DP and few algorithms

Algorithms/DynamicProgramming/C++/longest palindromic substring dp approch.cpp

@@ -0,0 +1,118 @@
+#include <iostream>
+#include <bits/stdc++.h> 
+using namespace std;
+
+//#pragma GCC optimize('O2') 
+#define ll long long 
+#define vll vector<ll>
+#define vi vector<int>
+#define tin tuple<ll,ll,ll>
+#define mll map<ll,ll>
+#define pi pair<ll,ll>
+#define vp vector<pi>
+#define pb push_back
+#define mp make_pair
+#define F first
+#define S second
+#define mt make_tuple
+#define all(x) (x).begin(),(x).end()
+#define rall(x) x.rbegin(), x.rend()
+#define watch(x) cout << (#x) << ' is ' << (x) << endl
+#define f(i,x,z) for(ll i=x;i<z;i++)
+#define rf(i,x,z) for(ll i=x-1;i>=z;i--)
+#define deb(x) cout<<'DEBUG------> '<<x<<endl
+#define srt(v) sort(v.begin(), v.end())
+#define rsrt(v) sort(v.rbegin(), v.rend())
+#define clr(x) memset(x, 0, sizeof(x)) 
+#define fa(i,vect) for(auto i : vect)
+#define fr(i,vect) for(VI :: reverse_iterator i = vect.rbegin(); i != vect.rend(); i++)
+#define mod 1000000007
+//  for (auto &a : v)
+//cin >> a;
+//for (auto me : m) {
+//std::vector<ll>::iterator it; 
+//it = std::find (v.begin(), v.end(), ser);
+//if (it != v.end())
+# define INF 0x3f3f3f3f 
+const int MAX = 1e3 + 7; 
+////////////////////////////////////////////////////////////////////////////////////////////
+
+ll power(ll base,ll por)
+{
+ll res=1;
+while(por>1){
+if(por%2==1)
+{
+res*=base;
+por--;
+}
+por/=2;
+base*=base;
+}
+res*=base;
+return res;
+}
+
+
+/////////////////////////////////////////////////////////////////////////////////////////
+int main()
+{
+//   freopen('a.txt', 'r', stdin); freopen('a_out.txt', 'w', stdout);
+
+    ios::sync_with_stdio(0);
+    cin.tie(0);
+    ll t,n;
+    string bb;
+    cin>>bb;
+    ll a,co=0,c=0,d=0,b=0,k;
+    n=bb.size();
+    int aa[n+1][n+1];
+    f(i,0,n+1)
+    {
+        f(j,0,n+1)
+        {
+            if(i==0)
+            {
+                aa[i][j]=1;
+            }
+            else if(i==1 && j>0)
+            {
+                aa[i][j]=1;
+            }
+            else if(i==2 && (j<n && j>0))
+            {
+                if(bb[j-1]==bb[j])
+                {
+                    aa[i][j]=1;
+                }
+                else
+                {
+                    aa[i][j]=0;
+                }
+            }
+            else
+            {
+                aa[i][j]=0;
+            }
+        }
+    }
+    int x=-1,y=-1;
+    f(i,3,n)
+    {
+        f(j,i,n+1)
+        {
+            if(bb[j-i]==bb[j-1] && aa[i-2][j-1]==1)
+            {
+                aa[i][j]=1;
+                x=i;
+                y=j;
+            }
+        }
+    }
+    cout<<x<<"\n";
+    f(i,y-x,y)
+    {
+        cout<<bb[i];
+    }
+   return 0;
+}

