1. Articulation Point in Graph
// C++ program to find articulation points in an undirected graph
#include <bits/stdc++.h>
using namespace std;
// A recursive function that find articulation
// points using DFS traversal
// adj[] --> Adjacency List representation of the graph
// u --> The vertex to be visited next
// visited[] --> keeps track of visited vertices
// disc[] --> Stores discovery times of visited vertices
// low[] -- >> earliest visited vertex (the vertex with minimum
// discovery time) that can be reached from subtree
// rooted with current vertex
// parent --> Stores the parent vertex in DFS tree
// isAP[] --> Stores articulation points
void APUtil(vector<int> adj[], int u, bool visited[],
int disc[], int low[], int& time, int parent,
bool isAP[])
{
// Count of children in DFS Tree
int children = 0;
// Mark the current node as visited
visited[u] = true;
// Initialize discovery time and low value
disc[u] = low[u] = ++time;
// Go through all vertices adjacent to this
for (auto v : adj[u]) {
// If v is not visited yet, then make it a child of u
// in DFS tree and recur for it
if (!visited[v]) {
children++;
APUtil(adj, v, visited, disc, low, time, u, isAP);
// Check if the subtree rooted with v has
// a connection to one of the ancestors of u
low[u] = min(low[u], low[v]);
// If u is not root and low value of one of
// its child is more than discovery value of u.
if (parent != -1 && low[v] >= disc[u])
isAP[u] = true;
}
// Update low value of u for parent function calls.
else if (v != parent)
low[u] = min(low[u], disc[v]);
}
// If u is root of DFS tree and has two or more children.
if (parent == -1 && children > 1)
isAP[u] = true;
}
void AP(vector<int> adj[], int V)
{
int disc[V] = { 0 };
int low[V];
bool visited[V] = { false };
bool isAP[V] = { false };
int time = 0, par = -1;
// Adding this loop so that the
// code works even if we are given
// disconnected graph
for (int u = 0; u < V; u++)
if (!visited[u])
APUtil(adj, u, visited, disc, low,
time, par, isAP);
// Printing the APs
for (int u = 0; u < V; u++)
if (isAP[u] == true)
cout << u << " ";
}
// Utility function to add an edge
void addEdge(vector<int> adj[], int u, int v)
{
adj[u].push_back(v);
adj[v].push_back(u);
}
int main()
{
// Create graphs given in above diagrams
cout << "Articulation points in first graph
";
int V = 5;
vector<int> adj1[V];
addEdge(adj1, 1, 0);
addEdge(adj1, 0, 2);
addEdge(adj1, 2, 1);
addEdge(adj1, 0, 3);
addEdge(adj1, 3, 4);
AP(adj1, V);
cout << "
Articulation points in second graph
";
V = 4;
vector<int> adj2[V];
addEdge(adj2, 0, 1);
addEdge(adj2, 1, 2);
addEdge(adj2, 2, 3);
AP(adj2, V);
cout << "
Articulation points in third graph
";
V = 7;
vector<int> adj3[V];
addEdge(adj3, 0, 1);
addEdge(adj3, 1, 2);
addEdge(adj3, 2, 0);
addEdge(adj3, 1, 3);
addEdge(adj3, 1, 4);
addEdge(adj3, 1, 6);
addEdge(adj3, 3, 5);
addEdge(adj3, 4, 5);
AP(adj3, V);
return 0;
}
2. CRC (C lan)
// Include headers
#include<stdio.h>
#include<string.h>
// length of the generator polynomial
#define N strlen(gen_poly)
// data to be transmitted and received
char data[28];
// CRC value
char check_value[28];
// generator polynomial
char gen_poly[10];
// variables
int data_length,i,j;
// function that performs XOR operation
void XOR(){
// if both bits are the same, the output is 0
// if the bits are different the output is 1
for(j = 1;j < N; j++)
check_value[j] = (( check_value[j] == gen_poly[j])?'0':'1');
}
// Function to check for errors on the receiver side
void receiver(){
// get the received data
printf("Enter the received data: ");
scanf("%s", data);
printf("\n-----------------------------\n");
