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dp_0_1_knapsack.cpp

@@ -0,0 +1,79 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int man(int a,int b)
+{
+	if(a>b)
+		return a;
+	return b;
+}
+
+int main()
+{
+	#ifndef ONLINE_JUDGE
+	freopen("input.txt", "r" ,stdin);
+	freopen("output.txt", "w" ,stdout);
+	#endif
+	int t;
+	cin>>t;
+	while(t--)
+	{
+		int n;
+		int max_wt;
+		cin>>n>>max_wt;
+		// cout<<endl;
+		struct  knapsack
+		{
+			int val;
+			int wt;
+		}knap[n];
+		for(int i=0;i<n;i++)
+		{
+			cin>>knap[i].val;
+		}
+		for(int i=0;i<n;i++)
+		{
+			cin>>knap[i].wt;
+		}
+		int dp[n][max_wt+1];
+		for(int j=0;j<=max_wt;j++)
+		{
+			int i=0;
+			if(knap[i].wt<=j)
+			{
+				dp[i][j]=knap[i].val;
+			}
+			else
+				dp[i][j]=0;
+		}
+		for(int i=0;i<n;i++)
+		{
+			dp[i][0] = 0;
+		}
+		for(int i=1;i<n;i++)
+		{
+			for(int j=1;j<=max_wt;j++)
+			{
+				if(knap[i].wt<=j)
+				{
+					dp[i][j] = max(knap[i].val+dp[i-1][j-knap[i].wt],dp[i-1][j]);
+				}
+				else
+				{
+					dp[i][j] = dp[i-1][j];
+				}
+			}
+		}
+
+		// for(int i=0;i<n;i++)
+		// {
+		// 	for(int j=0;j<=max_wt;j++)
+		// 	{
+		// 		cout<<dp[i][j]<<" ";
+		// 	}
+		// 	cout<<endl;
+		// }
+		cout<<dp[n-1][max_wt];
+		cout<<endl;
+	}
+}

dp_coin_change_number_of_ways.cpp

@@ -0,0 +1,53 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+	#ifndef ONLINE_JUDGE
+	freopen("input.txt", "r" ,stdin);
+	freopen("output.txt", "w" ,stdout);
+	#endif
+
+	int t;
+	cin>>t;
+	while(t--)
+	{
+		int n;
+		cin>>n;
+		int arr[n];
+		for(int i=0;i<n;i++)
+		{
+			cin>>arr[i];
+		}
+		int val;
+		cin>>val;
+		int dp[n][val+1];
+		for(int i=0;i<=val;i++)
+		{
+			if(i%arr[0] == 0)
+				dp[0][i] = 1;
+			else
+				dp[0][i] = 0;
+		}
+		for(int i=1;i<n;i++)
+		{
+			for(int j=0;j<=val;j++)
+			{
+				if(arr[i]>j)
+					dp[i][j] = dp[i-1][j];
+				else
+					dp[i][j] = dp[i-1][j] + dp[i][j-arr[i]];
+			}
+		}
+		// for(int i=0;i<n;i++)
+		// {
+		// 	for(int j=0;j<=val;j++)
+		// 	{
+		// 		cout<<dp[i][j]<<" ";
+		// 	}
+		// 	cout<<endl;
+		// }
+		cout<<dp[n-1][val];
+		cout<<endl;
+	}
+}

dp_coin_exchange.cpp

@@ -0,0 +1,73 @@
+#include <bits/stdc++.h>
+using namespace std;
+int min_value(int a, int b);
+
+int min_value(int a, int b)
+{
+	if(a<b)
+		return a;
+	return b;
+}
+
+int main()
+{
+		#ifndef ONLINE_JUDGE
+		freopen("input.txt", "r" ,stdin);
+		freopen("output.txt", "w" ,stdout);
+		#endif
+	int t;
+	cin>>t;
+	while(t--)
+	{
+		int n;
+		cin>>n;
+		int arr[10][n+1];
+		int denom[10]={1,2,5,10,20,50,100,200,500,2000};
+		for(int i=0;i<=n;i++)
+		{
+			arr[0][i]=i;
+		}
+		// cout<<n<<endl;
+		// cout<<arr[0][35];
+		for(int i=0;i<10;i++)
+		{
+			arr[i][0]=0;
+		}
+		// cout<<denom[9];
+		for(int i=1;i<10;i++)
+		{
+			for(int j=1;j<=n;j++)
+			{
+				if(j-denom[i]>=0)
+				{
+					arr[i][j] = min_value(arr[i-1][j],arr[i][j-denom[i]]+1);
+				}
+				else
+				{
+					arr[i][j] = arr[i-1][j];
+				}
+			}
+		}
+		int i=9,j=n;
+		vector<int>vec;
+		while(arr[i][j]!=0)
+		{
+			if(arr[i-1][j] == arr[i][j])
+			{
+				i--;
+				// vec.push_back(arr[i][j]);
+			}
+			else
+			{
+				j=j-denom[i];
+				vec.push_back(denom[i]);
+			}
+		}
+		for (int i = 0; i < vec.size(); ++i)
+		{
+			cout<<vec[i]<<" ";
+		}
+		// cout<<arr[9][n];
+		cout<<endl;
+	}
+}

