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Dynamic Programming/DP over Subsets/subsetpartition.cpp

@@ -0,0 +1,83 @@
+#include <iostream>
+#include <cstdio>
+#include <cstdlib>
+#include <algorithm>
+#include <cmath>
+#include <vector>
+#include <list>
+#include <set>
+#include <map>
+#include <unordered_set>
+#include <unordered_map>
+#include <queue>
+#include <ctime>
+#include <cassert>
+#include <complex>
+#include <stack>
+#include <string>
+#include <cstring>
+#include <chrono>
+#include <random>
+#include <bitset>
+#include <sstream>
+#include <iomanip>
+using namespace std;
+
+
+#define int int64_t
+#define vi vector<int>
+#define vb vector<bool>
+#define vbb vector< vector<bool> >
+#define all(x) (x).begin(), (x).end()
+#define vii vector< vector<int> >
+#define ff first
+#define ss second
+#define pii pair<int64_t, int64_t>
+#define mp make_pair
+#define pb push_back
+#define f(i,n) for(i=0;i<n;i++)
+#define pqb priority_queue<int>
+#define pqs priority_queue<int,vi,greater<int> >
+#define setbits(x)  __builtin_popcountll(x)
+#define zrobits(x)  __builtin_ctzll(x)
+#define mod 1000000007
+#define inf 1e18
+#define ps(x,y) fixed<<setprecision(y)<<x
+#define mk(arr,n,type)  type *arr=new type[n];
+#define w(x) int x; cin>>x; while(x--)
+#define FIO  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
+mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
+
+
+int32_t main()
+{
+    int i, n, j, k, l, t;
+    cin >> n;
+    vi v(n);
+    f(i,n) cin >> v[i];
+    l=0;
+    f(i,n) l += v[i];
+
+    // cout << l;
+    if(l&1) 
+    {
+        cout << -1;
+        return 0;
+    }
+    l/=2;
+
+    vbb dp(n+1, vb(l+1,false));
+    f(i,n+1) dp[i][0] = true;
+    for(i=1;i<=n;i++)
+    {
+        for(j=1;j<=l;j++)
+        {
+            // if(i==0) dp[i][]
+            if(j >= v[i-1]) dp[i][j] = dp[i-1][j-v[i-1]] + dp[i-1][j];
+            else dp[i][j] = dp[i-1][j];
+        }
+    }
+
+    if(dp[n][l]) cout << "Possible";
+    else cout << "Not Possible";
+}

Dynamic Programming/Recursion and DAC/Printlcs.cpp

@@ -0,0 +1,95 @@
+#include <iostream>
+#include <cstdio>
+#include <cstdlib>
+#include <algorithm>
+#include <cmath>
+#include <vector>
+#include <list>
+#include <set>
+#include <map>
+#include <unordered_set>
+#include <unordered_map>
+#include <queue>
+#include <ctime>
+#include <cassert>
+#include <complex>
+#include <stack>
+#include <string>
+#include <cstring>
+#include <chrono>
+#include <random>
+#include <bitset>
+#include <sstream>
+#include <iomanip>
+using namespace std;
+
+
+#define int int64_t
+#define vi vector<int>
+#define vb vector<bool>
+#define vbb vector< vector<bool> >
+#define all(x) (x).begin(), (x).end()
+#define vii vector< vector<int> >
+#define ff first
+#define ss second
+#define pii pair<int64_t, int64_t>
+#define mp make_pair
+#define pb push_back
+#define f(i,n) for(i=0;i<n;i++)
+#define pqb priority_queue<int>
+#define pqs priority_queue<int,vi,greater<int> >
+#define setbits(x)  __builtin_popcountll(x)
+#define zrobits(x)  __builtin_ctzll(x)
+#define mod 1000000007
+#define inf 1e18
+#define ps(x,y) fixed<<setprecision(y)<<x
+#define mk(arr,n,type)  type *arr=new type[n];
+#define w(x) int x; cin>>x; while(x--)
+#define FIO  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
+mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
+
+int32_t main()
+{
+    FIO;
+    int i, m, n, j, k, l, t;
+    string s1, s2;
+    cin >> s1 >> s2;
+    n = s1.length();
+    m = s2.length();
+    vii dp(n+1, vi(m+1,0));
+    for(i=1;i<=n;i++)
+    {
+        for(j=1;j<=m;j++)
+        {
+            if(s1[i-1]==s2[j-1]) 
+                dp[i][j] = dp[i-1][j-1]+1;
+            else
+                dp[i][j] = max(dp[i-1][j], dp[i][j-1]);
+        }
+    }
+
+    f(i,n+1)
+    {
+        f(j,m+1) cout << dp[i][j] << " ";
+        cout << endl;
+    }
+    i=n, j=m;
+    stack<char> s;
+
+    while(i and j)
+    {
+        if(s1[i-1]==s2[j-1]) 
+        {
+            s.push(s1[i-1]);
+            i--,j--;
+        }
+        else if(dp[i-1][j] > dp[i][j-1]) i--;
+        else j--; 
+    }
+
+    while(!s.empty())
+    {
+        cout << s.top();
+        s.pop();
+    }
+}