Algorithms/DynamicProgramming/C++/nCrmodp.cpp

@@ -0,0 +1,84 @@
+#include <iostream>
+#include <bits/stdc++.h> 
+using namespace std;
+
+//#pragma GCC optimize('O2') 
+#define ll long long 
+#define vll vector<ll>
+#define vi vector<int>
+#define tin tuple<ll,ll,ll>
+#define mll map<ll,ll>
+#define pi pair<ll,ll>
+#define vp vector<pi>
+#define pb push_back
+#define mp make_pair
+#define F first
+#define S second
+#define mt make_tuple
+#define all(x) (x).begin(),(x).end()
+#define rall(x) x.rbegin(), x.rend()
+#define watch(x) cout << (#x) << ' is ' << (x) << endl
+#define f(i,x,z) for(ll i=x;i<z;i++)
+#define rf(i,x,z) for(ll i=x-1;i>=z;i--)
+#define deb(x) cout<<'DEBUG------> '<<x<<endl
+#define srt(v) sort(v.begin(), v.end())
+#define rsrt(v) sort(v.rbegin(), v.rend())
+#define clr(x) memset(x, 0, sizeof(x)) 
+#define fa(i,vect) for(auto i : vect)
+#define fr(i,vect) for(VI :: reverse_iterator i = vect.rbegin(); i != vect.rend(); i++)
+#define mod 1000000007
+//  for (auto &a : v)
+//cin >> a;
+//for (auto me : m) {
+//std::vector<ll>::iterator it; 
+//it = std::find (v.begin(), v.end(), ser);
+//if (it != v.end())
+# define INF 0x3f3f3f3f 
+const int MAX = 1e3 + 7; 
+////////////////////////////////////////////////////////////////////////////////////////////
+
+ll power(ll base,ll por)
+{
+ll res=1;
+while(por>1){
+if(por%2==1)
+{
+res*=base;
+por--;
+}
+por/=2;
+base*=base;
+}
+res*=base;
+return res;
+}
+int nCrModp(int n,int r,int p)
+{
+	if(r>n-r)
+		r=n-r;
+	int c[r+1];
+	memset(c,0,sizeof(c));
+	c[0]=1;
+	for(int i=1;i<n+1;i++)
+	{
+		for(int j=min(i,r);j>=1;j--)
+		{
+			c[j]=(c[j]+c[j-1])%p;
+		}
+	}
+	return c[r];
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////
+int main()
+{
+//   freopen('a.txt', 'r', stdin); freopen('a_out.txt', 'w', stdout);
+
+	ios::sync_with_stdio(0);
+	cin.tie(0);
+	ll t,n;
+	ll a,co=0,c=0,d=0,b=0,k;
+	cin>>t>>n>>a;
+	cout<<nCrModp(t,n,a);
+   return 0;
+}

Algorithms/DynamicProgramming/C++/staircase problem tileng problem.cpp

@@ -0,0 +1,76 @@
+#include <iostream>
+#include <bits/stdc++.h> 
+using namespace std;
+
+//#pragma GCC optimize('O2') 
+#define ll long long 
+#define vll vector<ll>
+#define vi vector<int>
+#define tin tuple<ll,ll,ll>
+#define mll map<ll,ll>
+#define pi pair<ll,ll>
+#define vp vector<pi>
+#define pb push_back
+#define mp make_pair
+#define F first
+#define S second
+#define mt make_tuple
+#define all(x) (x).begin(),(x).end()
+#define rall(x) x.rbegin(), x.rend()
+#define watch(x) cout << (#x) << ' is ' << (x) << endl
+#define f(i,x,z) for(ll i=x;i<z;i++)
+#define rf(i,x,z) for(ll i=x-1;i>=z;i--)
+#define deb(x) cout<<'DEBUG------> '<<x<<endl
+#define srt(v) sort(v.begin(), v.end())
+#define rsrt(v) sort(v.rbegin(), v.rend())
+#define clr(x) memset(x, 0, sizeof(x)) 
+#define fa(i,vect) for(auto i : vect)
+#define fr(i,vect) for(VI :: reverse_iterator i = vect.rbegin(); i != vect.rend(); i++)
+#define mod 1000000007
+//  for (auto &a : v)
+//cin >> a;
+//for (auto me : m) {
+//std::vector<ll>::iterator it; 
+//it = std::find (v.begin(), v.end(), ser);
+//if (it != v.end())
+# define INF 0x3f3f3f3f 
+const int MAX = 1e3 + 7; 
+////////////////////////////////////////////////////////////////////////////////////////////
+
+ll power(ll base,ll por)
+{
+ll res=1;
+while(por>1){
+if(por%2==1)
+{
+res*=base;
+por--;
+}
+por/=2;
+base*=base;
+}
+res*=base;
+return res;
+}
+
+
+/////////////////////////////////////////////////////////////////////////////////////////
+int main()
+{
+//   freopen('a.txt', 'r', stdin); freopen('a_out.txt', 'w', stdout);
+
+    ios::sync_with_stdio(0);
+    cin.tie(0);
+    ll t,n;
+    cin>>n;
+    ll a,co=0,c=0,d=0,b=0,k;
+    vector<ll> v(n+1,0);
+    v[1]=1;
+    v[2]=1;
+    f(i,3,n+1)
+    {
+        v[i]=v[i-1]+v[i-2];
+    }
+    cout<<v[n];
+   return 0;
+}