printf("Data received: %s", data);
// Cyclic Redundancy Check
crc();
// Check if the remainder is zero to find the error
for(i=0;(i<N-1) && (check_value[i]!='1');i++);
if(i<N-1)
printf("\nError detected\n\n");
else
printf("\nNo error detected\n\n");
}
void crc(){
// initializing check_value
for(i=0;i<N;i++)
check_value[i]=data[i];
do{
// check if the first bit is 1 and calls XOR function
if(check_value[0]=='1')
XOR();
// Move the bits by 1 position for the next computation
for(j=0;j<N-1;j++)
check_value[j]=check_value[j+1];
// appending a bit from data
check_value[j]=data[i++];
}while(i<=data_length+N-1);
// loop until the data ends
}
int main()
{
// get the data to be transmitted
printf("\nEnter data to be transmitted: ");
scanf("%s",data);
printf("\n Enter the Generating polynomial: ");
// get the generator polynomial
scanf("%s",gen_poly);
// find the length of data
data_length=strlen(data);
// appending n-1 zeros to the data
for(i=data_length;i<data_length+N-1;i++)
data[i]='0';
printf("\n----------------------------------------");
// print the data with padded zeros
printf("\n Data padded with n-1 zeros : %s",data);
printf("\n----------------------------------------");
// Cyclic Redundancy Check
crc();
// print the computed check value
printf("\nCRC or Check value is : %s",check_value);
// Append data with check_value(CRC)
for(i=data_length;i<data_length+N-1;i++)
data[i]=check_value[i-data_length];
printf("\n----------------------------------------");
// printing the final data to be sent
printf("\n Final data to be sent : %s",data);
printf("\n----------------------------------------\n");
// Calling the receiver function to check errors
receiver();
return 0;
}
3. How to find Shortest Paths from Source to all Vertices using Dijkstra’s Algorithm
// C++ program for Dijkstra's single source shortest path
// algorithm. The program is for adjacency matrix
// representation of the graph
#include <iostream>
using namespace std;
#include <limits.h>
// Number of vertices in the graph
#define V 9
// A utility function to find the vertex with minimum
// distance value, from the set of vertices not yet included
// in shortest path tree
int minDistance(int dist[], bool sptSet[])
{
// Initialize min value
int min = INT_MAX, min_index;
for (int v = 0; v < V; v++)
if (sptSet[v] == false && dist[v] <= min)
min = dist[v], min_index = v;
return min_index;
}
// A utility function to print the constructed distance
// array
void printSolution(int dist[])
{
cout << "Vertex \t Distance from Source" << endl;
for (int i = 0; i < V; i++)
cout << i << " \t\t\t\t" << dist[i] << endl;
}
// Function that implements Dijkstra's single source
// shortest path algorithm for a graph represented using
// adjacency matrix representation
void dijkstra(int graph[V][V], int src)
{
int dist[V]; // The output array. dist[i] will hold the
// shortest
// distance from src to i
bool sptSet[V]; // sptSet[i] will be true if vertex i is
// included in shortest
// path tree or shortest distance from src to i is
// finalized
// Initialize all distances as INFINITE and stpSet[] as
// false
for (int i = 0; i < V; i++)
dist[i] = INT_MAX, sptSet[i] = false;
// Distance of source vertex from itself is always 0
dist[src] = 0;
// Find shortest path for all vertices
for (int count = 0; count < V - 1; count++) {
// Pick the minimum distance vertex from the set of
// vertices not yet processed. u is always equal to
// src in the first iteration.
int u = minDistance(dist, sptSet);
// Mark the picked vertex as processed
sptSet[u] = true;
// Update dist value of the adjacent vertices of the
// picked vertex.
