Implementation of Dijkstra's Algorithm in C++

#include <stdio.h>

#include <limits.h>

  

#define V 9

   

int minDistance(int  dist[], bool s ptSet[])

{

   // 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;

}

  

int printSolution(int dist[], int n)

{

   printf("Vertex   Distance from Source\n");

   for (int i = 0; i < V; i++)

      printf("%d tt %d\n", i, dist[i]);

}

   

void  dijkstra(int  graph[V][V], int  src)

{

     int dist[V];    

                      

   

     bool sptSet[V];

     for (int i = 0; i < V; i++)

        dist[i] = INT_MAX, sptSet[i] = false;

     dist[src] = 0;

   

     

     for (int count = 0; count < V-1; count++)

     {

      

       int u = minDistance(dist, sptSet);

       sptSet[u] = true;

       for (int v = 0; v < V; 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];

     }

   

     printSolution(dist, V);

}

  

int  main()

{

   

   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}

                     };

   

    dijkstra(graph, 0);

   

    return 0;

} 


OUTPUT:

Vertex   Distance from Source
0                0
1                4
2                12
3                19
4                21
5                11
6                9
7                8
8                14

Binary Search in C++

#include <algorithm>

#include <iostream>

  

using namespace std;

  

void show(int a[], int arraysize)

{

    for (int i = 0; i < arraysize; ++i)

        cout << a[i] << " ";

}

  

int main()

{

    int a[] = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };

    int asize = sizeof(a) / sizeof(a[0]);

    cout << "\n The array is : ";

    show(a, asize);

  

    cout << "\n\nLet's say we want to search for 2 in the array";

    cout << "\n So, we first sort the array";

    sort(a, a + asize);

    cout << "\n\n The array after sorting is : ";

    show(a, asize);

    cout << "\n\nNow, we do the binary search";

    if (binary_search(a, a + 10, 2))

        cout << "\nElement found in the array";

    else

        cout << "\nElement not found in the array";

  

    cout << "\n\nNow, say we want to search for 10";

    if (binary_search(a, a + 10, 10))

        cout << "\nElement found in the array";

    else

        cout << "\nElement not found in the array";

  

    return 0;

}

implementation of Prims's Algorithm in C++

// STL implementation of Prim's algorithm for MST
#include<bits/stdc++.h>
using namespace std;
# define INF 0x3f3f3f3f
 
// iPair ==>  Integer Pair
typedef pair<int, int> iPair;
 
// This class represents a directed graph using
// adjacency list representation
class Graph
{
    int V;    // No. of vertices
 
    // In a weighted graph, we need to store vertex
    // and weight pair for every edge
    list< pair<int, int> > *adj;
 
public:
    Graph(int V);  // Constructor
 
    // function to add an edge to graph
    void addEdge(int u, int v, int w);
 
    // Print MST using Prim's algorithm
    void primMST();
};
 
// Allocates memory for adjacency list
Graph::Graph(int V)
{
    this->V = V;
    adj = new list<iPair> [V];
}
 
void Graph::addEdge(int u, int v, int w)
{
    adj[u].push_back(make_pair(v, w));
    adj[v].push_back(make_pair(u, w));
}
 
// Prints shortest paths from src to all other vertices
void Graph::primMST()
{
    // Create a priority queue to store vertices that
    // are being preinMST. This is weird syntax in C++.
    // Refer below link for details of this syntax
    // http://geeksquiz.com/implement-min-heap-using-stl/
    priority_queue< iPair, vector <iPair> , greater<iPair> > pq;
 
    int src = 0; // Taking vertex 0 as source
 
    // Create a vector for keys and initialize all
    // keys as infinite (INF)
    vector<int> key(V, INF);
 
    // To store parent array which in turn store MST
    vector<int> parent(V, -1);
 
    // To keep track of vertices included in MST
    vector<bool> inMST(V, false);
 
    // Insert source itself in priority queue and initialize
    // its key as 0.
    pq.push(make_pair(0, src));
    key[src] = 0;
 
    /* Looping till priority queue becomes empty */
    while (!pq.empty())
    {
        // The first vertex in pair is the minimum key
        // vertex, extract it from priority queue.
        // vertex label is stored in second of pair (it
        // has to be done this way to keep the vertices
        // sorted key (key must be first item
        // in pair)
        int u = pq.top().second;
        pq.pop();
 
        inMST[u] = true;  // Include vertex in MST
 
        // 'i' is used to get all adjacent vertices of a vertex
        list< pair<int, int> >::iterator i;
        for (i = adj[u].begin(); i != adj[u].end(); ++i)
        {
            // Get vertex label and weight of current adjacent
            // of u.
            int v = (*i).first;
            int weight = (*i).second;
 
            //  If v is not in MST and weight of (u,v) is smaller
            // than current key of v
            if (inMST[v] == false && key[v] > weight)
            {
                // Updating key of v
                key[v] = weight;
                pq.push(make_pair(key[v], v));
                parent[v] = u;
            }
        }
    }
 