Algorithms/DynamicProgramming/C++/subset sum.cpp

@@ -0,0 +1,99 @@
+#include <iostream>
+#include <bits/stdc++.h> 
+using namespace std;
+
+//#pragma GCC optimize('O2') 
+#define ll long long 
+#define vll vector<ll>
+#define vi vector<int>
+#define tin tuple<ll,ll,ll>
+#define mll map<ll,ll>
+#define pi pair<ll,ll>
+#define vp vector<pi>
+#define pb push_back
+#define mp make_pair
+#define F first
+#define S second
+#define mt make_tuple
+#define all(x) (x).begin(),(x).end()
+#define rall(x) x.rbegin(), x.rend()
+#define watch(x) cout << (#x) << ' is ' << (x) << endl
+#define f(i,x,z) for(ll i=x;i<z;i++)
+#define rf(i,x,z) for(ll i=x-1;i>=z;i--)
+#define deb(x) cout<<'DEBUG------> '<<x<<endl
+#define srt(v) sort(v.begin(), v.end())
+#define rsrt(v) sort(v.rbegin(), v.rend())
+#define clr(x) memset(x, 0, sizeof(x)) 
+#define fa(i,vect) for(auto i : vect)
+#define fr(i,vect) for(VI :: reverse_iterator i = vect.rbegin(); i != vect.rend(); i++)
+#define mod 1000000007
+//  for (auto &a : v)
+//cin >> a;
+//for (auto me : m) {
+//std::vector<ll>::iterator it; 
+//it = std::find (v.begin(), v.end(), ser);
+//if (it != v.end())
+# define INF 0x3f3f3f3f 
+const int MAX = 1e3 + 7; 
+////////////////////////////////////////////////////////////////////////////////////////////
+
+ll power(ll base,ll por)
+{
+ll res=1;
+while(por>1){
+if(por%2==1)
+{
+res*=base;
+por--;
+}
+por/=2;
+base*=base;
+}
+res*=base;
+return res;
+}
+
+
+/////////////////////////////////////////////////////////////////////////////////////////
+int main()
+{
+//   freopen('a.txt', 'r', stdin); freopen('a_out.txt', 'w', stdout);
+
+    ios::sync_with_stdio(0);
+    cin.tie(0);
+    int t,n;
+    cin>>t>>n;
+    int a,co=0,c=0,d=0,b=0,k,te;
+    vector<int> v(t);
+    f(i,0,t)
+    {
+        cin>>v[i];
+    }
+    bool aa[n+1];
+
+        f(j,0,n+1)
+        {
+            aa[j]=0;
+        }
+
+    aa[0]=1;
+    f(i,0,t)
+    {
+        te=v[i];
+        f(j,te,n+1)
+        {
+            if(te==j)aa[j]=1;
+            else if(aa[j-te]==1)aa[j]=1;
+        }
+    }
+    if(aa[n]==1)
+    {
+        cout<<"Yes";
+    }
+    else
+    {
+        cout<<"No";
+    }
+
+   return 0;
+}