dp_longest_common_substring.cpp

@@ -0,0 +1,82 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+	#ifndef ONLINE_JUDGE
+	freopen("input.txt", "r" ,stdin);
+	freopen("output.txt", "w" ,stdout);
+	#endif
+	int t;
+	cin>>t;
+	while(t--)
+	{
+		int m,n;
+		cin>>m>>n;
+		string st1,st2;
+		cin>>st1>>st2;
+		// cout<<st1<<" "<<st2;
+		int dp[m][n];
+		int max = 0;
+		for(int i=0;i<m;i++)
+		{
+			if(st2[0] == st1[i])
+			{
+				dp[i][0]=1;
+			}
+			else
+				dp[i][0]=0;
+			if(max<dp[i][0])
+				max=dp[i][0];
+			// cout<<dp[i][0]<<" ";
+		}
+		// cout<<endl<<max<<endl;
+		for(int i=0;i<n;i++)
+		{
+			if(st1[0] == st2[i])
+			{
+				dp[0][i]=1;
+			}
+			else
+				dp[0][i]=0;
+			if(max<dp[0][i])
+				max=dp[0][i];
+			// cout<<dp[0][i]<<" ";
+		}
+		// cout<<st2[1]<<" "<<st1[2];
+		for(int i=1;i<m;i++)
+		{
+			for(int j=1;j<n;j++)
+			{
+				if(st2[j]==st1[i])
+				{
+					// cout<<"hello"<<" ";
+					dp[i][j] = dp[i-1][j-1]+1;
+				}
+				else
+				{
+					dp[i][j] = 0;
+				}
+				if(max<dp[i][j])
+					max=dp[i][j];
+			}
+		}
+		cout<<"  ";
+		// for(int i=0;i<n;i++) TO Print the grid
+		// {
+		// 	cout<<st2[i]<<" ";
+		// }
+		// cout<<endl;
+		// for(int i=0;i<m;i++)
+		// {
+		// 	cout<<st1[i]<<" ";
+		// 	for(int j=0;j<n;j++)
+		// 	{
+		// 		cout<<dp[i][j]<<" ";
+		// 	}
+		// 	cout<<endl;
+		// }
+		cout<<max;
+		cout<<endl;
+	}
+}

dp_longest_increasing_subsequence.cpp

@@ -0,0 +1,42 @@
+#include<bits/stdc++.h>
+using namespace std;
+int main()
+{
+	#ifndef ONLINE_JUDGE
+	freopen("input.txt", "r" ,stdin);
+	freopen("output.txt", "w" ,stdout);
+	#endif
+
+	int t;
+	cin>>t;
+	while(t--)
+	{
+		int n;
+		cin>>n;
+		int arr[n];
+		for(int i=0;i<n;i++)
+		{
+			cin>>arr[i];
+		}
+		int dp[n];
+		for(int i=0;i<n;i++)
+		{
+			dp[i]=1;
+		}
+		int max=1;
+		for(int i=1;i<n;i++)
+		{
+			for(int j=0;j<i;j++)
+			{
+				if(arr[i]>arr[j] && dp[i]<=dp[j])
+				{
+					dp[i]=dp[j]+1;
+				}
+				if(max<dp[i])
+					max=dp[i];
+			}
+		}
+		cout<<max<<endl;
+
+	}
+}

dp_minimum_number_of_steps.cpp

@@ -0,0 +1,53 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+	#ifndef ONLINE_JUDGE
+	freopen("input.txt", "r" ,stdin);
+	freopen("output.txt", "w" ,stdout);
+	#endif
+
+	int t;
+	cin>>t;
+	while(t--)
+	{
+		int n;
+		cin>>n;
+		int arr[n];
+		for(int i=0;i<n;i++)
+		{
+			cin>>arr[i];
+		}
+		int dp[n];
+		for (int i = 0; i < n; ++i)
+		{
+			/* code */
+			dp[i] = 0;
+		}
+		dp[0] = 0;
+		for(int i=1;i<n;i++)
+		{
+			for(int j=0;j<i;j++)
+			{
+				if(arr[j]+j >= i)
+				{
+					if(dp[i]==0 || dp[j]+1 < dp[i])
+					{
+						dp[i] = dp[j]+1;
+					}
+				}
+			}
+		}
+		// for (int i = 0; i < n; ++i)
+		// {
+		// 	 code 
+		// 	cout<<dp[i]<<" ";
+		// }
+		if(arr[0] == 0)
+			cout<<0;
+		else
+		cout<<dp[n-1];
+		cout<<endl;
+	}
+}