Dp

Author: Skm2000

.gitignore

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+./a.out

Coin_Changing_1.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+int Max_ways(int coins[],int size,int sum){
+    int dp[size+1][sum+1];
+    for(int i=0;i<=sum;i++){
+        dp[0][i]=0;
+    }
+    for(int i=0;i<=size;i++){
+        dp[i][0]=1;
+    }
+    for(int i=1;i<=size;i++){
+        for(int j=1;j<=sum;j++){
+            if(coins[i-1]<=j){
+                dp[i][j] = dp[i-1][j] + dp[i][j-coins[i-1]];
+            }
+            else{
+                dp[i][j] = dp[i-1][j];
+            }
+        }
+    }
+    for(int i=0;i<=size;i++){
+        for(int j=0;j<=sum;j++){
+            cout<<dp[i][j]<<" ";
+        }
+        cout<<"\n";
+    }
+
+    return dp[size][sum];
+}
+
+int main() {
+    int coins[] = {1, 2, 3}; 
+    int size = sizeof(coins)/sizeof(coins[0]);
+    int sum = 4;
+    cout<<Max_ways(coins,size,sum)<<"\n"; 
+}

Coin_Changing_2.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+int CountSubsets(int a[],int size,int sum) {
+    int dp[size+1][sum+1];
+    for(int i=0;i<=sum;i++){
+        dp[0][i] = 0;
+    }
+    for(int i=0;i<=size;i++){
+        dp[i][0]=1;
+    }
+    for(int i=1;i<=size;i++){
+        for(int j=1;j<=sum;j++){
+            if(a[i-1]<=j){
+                dp[i][j] = dp[i-1][j] + dp[i-1][j-a[i-1]];
+            }
+            else {
+                dp[i][j] = dp[i-1][j];
+            }
+        }
+    }
+    for(int i=0;i<=size;i++){
+        for(int j=0;j<=sum;j++){
+            cout<<dp[i][j]<<" ";
+        }
+        cout<<"\n";
+    }
+    return dp[size][sum];
+}
+
+int main() {
+    int a[] = { 1, 2, 3, 3 }; 
+    int size = 4;
+    int sum = 6;
+    cout<<CountSubsets(a,size,sum)<<"\n";
+}

Count_Subsets_of_given_Sum.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+bool EqualSubsetSum(int a[],int size) {
+    int sum=0;
+    for(int i=0;i<size;i++){
+        sum+=a[i];
+    }
+    if(sum%2!=0) return false;
+    bool dp[size+1][sum/2+1];
+    for(int i=0;i<=sum/2;i++){
+        dp[0][i] = false;
+    }
+    for(int i=0;i<=size;i++){
+        dp[i][0]=true;
+    }
+    for(int i=1;i<=size;i++){
+        for(int j=1;j<=sum/2;j++){
+            if(a[i-1]<=j){
+                dp[i][j] = dp[i-1][j] || dp[i-1][j-a[i-1]];
+            }
+            else{
+                dp[i][j] = dp[i-1][j];
+            }
+        }
+    }
+    return dp[size][sum/2];
+}
+
+int main() {
+
+    int a[] = {3, 1, 1, 2, 2, 1};  
+    int size = sizeof(a) / sizeof(a[0]);
+    cout<<EqualSubsetSum(a,size)<<"\n";
+
+}

Equal_Sum_Partition.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+int knapsack(int wt[],int val[],int W,int size){
+    int dp[size+1][W+1];
+    for(int i=0;i<=size;i++){
+        for(int j=0;j<=W;j++){
+            if(i==0 || j==0){
+                dp[i][j] = 0;
+            }
+            else if(wt[i-1]<=j){
+                dp[i][j] = max(dp[i-1][j],val[i-1] + dp[i-1][j-wt[i-1]]);
+            }
+            else{
+                dp[i][j] = dp[i-1][j];
+            }
+        }
+    }
+    return dp[size][W];
+}
+
+int main() {
+    
+    int val[] = {60, 100, 120}; 
+    int wt[] = {10, 20, 30}; 
+    int  W = 50; 
+    int size = sizeof(val)/sizeof(val[0]); 
+    cout<<knapsack(wt,val,W,size)<<"\n";
+
+}

Knapsack_0_1.cpp

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+#include<bits/stdc++.h>
+using namespace std;

Minimum_Subset_Sum_Difference.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+int rodCutting(int cost[],int len[],int size) {
+    int dp[size+1][size+1];
+    for(int i=0;i<=size;i++){
+        for(int j=0;j<=size;j++){
+            if(i==0 || j==0){
+                dp[i][j] = 0;
+            }
+            else if(len[i-1]<=j){
+                dp[i][j] = max(dp[i-1][j],cost[i-1] + dp[i][j-len[i-1]]);
+            }
+            else{
+                dp[i][j] = dp[i-1][j];
+            }
+        }
+    }
+    for(int i=0;i<=size;i++){
+        for(int j=0;j<=size;j++){
+            cout<<dp[i][j]<<" ";
+        }
+        cout<<"\n";
+    }
+    return dp[size][size];
+}
+
+int main() {
+    int len[] = {1, 2, 3, 4, 5, 6, 7, 8};
+    int cost[] = {1, 5, 8, 9, 10, 17, 17, 20};
+    int size = sizeof(cost)/sizeof(cost[0]);
+    cout<<rodCutting(cost,len,size);
+}

Rod_Cutting.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+bool SubsetSum(int a[],int size,int sum) {
+    bool dp[size+1][sum+1];
+    for(int i=0;i<=sum;i++){
+        dp[0][i] = false;
+    }
+    for(int i=0;i<=size;i++){
+        dp[i][0]=true;
+    }
+    for(int i=1;i<=size;i++){
+        for(int j=1;j<=sum;j++){
+            if(a[i-1] <= j) {
+                dp[i][j] = dp[i-1][j] || dp[i-1][j-a[i-1]];
+            }
+            else {
+                dp[i][j] = dp[i-1][j];
+            }
+        }
+    }
+    return dp[size][sum];
+}
+
+int main() {
+    int a[] = {3, 34, 4, 12, 5, 2}; 
+    int sum = 1; 
+    int size = sizeof(a)/sizeof a[0];
+    cout<<SubsetSum(a,size,sum)<<"\n";
+}

SubsetSum.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+int knapsack(int wt[],int val[],int W,int size){
+    int dp[size+1][W+1];
+    for(int i=0;i<=size;i++){
+        for(int j=0;j<=W;j++){
+            if(i==0 || j==0){
+                dp[i][j] = 0;
+            }
+            else if(wt[i-1]<=j){
+                dp[i][j] = max(dp[i-1][j],val[i-1] + dp[i][j-wt[i-1]]);
+            }
+            else{
+                dp[i][j] = dp[i-1][j];
+            }
+        }
+    }
+    for(int i=0;i<=size;i++){
+        for(int j=0;j<=W;j++){
+            cout<<dp[i][j]<<" ";
+        }
+        cout<<"\n";
+    }
+    return dp[size][W];
+}
+
+int main() {
+    
+    int wt[] = {1, 3, 2}; 
+    int val[] = {50, 10, 15}; 
+    int  W = 10; 
+    int size = sizeof(val)/sizeof(val[0]); 
+    cout<<knapsack(wt,val,W,size)<<"\n";
+
+}