Assignment question, submitted solution and professor's solution
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Manish
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Assignment 3.pdf
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BIN
Assignment 3.pdf
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369
ass3.c
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ass3.c
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/* License: AGPLv3 or later. https://www.gnu.org/licenses/licenses.html
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*
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* IMPORTANT: THIS PROGRAM REQUIRES THE -lm FLAG TO COMPILE.
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* Compile it as:
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* gcc -Wall -std=c11 ass3.c -o ass3 -lm
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*
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* Assignment 3 - Optimum Routing
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* Manish
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* Student Login: *****
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*
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* NOTE: I have not implemented memorisation for heuristics (euclidean
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* distance) even though we find shortest path several times (as we also find
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* second shortest path). Because, it would have marginal speed improvement
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* (and has complexity of O(1)) but can potentially require (no. of vertices)^2
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* space which is not very scalable.
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*/
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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typedef struct
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{
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double x;
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double y;
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} vertex;
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vertex * V = NULL; // Vertices
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int nV; // Number of Vertices
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double * E = NULL; // Edge Weights
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int nE; // Number of Edges
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int src; // source/from
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int dst; // destination/to
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// reused in multiple aStar calls
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double* D = NULL; // Best path distance/weight
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int* P = NULL; // Parent of current vertices following best path
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int* C = NULL; // Candidate vertices. It's min heap
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int nC; // Number of Candidate vertices/ C size.
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/* NOTE: Same memory as for V is allocated as dynamic
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* memory allocation later is not allowed and in worst case
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* would have to go through all vertices (or path does not exist).
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*/
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// Used for removing edges while finding second_shortest path
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int* shortestPath = NULL;
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int shortestPathVertices = 0;
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// Used for storing second best candidate yet while search remaining options
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int* secondShortestPath = NULL;
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int secondShortestPathVertices = 0;
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void aStar();
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double euclidianDistance(int i, int j); // Heuristics
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double absolute(double n);
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// Work on C (Candidate List)
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void heapify();
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void shiftdown(int i);
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void shiftup(int i);
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void swap(int i, int j);
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int main(void)
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{
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printf("Enter file name containing graph details: ");
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char filename[257];
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// Assuming filename/file path won't be longer than 256 characters
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scanf("%256s", filename);
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FILE* file = fopen(filename, "r");
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if (!file)
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{
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perror(filename);
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exit(EXIT_FAILURE);
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}
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// Read nV & nE and dynamically allocate memory
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if (fscanf(file, " %d %d ", &nV, &nE) != EOF)
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{
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// +1 as keeping 1 indexed for code readability
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V = malloc(sizeof(vertex)*(nV+1));
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E = malloc(sizeof(double)*(nV+1)*(nV+1));
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D = malloc(sizeof(double)*(nV+1));
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P = malloc(sizeof(int)*(nV+1));
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// Can be nV-1 since one would always be source node
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C = malloc(sizeof(int)*nV);
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shortestPath = malloc(sizeof(vertex)*nV);
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secondShortestPath = malloc(sizeof(vertex)*nV);
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if (
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V == NULL
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|| E == NULL
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|| D == NULL
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|| P == NULL
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|| C == NULL
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|| shortestPath == NULL
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|| secondShortestPath == NULL
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)
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{
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fprintf(stderr, "Failed to allocate memory\n");
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return 1;
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}
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}
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else
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{
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fprintf(stderr, "File read error\n");
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return 1;
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}
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// Initializing all edge weights to double max;
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for (int i=0; i <= nV; i++)
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{
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for (int j=0; j <= nV; j++)
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{
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E[i*nV+j] = DBL_MAX;
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if (i == j)
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E[i*nV+j] = 0; // Distance/weight to self is 0
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}
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}
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// Read vertices
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int v;
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double x, y;
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for (int i=1; i <= nV; i++)
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{
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fscanf(file, " %d %lf %lf ", &v, &x, &y);
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if (v <= nV)
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{
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V[v].x = x;
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V[v].y = y;
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}
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else
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{
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fprintf(stderr, "Vertex i (%d) > nV (%d)\n", v, nV);
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return 1;
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}
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}
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// Read Edges/Weights
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int v1, v2;
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double w;
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for (int i=0; i < nE; i++)
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{
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fscanf(file, " %d %d %lf", &v1, &v2, &w);
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if (v1 <= nV && v2 <= nV)