    // Print edges of MST using parent array
    for (int i = 1; i < V; ++i)
        printf("%d - %d\n", parent[i], i);
}
 
// Driver program to test methods of graph class
int main()
{
    // create the graph given in above fugure
    int V = 9;
    Graph g(V);
 
    //  making above shown graph
    g.addEdge(0, 1, 4);
    g.addEdge(0, 7, 8);
    g.addEdge(1, 2, 8);
    g.addEdge(1, 7, 11);
    g.addEdge(2, 3, 7);
    g.addEdge(2, 8, 2);
    g.addEdge(2, 5, 4);
    g.addEdge(3, 4, 9);
    g.addEdge(3, 5, 14);
    g.addEdge(4, 5, 10);
    g.addEdge(5, 6, 2);
    g.addEdge(6, 7, 1);
    g.addEdge(6, 8, 6);
    g.addEdge(7, 8, 7);
 
    g.primMST();
 
    return 0;
}

Implement Binary Heap using C++

// A C++ program to demonstrate common Binary Heap Operations

#include<iostream>

#include<climits>

using namespace std;

// Prototype of a utility function to swap two integers

void swap(int *x, int *y);

// A class for Min Heap

class MinHeap

{

    int *harr; // pointer to array of elements in heap

    int capacity; // maximum possible size of min heap

    int heap_size; // Current number of elements in min heap

public:

    // Constructor

    MinHeap(int capacity);

    // to heapify a subtree with the root at given index

    void MinHeapify(int );

    int parent(int i) { return (i-1)/2; }

    // to get index of left child of node at index i

    int left(int i) { return (2*i + 1); }

    // to get index of right child of node at index i

    int right(int i) { return (2*i + 2); }

    // to extract the root which is the minimum element

    int extractMin();

    // Decreases key value of key at index i to new_val

    void decreaseKey(int i, int new_val);

    // Returns the minimum key (key at root) from min heap

    int getMin() { return harr[0]; }

    // Deletes a key stored at index i

    void deleteKey(int i);

    // Inserts a new key 'k'

    void insertKey(int k);

};

// Constructor: Builds a heap from a given array a[] of given size

MinHeap::MinHeap(int cap)

{

    heap_size = 0;

    capacity = cap;

    harr = new int[cap];

}

// Inserts a new key 'k'

void MinHeap::insertKey(int k)

{

    if (heap_size == capacity)

    {

        cout << "\nOverflow: Could not insertKey\n";

        return;

    }

    // First insert the new key at the end

    heap_size++;

    int i = heap_size - 1;

    harr[i] = k;

    // Fix the min heap property if it is violated

    while (i != 0 && harr[parent(i)] > harr[i])

    {

       swap(&harr[i], &harr[parent(i)]);

       i = parent(i);

    }

}

// Decreases value of key at index 'i' to new_val.  It is assumed that

// new_val is smaller than harr[i].

void MinHeap::decreaseKey(int i, int new_val)

{

    harr[i] = new_val;

    while (i != 0 && harr[parent(i)] > harr[i])

    {

       swap(&harr[i], &harr[parent(i)]);

       i = parent(i);

    }

}

// Method to remove minimum element (or root) from min heap

int MinHeap::extractMin()

{

    if (heap_size <= 0)

        return INT_MAX;

    if (heap_size == 1)

    {

        heap_size--;

        return harr[0];

    }

    // Store the minimum value, and remove it from heap

    int root = harr[0];

    harr[0] = harr[heap_size-1];

    heap_size--;

    MinHeapify(0);

    return root;

}

// This function deletes key at index i. It first reduced value to minus

// infinite, then calls extractMin()

void MinHeap::deleteKey(int i)

{

    decreaseKey(i, INT_MIN);

    extractMin();

}

// A recursive method to heapify a subtree with the root at given index

// This method assumes that the subtrees are already heapified

void MinHeap::MinHeapify(int i)

{

    int l = left(i);

    int r = right(i);

    int smallest = i;

    if (l < heap_size && harr[l] < harr[i])

        smallest = l;

    if (r < heap_size && harr[r] < harr[smallest])

        smallest = r;

    if (smallest != i)

    {

        swap(&harr[i], &harr[smallest]);

        MinHeapify(smallest);

    }

}

// A utility function to swap two elements

void swap(int *x, int *y)

{

    int temp = *x;

    *x = *y;

    *y = temp;

}

// Driver program to test above functions

int main()

{

    MinHeap h(11);

    h.insertKey(3);

    h.insertKey(2);

    h.deleteKey(1);

    h.insertKey(15);

    h.insertKey(5);

    h.insertKey(4);

    h.insertKey(45);

    cout << h.extractMin() << " ";

    cout << h.getMin() << " ";

    h.decreaseKey(2, 1);

    cout << h.getMin();

    return 0;

}