Dynamic Programming/Recursion and DAC/knapsackDown.cpp

@@ -0,0 +1,101 @@
+#include <iostream>
+#include <cstdio>
+#include <cstdlib>
+#include <algorithm>
+#include <cmath>
+#include <vector>
+#include <list>
+#include <set>
+#include <map>
+#include <unordered_set>
+#include <unordered_map>
+#include <queue>
+#include <ctime>
+#include <cassert>
+#include <complex>
+#include <stack>
+#include <string>
+#include <cstring>
+#include <chrono>
+#include <random>
+#include <bitset>
+#include <sstream>
+#include <iomanip>
+using namespace std;
+
+
+#define int int64_t
+#define vi vector<int>
+#define all(x) (x).begin(), (x).end()
+#define vii vector< vector<int> >
+#define ff first
+#define ss second
+#define pii pair<int64_t, int64_t>
+#define mp make_pair
+#define pb push_back
+#define f(i,n) for(i=0;i<n;i++)
+#define pqb priority_queue<int>
+#define pqs priority_queue<int,vi,greater<int> >
+#define setbits(x)  __builtin_popcountll(x)
+#define zrobits(x)  __builtin_ctzll(x)
+#define mod 1000000007
+#define inf 1e18
+#define ps(x,y) fixed<<setprecision(y)<<x
+#define mk(arr,n,type)  type *arr=new type[n];
+#define w(x) int x; cin>>x; while(x--)
+#define FIO  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
+mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
+
+int32_t main()
+{
+    int n, W, i, j; cin >> n >> W;
+    vi val(n), wt(n);
+    f(i,n) cin >> val[i];
+    f(i,n) cin >> wt[i];
+
+//    int i, j;
+     vector<int> dp(W+1,0), cur_dp(W+1,0);
+
+
+    bool k=true;
+    for(i=1;i<n+1;i++)
+    {
+        for(j=W;j>=0;j--)
+        {
+            if(k)
+            {
+                if(wt[i-1]<j)
+                    cur_dp[j] = max(cur_dp[j-1], dp[j-wt[i-1]]+val[i-1]); 
+
+                else cur_dp[j] = cur_dp[j-1];
+
+            }
+
+            else
+            {
+                if(wt[i-1]<j)
+                    dp[j] = max(dp[j-1], cur_dp[j-wt[i-1]]+val[i-1]); 
+
+                else dp[j] = dp[j-1];
+
+            }
+        }
+
+        k^=1;
+    }
+
+     if(k) 
+    {
+        int temp=INT_MIN;
+        for(i=0;i<W+1;i++) temp = max(temp, dp[i]);
+        cout <<  temp;
+    }
+    else 
+    {int temp=INT_MIN;
+        for(i=0;i<W+1;i++) temp = max(temp, cur_dp[i]);
+
+        cout <<  temp;
+
+    }
+
+}

Dynamic Programming/Recursion and DAC/knapsackUp.cpp

@@ -0,0 +1,77 @@
+#include <iostream>
+#include <cstdio>
+#include <cstdlib>
+#include <algorithm>
+#include <cmath>
+#include <vector>
+#include <list>
+#include <set>
+#include <map>
+#include <unordered_set>
+#include <unordered_map>
+#include <queue>
+#include <ctime>
+#include <cassert>
+#include <complex>
+#include <stack>
+#include <string>
+#include <cstring>
+#include <chrono>
+#include <random>
+#include <bitset>
+#include <sstream>
+#include <iomanip>
+using namespace std;
+
+
+#define int int64_t
+#define vi vector<int>
+#define all(x) (x).begin(), (x).end()
+#define vii vector< vector<int> >
+#define ff first
+#define ss second
+#define pii pair<int64_t, int64_t>
+#define mp make_pair
+#define pb push_back
+#define f(i,n) for(i=0;i<n;i++)
+#define pqb priority_queue<int>
+#define pqs priority_queue<int,vi,greater<int> >
+#define setbits(x)  __builtin_popcountll(x)
+#define zrobits(x)  __builtin_ctzll(x)
+#define mod 1000000007
+#define inf 1e18
+#define ps(x,y) fixed<<setprecision(y)<<x
+#define mk(arr,n,type)  type *arr=new type[n];
+#define w(x) int x; cin>>x; while(x--)
+#define FIO  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
+mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
+
+// int dp[1000][1000]={-1};
+vii dp(1000,vi(1000, -1));
+int ans(const vector<pii> v, int n, int w)
+{
+    if(n==0 or w==0) return 0;
+    if(dp[n][w]!=-1) return dp[n][w];
+    else
+    {
+        if(n >= v[n-1].ff)
+            dp[n][w] = max(ans(v,n-1,w), ans(v, n-1, w - v[n-1].ff)+v[n-1].ss);
+
+        else
+            dp[n][w] = ans(v,n-1,w);
+
+        return dp[n][w];
+    }
+
+}
+
+
+int32_t main()
+{
+    int i, n, j, w, k, l, t;
+    cin >> n >> w;
+    vector<pii> v(n);
+    f(i,n) cin >> v[i].ff >> v[i].ss ;
+    cout << ans(v, n, w);
+
+}