added important_DP_algorithms

Leetcode/C++/Count_Derangements_DP.cpp

@@ -0,0 +1,66 @@
+    /*
+
+    Count Derangements!
+    (Permutation such that no element appears in its original position)
+
+
+    */
+
+    #include <bits/stdc++.h>
+    #include <cstdio>
+    #include <cstring>
+    #include <cmath>
+    #include <cstring>
+    #include <chrono>
+    #include <complex>
+    #define endl "\n"
+    #define ll long long int
+    #define vi vector<int>
+    #define vll vector<ll>
+    #define vvi vector < vi >
+    #define pii pair<int,int>
+    #define pll pair<long long, long long>
+    #define mod 1000000007
+    #define inf 1000000000000000001;
+    #define all(c) c.begin(),c.end()
+    #define mp(x,y) make_pair(x,y)
+    #define mem(a,val) memset(a,val,sizeof(a))
+    #define eb emplace_back
+    #define f first
+    #define s second
+
+    using namespace std;
+    int main()
+    {
+
+        std::ios::sync_with_stdio(false);
+        int T;
+        cin>>T;
+        // cin.ignore(); must be there when using getline(cin, s)
+        while(T--)
+        {
+
+            int n;
+
+            cin>>n;
+
+            int dp[n+1];
+            memset(dp,0,sizeof(dp));
+
+            dp[0]=0;
+
+            dp[1]=0;
+
+            dp[2]=1;
+
+            for(int i=3;i<=n;i++) {
+                dp[i] = (i-1)*(dp[i-1]+dp[i-2]);
+            }
+
+
+            cout<<dp[n]<<endl;
+
+
+        }
+        return 0;
+    }

Leetcode/C++/Count_Of_All_Palindromic_Substrings_DP.cpp

@@ -0,0 +1,88 @@
+    #include <bits/stdc++.h>
+    #include <cstdio>
+    #include <cstring>
+    #include <cmath>
+    #include <cstring>
+    #include <chrono>
+    #include <complex>
+    #define endl "\n"
+    #define ll long long int
+    #define vi vector<int>
+    #define vll vector<ll>
+    #define vvi vector < vi >
+    #define pii pair<int,int>
+    #define pll pair<long long, long long>
+    #define mod 1000000007
+    #define inf 1000000000000000001;
+    #define all(c) c.begin(),c.end()
+    #define mp(x,y) make_pair(x,y)
+    #define mem(a,val) memset(a,val,sizeof(a))
+    #define eb emplace_back
+    #define f first
+    #define s second
+
+    using namespace std;
+
+    int dp[1001][1001];
+
+    bool ispalin(string s, int i,int j) {
+
+
+        if(i>j) {
+            return 1;
+        }
+
+        if(dp[i][j]!=-1) {
+            return dp[i][j];
+        }
+
+
+        if(s[i]!=s[j]) {
+            return dp[i][j]=0;
+        }
+
+        return dp[i][j]=ispalin(s,i+1,j-1);
+
+    }
+
+
+
+    int countPalin(string s) {
+
+        memset(dp,-1,sizeof(dp));
+
+        int n=s.size();
+
+        int c=0;
+
+
+        for(int i=0;i<n;i++) {
+            for(int j=i+1;j<n;j++) {
+                if(ispalin(s,i,j)) {
+                    c++;
+                }
+            }
+        }
+
+        return c;
+    }
+
+
+    int main()
+    {
+
+    #ifndef ONLINE_JUDGE
+        freopen("input.txt","r",stdin);
+        freopen("output.txt","w",stdout);
+    #endif
+
+
+       string s;
+
+       cin>>s;
+
+       cout<<countPalin(s);       
+
+
+        return 0;
+    }