for (int v = 0; v < V; v++)
// Update dist[v] only if is not in sptSet,
// there is an edge from u to v, and total
// weight of path from src to v through u is
// smaller than current value of dist[v]
if (!sptSet[v] && graph[u][v]
&& dist[u] != INT_MAX
&& dist[u] + graph[u][v] < dist[v])
dist[v] = dist[u] + graph[u][v];
}
// print the constructed distance array
printSolution(dist);
}
// driver's code
int main()
{
/* Let us create the example graph discussed above */
int graph[V][V] = { { 0, 4, 0, 0, 0, 0, 0, 8, 0 },
{ 4, 0, 8, 0, 0, 0, 0, 11, 0 },
{ 0, 8, 0, 7, 0, 4, 0, 0, 2 },
{ 0, 0, 7, 0, 9, 14, 0, 0, 0 },
{ 0, 0, 0, 9, 0, 10, 0, 0, 0 },
{ 0, 0, 4, 14, 10, 0, 2, 0, 0 },
{ 0, 0, 0, 0, 0, 2, 0, 1, 6 },
{ 8, 11, 0, 0, 0, 0, 1, 0, 7 },
{ 0, 0, 2, 0, 0, 0, 6, 7, 0 } };
// Function call
dijkstra(graph, 0);
return 0;
}
// This code is contributed by shivanisinghss2110
4. Huffman Encoding // generate tree
// C++(STL) program for Huffman Coding with STL
#include <bits/stdc++.h>
using namespace std;
// A Huffman tree node
struct MinHeapNode {
// One of the input characters
char data;
// Frequency of the character
unsigned freq;
// Left and right child
MinHeapNode *left, *right;
MinHeapNode(char data, unsigned freq)
{
left = right = NULL;
this->data = data;
this->freq = freq;
}
};
// For comparison of
// two heap nodes (needed in min heap)
struct compare {
bool operator()(MinHeapNode* l, MinHeapNode* r)
{
return (l->freq > r->freq);
}
};
// Prints huffman codes from
// the root of Huffman Tree.
void printCodes(struct MinHeapNode* root, string str)
{
if (!root)
return;
if (root->data != '$')
cout << root->data << ": " << str << "\n";
printCodes(root->left, str + "0");
printCodes(root->right, str + "1");
}
// The main function that builds a Huffman Tree and
// print codes by traversing the built Huffman Tree
void HuffmanCodes(char data[], int freq[], int size)
{
struct MinHeapNode *left, *right, *top;
// Create a min heap & inserts all characters of data[]
priority_queue<MinHeapNode*, vector<MinHeapNode*>,
compare>
minHeap;
for (int i = 0; i < size; ++i)
minHeap.push(new MinHeapNode(data[i], freq[i]));
// Iterate while size of heap doesn't become 1
while (minHeap.size() != 1) {
// Extract the two minimum
// freq items from min heap
left = minHeap.top();
minHeap.pop();
right = minHeap.top();
minHeap.pop();
// Create a new internal node with
// frequency equal to the sum of the
// two nodes frequencies. Make the
// two extracted node as left and right children
// of this new node. Add this node
// to the min heap '$' is a special value
// for internal nodes, not used
top = new MinHeapNode('$',
left->freq + right->freq);
top->left = left;
top->right = right;
minHeap.push(top);
}
// Print Huffman codes using
// the Huffman tree built above
printCodes(minHeap.top(), "");
}
// Driver Code
int main()
{
char arr[] = { 'a', 'b', 'c', 'd', 'e', 'f' };
int freq[] = { 5, 9, 12, 13, 16, 45 };
int size = sizeof(arr) / sizeof(arr[0]);
HuffmanCodes(arr, freq, size);
return 0;
}
// get tree:: https://www.csfieldguide.org.nz/en/interactives/huffman-tree/
Write something awesome.
A rich text editor for writing,
collaborating and sharing