Graph Data Structure

If you want to solve a Rubik’s cube or understand what technology google uses for its maps, this is the place for you.

Many programming problems require you to represent a non-hierarchical relationship between pairs of items. Such problems can be solved by using data structure called graph. I will discuss the concept and implementation of graphs. I will also give various applications of graphs.

We shall see the following :
– Store data in a graph
– Implement a graph
– Apply graphs to solve Programming problems

 

One Reply to “Graph Data Structure”

  1. boarding pass: Src and dest?
    you have a stack of unsorted flight boarding passes of a passenger. Only the departure city and destination city are on the boarding pass. how do you find the first departure city and the final destination city

    Depth First Search (DFS) algorithm traverses a graph data structure in a depth ward motion and uses a stack to remember to get the next vertex to start a search, when a dead end occurs in any iteration, It employs the following rules.

    Rule 1 − Visit the adjacent unvisited vertex. Mark it as visited. Display it. Push it in a stack.
    Rule 2 − If no adjacent vertex is found, pop up a vertex from the stack. (It will pop up all the vertices from the stack, which do not have adjacent vertices.)
    Rule 3 − Repeat Rule 1 and Rule 2 until the stack is empty.

    The Code in “C” :

    #include
    #include
    #include

    #define MAX 5

    struct Vertex {
    char label;
    bool visited;
    };

    //stack variables

    int stack[MAX];
    int top = -1;

    //graph variables

    //array of vertices
    struct Vertex* lstVertices[MAX];

    //adjacency matrix
    int adjMatrix[MAX][MAX];

    //vertex count
    int vertexCount = 0;

    //stack functions

    void push(int item) {
    stack[++top] = item;
    }

    int pop() {
    return stack[top–];
    }

    int peek() {
    return stack[top];
    }

    bool isStackEmpty() {
    return top == -1;
    }

    //graph functions

    //add vertex to the vertex list
    void addVertex(char label) {
    struct Vertex* vertex = (struct Vertex*) malloc(sizeof(struct Vertex));
    vertex->label = label;
    vertex->visited = false;
    lstVertices[vertexCount++] = vertex;
    }

    //add edge to edge array
    void addEdge(int start,int end) {
    adjMatrix[start][end] = 1;
    adjMatrix[end][start] = 1;
    }

    //display the vertex
    void displayVertex(int vertexIndex) {
    printf(“%c “,lstVertices[vertexIndex]->label);
    }

    //get the adjacent unvisited vertex
    int getAdjUnvisitedVertex(int vertexIndex) {
    int i;

    for(i = 0; i < vertexCount; i++) { if(adjMatrix[vertexIndex][i] == 1 && lstVertices[i]->visited == false) {
    return i;
    }
    }

    return -1;
    }

    void depthFirstSearch() {
    int i;

    //mark first node as visited
    lstVertices[0]->visited = true;

    //display the vertex
    displayVertex(0);

    //push vertex index in stack
    push(0);

    while(!isStackEmpty()) {
    //get the unvisited vertex of vertex which is at top of the stack
    int unvisitedVertex = getAdjUnvisitedVertex(peek());

    //no adjacent vertex found
    if(unvisitedVertex == -1) {
    pop();
    } else {
    lstVertices[unvisitedVertex]->visited = true;
    displayVertex(unvisitedVertex);
    push(unvisitedVertex);
    }
    }

    //stack is empty, search is complete, reset the visited flag
    for(i = 0;i < vertexCount;i++) { lstVertices[i]->visited = false;
    }
    }

    int main() {
    int i, j;

    for(i = 0; i < MAX; i++) // set adjacency { for(j = 0; j < MAX; j++) // matrix to 0 adjMatrix[i][j] = 0; } addVertex('S'); // 0 addVertex('A'); // 1 addVertex('B'); // 2 addVertex('C'); // 3 addVertex('D'); // 4 addEdge(0, 1); // S - A addEdge(0, 2); // S - B addEdge(0, 3); // S - C addEdge(1, 4); // A - D addEdge(2, 4); // B - D addEdge(3, 4); // C - D printf("Depth First Search: ") depthFirstSearch(); return 0; } Output: Depth First Search: S A D B C

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