From cf7a713fd940ff6ce6bcd7d4d67c2d245cc9a174 Mon Sep 17 00:00:00 2001
From: Akanksha Shukla <63357474+sakanksha19@users.noreply.github.com>
Date: Fri, 8 Oct 2021 18:29:37 +0530
Subject: [PATCH] chore(CPlusPlus): add matrix multiplication (#527)

---
 .../Arrays/matrix-multiplication.cpp          | 78 +++++++++++++++++++
 .../Graphs/dfs-through-stackdatastructure.cpp | 54 +++++++++++++
 algorithms/CPlusPlus/Graphs/dfs-traversal.cpp | 49 ++++++++++++
 .../Graphs/total-connected-components.cpp     | 69 ++++++++++++++++
 algorithms/CPlusPlus/README.md                |  4 +
 5 files changed, 254 insertions(+)
 create mode 100644 algorithms/CPlusPlus/Arrays/matrix-multiplication.cpp
 create mode 100644 algorithms/CPlusPlus/Graphs/dfs-through-stackdatastructure.cpp
 create mode 100644 algorithms/CPlusPlus/Graphs/dfs-traversal.cpp
 create mode 100644 algorithms/CPlusPlus/Graphs/total-connected-components.cpp

diff --git a/algorithms/CPlusPlus/Arrays/matrix-multiplication.cpp b/algorithms/CPlusPlus/Arrays/matrix-multiplication.cpp
new file mode 100644
index 00000000..9acfccf5
--- /dev/null
+++ b/algorithms/CPlusPlus/Arrays/matrix-multiplication.cpp
@@ -0,0 +1,78 @@
+//given two matrices of sizes n*m and n1*m1 
+//find multiplication of the two matrices and print it
+#include <bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+    int n,m,n1,m1;
+   // cout<<"Enter the dimensions of first matrix\n";
+    cin>>n>>m;
+    int a[n][m];
+   // cout<<"Enter the elements of first matrix\n";
+    for(int i=0;i<n;i++)
+    {
+        for(int j=0;j<m;j++)
+        {
+            cin>>a[i][j];
+        }
+    }
+    //cout<<"Enter the dimensions of Second matrix\n";
+    cin>>n1>>m1;
+    int b[n1][m1];
+    //cout<<"Enter the elements of second matrix\n";
+    for(int i=0;i<n1;i++)
+    {
+        for(int j=0;j<m1;j++)
+        {
+            cin>>b[i][j];
+        }
+    }
+    if(m!=n1)
+    {
+        cout<<"Multiplication of the matrices is not possible";
+    }
+    else
+    {
+        int c[n][m1];
+        for(int i=0;i<n;i++)
+        {
+            for(int j=0;j<m1;j++)
+            {
+                c[i][j]=0;
+            }
+        }
+        for(int i=0;i<n;i++)
+        {
+            for(int j=0;j<m1;j++)
+            {
+                for(int k=0;k<n1;k++)
+               {
+                  c[i][j]+=a[i][k]*b[k][j];
+               }
+            }
+        }
+        for(int i=0;i<n;i++)
+        {
+            for(int j=0;j<m1;j++)
+            {
+                cout<<c[i][j]<<" ";
+            }
+            cout<<"\n";
+        }
+    }    
+    return 0;
+}
+//INPUT
+//2 3
+//1 2 1
+//3 4 1
+//3 2
+//1 2 
+//1 1
+//3 7
+//OUTPUT
+//6 11 
+//10 17 
+//TIME COMPLEXITY OF THE PROGRAM
+//O(n^3)
diff --git a/algorithms/CPlusPlus/Graphs/dfs-through-stackdatastructure.cpp b/algorithms/CPlusPlus/Graphs/dfs-through-stackdatastructure.cpp
new file mode 100644
index 00000000..564c07f8
--- /dev/null
+++ b/algorithms/CPlusPlus/Graphs/dfs-through-stackdatastructure.cpp
@@ -0,0 +1,54 @@
+//dfs traversal of undirected graph using stack approach
+#include <bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+    int n,m;
+    cin>>n>>m;//enter the number of vertices and number of edges
+    vector<vector<int>>adj(n+1,vector<int>());
+    //create an adjacency list according to the edges given in input
+    for(int i=0;i<m;i++)
+    {
+        int u,v;
+        cin>>u>>v;
+        adj[u].push_back(v);
+        adj[v].push_back(u);
+    }
+    cout<<"The dfs traversal is \n";
+    vector<int>v(n+1,0);
+    stack<int>s;
+    s.push(1);
+    while(!s.empty())
+    {
+        int t=s.top();
+        if(!v[t])
+        {
+           v[t]=1;//mark the vertex as visited
+           cout<<t<<" ";//print the vertex you visited
+        }   
+        s.pop();
+        for(int i=0;i<adj[t].size();i++)
+        {
+            if(!v[adj[t][i]])
+            {
+                s.push(adj[t][i]);//if a vertex is not visited push it in stack
+            }
+        }
+    }
