Write me a C code for an weighted, un-directed graph that performs dijkstra's algorithm on graph along with some basic functions as mentioned in description.

Problem Statement • Input: A directed graph G = (V, E) with weight function w : E → N. • Goal: Serve the following requests: – Given u, v ∈ V , what is the weight of edge (u, v)? – Given v ∈ V , run Dijkstra’s algorithm on G from vertex v. – Given u, v ∈ V , output shortest path from a vertex u to v. Input Format General format: A graph G = (V, E) is defined by first providing the number of vertices n = |V |. Henceforth you shall assume that the vertex set is V = {1, 2, . . . , n}. The edge set E and the weight function w are provided together. Each neighbour v of a vertex u will be given in the adjacency list of u along with w(u, v). Requests arrive only after the definition of G. Format in detail: Each line of the input looks like one of the following: • ‘N’ followed by number of vertices n ∈ N. • ‘E’ followed by a vertex and vertex-weight pairs that look like: u, v1,w(u, v1), v2,w(u, v2) · · · , vk,w(u, vk) This list gives the adjacency list of vertex u along with the respective edge weights. The list is given as a space-separated list. • ‘?’ followed by u, v ∈ [n] with a space separating them. • ‘D’ followed by a u ∈ [n]. • ‘P’ followed by u, v ∈ [n] with a space separating them. Each of the lines above ends with a ‘\n’ character. All lists are given as elements separated by a space. No commas are used anywhere. All numbers used will fit inside an int. End of input is indicated by EOF. Output Format • If input line started with ‘N’ or ‘E’, then no corresponding output. • If input line was “? u v”: Output w(u, v) if (u, v) ∈ E, −1 otherwise. • If input line was “D u”: Let v1, v2, . . . , vn be the order of vertices visited on a run of of Dijkstra’s algorithm from u (note that u = v1). Let δ(u, v) denote the shortest path from u to v. Output a list of pairs: (v1, δ(u, v1)), . . . ,(vn, δ(u, vn)). If δ(u, v) = ∞ then output −1 in its place. Use a space to separate v and δ(u, v) within a pair. Use a ‘\n’ between pairs. • If input line was “P u v”: If v is not reachable from u, output −1. Else output the shortest distance from u to v followed by a shortest path from u to v as a space-separated list of vertices starting with u. All output lines have to end with a ‘\n’ character. Implementation rules • The input graph G = (V, E) is stored similar to Assignment 4. The edge weights are stored in an additional variable inside the nodes in the adjacency list (see CLRS). • Store each vertex’s adjacency list in the same order as provided in the input. • Dijkstra’s algorithm requires a min-priority queue. Implement a min-priority queue by using a min-heap.