Leetcode/C++/Count_Of_Longest_Increasing_Subsequences_DP.cpp

@@ -0,0 +1,85 @@
+
+    #include <bits/stdc++.h>
+    #include <cstdio>
+    #include <cstring>
+    #include <cmath>
+    #include <cstring>
+    #include <chrono>
+    #include <complex>
+    #define endl "\n"
+    #define ll long long int
+    #define vi vector<int>
+    #define vll vector<ll>
+    #define vvi vector < vi >
+    #define pii pair<int,int>
+    #define pll pair<long long, long long>
+    #define mod 1000000007
+    #define inf 1000000000000000001;
+    #define all(c) c.begin(),c.end()
+    #define mp(x,y) make_pair(x,y)
+    #define mem(a,val) memset(a,val,sizeof(a))
+    #define eb emplace_back
+    #define f first
+    #define s second
+
+    using namespace std;
+    int main()
+    {
+
+    #ifndef ONLINE_JUDGE
+        freopen("input.txt","r",stdin);
+        freopen("output.txt","w",stdout);
+    #endif
+
+
+
+        int n;
+
+        cin>>n;
+
+        int a[n];
+
+        for(int i=0;i<n;i++) {
+            cin>>a[i];
+        }
+
+        int lis[n];
+        int dp[n];
+
+        for(int i=0;i<n;i++) {
+            dp[i]=1;
+            lis[i]=1;
+        }
+
+        for(int i=1;i<n;i++) {
+            for(int j=0;j<i;j++) {
+                if(a[i]>a[j]) {
+
+                    if(lis[i]<=lis[j]) {
+                        lis[i]=lis[j]+1;
+                        dp[i]=dp[j];
+                    }
+
+                    else if(lis[i]==lis[j]+1) {
+                        dp[i]+=dp[j];
+                    }
+
+                }
+            }
+        }
+
+        int y=*max_element(lis,lis+n);
+
+        int c=0;
+
+        for(int i=0;i<n;i++) {
+            if(lis[i]==y) {
+                c+=dp[i];
+            }
+        }
+
+        cout<<c;
+
+
+        return 0;
+    }

Leetcode/C++/Count_Of_String_Appears_As_A_Subsequence_DP.cpp

@@ -0,0 +1,62 @@
+// Initial Template for C++
+
+#include <bits/stdc++.h>
+using namespace std;
+
+ // } Driver Code Ends
+
+
+// User function Template for C++
+
+class Solution{
+public:
+    int countWays(string S1, string S2){
+
+        int n=S1.size();
+        int m=S2.size();
+
+        int dp[n+1][m+1];
+        memset(dp,0,sizeof(dp));
+
+        for(int i=0;i<n+1;i++) {
+            dp[i][0]=1;
+        }
+
+        for(int j=0;j<m+1;j++) {
+            dp[0][j]=0;
+        }
+
+        dp[0][0]=1;
+
+
+        for(int i=1;i<=n;i++) {
+            for(int j=1;j<=m;j++) {
+                if(S1[i-1]==S2[j-1]) {
+                    dp[i][j]=dp[i-1][j]+dp[i-1][j-1];
+                }
+                else {
+                    dp[i][j]=dp[i-1][j];
+                }
+            }
+        }
+
+        return dp[n][m];
+
+
+    }
+};
+
+// { Driver Code Starts.
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        string S1, S2;
+        cin>>S1;
+        cin>>S2;
+
+        Solution ob;
+        cout<<ob.countWays(S1, S2)<<endl;
+    }
+    return 0;
+}  // } Driver Code Ends

Leetcode/C++/Count_Of_Subsequences_Having_Product_Less_Than_K_DP.cpp

@@ -0,0 +1,74 @@
+    #include <bits/stdc++.h>
+    #include <cstdio>
+    #include <cstring>
+    #include <cmath>
+    #include <cstring>
+    #include <chrono>
+    #include <complex>
+    #define endl "\n"
+    #define ll long long int
+    #define vi vector<int>
+    #define vll vector<ll>
+    #define vvi vector < vi >
+    #define pii pair<int,int>
+    #define pll pair<long long, long long>
+    #define mod 1000000007
+    #define inf 1000000000000000001;
+    #define all(c) c.begin(),c.end()
+    #define mp(x,y) make_pair(x,y)
+    #define mem(a,val) memset(a,val,sizeof(a))
+    #define eb emplace_back
+    #define f first
+    #define s second
+
+    using namespace std;
+
+    int max_count(int a[],int n,int k) {
+
+
+        int dp[n+1][k+1];
+
+        memset(dp,0,sizeof(dp));
+
+        for(int i=1;i<=n;i++) {
+
+            for(int j=1;j<=k;j++) {
+
+                dp[i][j]+=dp[i-1][j];
+
+                if(a[i-1]<=j&&a[i-1]>0) {
+                    dp[i][j]+=dp[i-1][j/a[i-1]]+1;
+                }
+            }
+
+        }
+
+        return dp[n][k];
+    }
+
+
+
+    int main()
+    {
+
+    #ifndef ONLINE_JUDGE
+        freopen("input.txt","r",stdin);
+        freopen("output.txt","w",stdout);
+    #endif
+
+
+        int n,k;
+
+        cin>>n>>k;
+
+        int a[n];
+
+        for(int i=0;i<n;i++) {
+            cin>>a[i];
+        }
+
+        cout<<max_count(a,n,k);
+
+
+        return 0;
+    }