", stdout)
 
 #include <ext/pb_ds/assoc_container.hpp>
 #include <ext/pb_ds/tree_policy.hpp>
 using namespace __gnu_pbds;
 
-template<class TIn>
-using indexed_set = tree<
-                    TIn, null_type, less<TIn>,
-                    rb_tree_tag, tree_order_statistics_node_update>;
+template<class TIn>using indexed_set = tree<TIn, null_type, less<TIn>,rb_tree_tag, tree_order_statistics_node_update>;
+
+/**
 
-/*
 PBDS
 -------------------------------------------------
 1) insert(value)
 2) erase(value)
 3) order_of_key(value) // 0 based indexing
 4) *find_by_order(position) // 0 based indexing
 
-*/
+**/
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p);
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v);
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v);
 
 inline void optimizeIO()
 {
     ios_base::sync_with_stdio(false);
     cin.tie(NULL);
 }
 
-const int nmax = 100+7;
+const int nmax = 1e2+7;
+const int nmax2 = 1e5+7;
 const LL LINF = 1e17;
 
-string to_str(LL x)
+template <class T>
+string to_str(T x)
 {
     stringstream ss;
     ss<<x;
     return ss.str();
 }
 
-//bool cmp(const PII &A,const PII &B)
-//{
-//
-//}
-
-vector<int> vara = { -1, 20, 5, 10, 40, 15, 25 };
-vector<int> wara = { -1, 1, 2,  3,  8,  7, 4 };
-int max_cap = 10;
+int n,MAX_WEIGHT;
 
-/** 1 based indexing **/
+LL w[nmax];
+LL v[nmax];
+LL dp[nmax][nmax2];
 
-/**
-
-dp[i][j] = max(include the item , exclude the item)
-
-**/
-
-int dp[nmax][nmax];
-
-int solve(int i,int w)
+LL solve(int pos,int W) /** maximum value to get using maximum weight W **/
 {
-    if(w<0) return INT_MIN; /** **/
-
-    if(i==0 || w==0) return 0;
+    if(W>MAX_WEIGHT) return INT_MIN; /** if anytime W>MAX_HEIGHT , not possible . This is used just to avoid RTE **/
 
-    int &ret = dp[i][w];
+    if(pos>n) /** Done with n items and now check condition **/
+    {
+        return W<=MAX_WEIGHT ? 0 : INT_MIN;
+    }
 
+    LL &ret = dp[pos][W];
     if(ret!=-1) return ret;
 
-    int inc = vara[i] + solve(i-1,w-wara[i]);
-    int exc = solve(i-1,w);
+    LL inc = solve(pos+1,W+w[pos]) + v[pos];
+    LL exc = solve(pos+1,W);
 
     return ret = max(inc,exc);
 }
 
-string solve_print(int i,int w)
+string solve_print(int pos,int W)
 {
-    if(w<0) return ""; /** **/
+    if(W>MAX_WEIGHT) return "";
+    if(pos>n) return "";
 
-    if(i==0 || w==0) return "";
+    LL inc = solve(pos+1,W+w[pos]) + v[pos];
+    LL exc = solve(pos+1,W);
 
-    int inc = vara[i] + dp[i-1][w-wara[i]];
-    int exc = dp[i-1][w];
-
-    if(inc>exc)
-        return to_str(vara[i]) + " " + solve_print(i-1,w-wara[i]);
-    else
-        return solve_print(i-1,w);
+    if(inc>exc) return to_str(v[pos]) + " " + solve_print(pos+1,W+w[pos]);
+    else return solve_print(pos+1,W);
 }
 
-
 int main()
 {
     optimizeIO();
 
-    memset(dp,-1,sizeof dp);
+    cin>>n>>MAX_WEIGHT;
 
-    int n = vara.size()-1;
+    for(int i=1;i<=n;i++)
+        cin>>w[i]>>v[i];
 
-    cout<<solve(n,max_cap)<<endl;
-    cout<<solve_print(n,max_cap)<<endl;
+    memset(dp,-1,sizeof dp);
 
-//    for(int i=1; i<=n; i++)
-//    {
-//        for(int j=1; j<=max_cap; j++)
-//            cout<<dp[i][j]<<" ";
-//        cout<<endl;
-//    }
+    cout<<solve(0,0)<<endl;
+    cout<<solve_print(0,0)<<endl;
 
     return 0;
 }
 
+/**
+
+**/
+
+template<class T1, class T2>
+ostream &operator <<(ostream &os, pair<T1,T2>&p)
+{
+    os<<"{"<<p.first<<", "<<p.second<<"} ";
+    return os;
+}
+template <class T>
+ostream &operator <<(ostream &os, vector<T>&v)
+{
+    os<<"[ ";
+    for(int i=0; i<v.size(); i++)
+    {
+        os<<v[i]<<" " ;
+    }
+    os<<" ]";
+    return os;
+}
+
+template <class T>
+ostream &operator <<(ostream &os, set<T>&v)
+{
+    os<<"[ ";
+    for(T i:v)
+    {
+        os<<i<<" ";
+    }
+    os<<" ]";
+    return os;
+}
 
+//string solve_print(int i,int w)
+//{
+//    if(w<0) return ""; /** **/
+//
+//    if(i==0 || w==0) return "";
+//
+//    int inc = vara[i] + dp[i-1][w-wara[i]];
+//    int exc = dp[i-1][w];
+//
+//    if(inc>exc)
+//        return to_str(vara[i]) + " " + solve_print(i-1,w-wara[i]);
+//    else
+//        return solve_print(i-1,w);
+//}