+    return 0;
+}
+//INPUT
+//6 5
+//1 2 
+//2 6 
+//1 3 
+//3 4 
+//3 5 
+//OUTPUT
+//The dfs traversal is 
+//1 3 5 4 2 6 
+//TIME COMPLEXITY OF THE PROGRAM
+//O(V+E)
+//where V is number of vertices
+//E is number of edges
diff --git a/algorithms/CPlusPlus/Graphs/dfs-traversal.cpp b/algorithms/CPlusPlus/Graphs/dfs-traversal.cpp
new file mode 100644
index 00000000..b7963451
--- /dev/null
+++ b/algorithms/CPlusPlus/Graphs/dfs-traversal.cpp
@@ -0,0 +1,49 @@
+//dfs traversal of undirected graph using recursive approach
+#include <bits/stdc++.h>
+using namespace std;
+
+void dfs(vector<vector<int>>&adj, vector<int>&v,int x)
+{
+    v[x]=1;
+    cout<<x<<" ";//print the vertex visited 
+    for(int i=0;i<adj[x].size();i++)
+    {
+        if(v[adj[x][i]]==0)
+        {
+            dfs(adj,v,adj[x][i]);//call the dfs function if a node is not visited
+        }
+    }
+}
+int main()
+{
+    int n,m;
+    cin>>n>>m;//enter the number of vertices and number of edges
+    vector<vector<int>>adj(n+1,vector<int>());
+    //create an adjacency list according to the edges given in input
+    for(int i=0;i<m;i++)
+    {
+        int u,v;
+        cin>>u>>v;
+        adj[u].push_back(v);
+        adj[v].push_back(u);
+    }
+    cout<<"The dfs traversal is \n";
+    vector<int>v(n+1,0);
+    dfs(adj,v,1);
+    return 0;
+}
+
+//INPUT
+//6 5
+//1 2
+//2 6
+//1 3
+//3 4
+//3 5
+//OUTPUT
+//The dfs traversal is 
+//1 2 6 3 4 5    
+//TIME COMPLEXITY OF THE PROGRAM
+//O(V+E)
+//where V is number of vertices
+//and E is number of edges
diff --git a/algorithms/CPlusPlus/Graphs/total-connected-components.cpp b/algorithms/CPlusPlus/Graphs/total-connected-components.cpp
new file mode 100644
index 00000000..fb784be9
--- /dev/null
+++ b/algorithms/CPlusPlus/Graphs/total-connected-components.cpp
@@ -0,0 +1,69 @@
+//find total number of Connected Components in a graph
+//implementation of dsu
+#include<bits/stdc++.h>
+#define ll long long int 
+using namespace std;
+ll find(ll x,vector<ll>&p)
+{
+    if(p[x]==x)
+    return x;
+    else
+    return p[x]=find(p[x],p);
+}
+void merge(ll a,ll b,vector<ll>&r,vector<ll>&p)
+{
+    ll s1=find(a,p);
+    ll s2=find(b,p);
+    if(s1!=s2)
+    {
+        if(r[s1]<r[s2])
+        {
+            p[s1]=s2;
+            r[s2]+=r[s1];
+        }
+        else
+        {
+            p[s2]=s1;
+            r[s1]+=r[s2];
+        }
+    }
+}
+int main()
+{
+    int n,m;
+    cin>>n>>m;//enter the number of vertices and number of edges
+    vector<ll>r(n,0);
+    vector<ll>p;
+    for(int i=0;i<n;i++)
+    {
+        p.push_back(i);
+    }
+    for(int i=0;i<m;i++)
+    {
+        int u,v;
+        cin>>u>>v;
+        u--;
+        v--;
+        merge(u,v,r,p);
+    }
+    map<ll,ll>mp;
+    for(int i=0;i<n;i++)
+    {
+       ll x=find(i,p);
+        mp[x]++;
+    }
+    cout<<"Total Number of Connected Components are - ";
+    cout<<mp.size();
+    return 0;
+}
+//INPUT
+//5 3
+//1 2
+//2 3
+//4 5
+//OUTPUT
+//Total Number of Connected Components are - 2
+//TIME COMPLEXITY OF THE PROGRAM
+//O(V+E)
+//where V is number of vertices
+//E is number of edges
diff --git a/algorithms/CPlusPlus/README.md b/algorithms/CPlusPlus/README.md
index 766f4a0d..ddeb9168 100644
--- a/algorithms/CPlusPlus/README.md
+++ b/algorithms/CPlusPlus/README.md
@@ -19,6 +19,7 @@
 15. [Occurrence of one in sorted array](Arrays/occurence-of-one-in-sorted-array.cpp)
 16. [Segregate 0s and 1s](Arrays/segregate-0-and-1.cpp)
 17. [Search insert position](Arrays/search-insert-position.cpp)
+18. [Matrix Multiplication](Arrays/matrix-multiplication.cpp)
 
 ## Dynamic-Programming
 
@@ -34,6 +35,9 @@
 2. [kruskal Algorithm](Graphs/kruskal-algorithm.cpp)
 3. [Breadth First Search](Graphs/breadth-first-search.cpp)
 4. [Topological sort](Graphs/topological-sort.cpp)
+5. [Dfs traversal with stack](Graphs/dfs-through-stackdatastructure.cpp)
+6. [Dfs traversal with recursion](Graphs/dfs-traversal.cpp)
+7. [Connected Components](Graphs/total-connected-components.cpp)
 
 ## Multiplication