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{
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if (E[v1*nV+v2] > w)
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{
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E[v1*nV+v2] = w;
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E[v1+v2*nV] = w;
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}
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}
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else
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{
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fprintf(stderr, "v1 or v2 > nE in Edges\n");
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return 1;
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}
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}
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// Read source and destination vertices for path finding
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fscanf(file, " %d %d ", &src, &dst);
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fclose(file);
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aStar(); // Find shortest path
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if (D[dst] == DBL_MAX)
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printf(
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"Path from vertex %d to vertex %d does not exist\n", src, dst);
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else
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{
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// Recreate path from P (parents array)
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int parent = dst;
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while (P[parent] != parent)
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{
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shortestPath[shortestPathVertices++] = parent;
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parent = P[parent];
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}
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shortestPath[shortestPathVertices++] = parent;
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printf(
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"Shortest path from vertex %d to vertex %d is:\n%d",
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src,
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dst,
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src);
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for (int i=shortestPathVertices-2; i >= 0; i--)
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printf(" -> %d", shortestPath[i]);
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printf(
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"\nDistance/weight from vertex %d to vertex %d following the "
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"shortest path is %.2lf\n\n",
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src,
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dst,
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D[dst]);
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// Find second shortest path
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double secondShortestDistance = DBL_MAX;
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for (int i=0; i < shortestPathVertices-1; i++)
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{
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double w = E[shortestPath[i]*nV+shortestPath[i+1]];
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// Remove ith edge from shortest path
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E[shortestPath[i]*nV+shortestPath[i+1]] = DBL_MAX;
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E[shortestPath[i+1]*nV+shortestPath[i]] = DBL_MAX;
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aStar(); // Find new path
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// Add back ith edge from shortest path
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E[shortestPath[i]*nV+shortestPath[i+1]] = w;
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E[shortestPath[i+1]*nV+shortestPath[i]] = w;
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// if current distance is shorter than previously found 2nd best
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if (D[dst] < secondShortestDistance)
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{ // Update 2nd shortest distance and path
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secondShortestDistance = D[dst];
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secondShortestPathVertices = 0;
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int parent = dst;
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while (P[parent] != parent)
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{
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secondShortestPath[
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secondShortestPathVertices++] = parent;
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parent = P[parent];
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}
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secondShortestPath[secondShortestPathVertices++] = parent;
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}
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}
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// Print second shortest path found (or not found)
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if (secondShortestDistance == DBL_MAX)
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printf(
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"Another/second Path from vertex %d to vertex %d does not "
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"exist\n",
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src,
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dst);
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else
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{
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printf("Second shortest path from vertex %d to vertex %d is:\n%d", src, dst, src);
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for (int i=secondShortestPathVertices-2; i >= 0; i--)
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printf(" -> %d", secondShortestPath[i]);
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printf(
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"\nDistance/weight from vertex %d to vertex %d following the "
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"second shortest path is %.2lf\n",
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src,
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dst,
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secondShortestDistance
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);
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}
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}
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// Free dynamically allocated memory
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free(V);
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free(E);
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free(D);
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free(P);
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free(C);
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free(shortestPath);
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free(secondShortestPath);
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return 0;
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}
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void aStar()
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{
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// Infantilise/Reset global variables for each iteration.
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nC = 0;
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for (int i=1; i <= nV; i++)
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{
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D[i] = DBL_MAX;
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P[i] = i;
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C[nC++] = i;
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}
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// Remove source vertex from candidate list
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swap(src-1, --nC);
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int v = src;
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D[src] = 0; // distance from src to src is 0
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for (int i=1; i <= nV; i++)
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{
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D[i] = E[src*nV+i];
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if (D[i] != DBL_MAX)
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P[i] = src;
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}
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heapify();
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while (nC)
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{
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v = C[0];
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swap(0, --nC);
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shiftdown(0);
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if (v == dst)
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break;
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for (int j=0; j < nC; j++)
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{
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if (D[C[j]] > D[v] + E[v*nV+C[j]])
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{
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D[C[j]] = D[v] + E[v*nV+C[j]];
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P[C[j]] = v;
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shiftup(j);
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}
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}
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}
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}
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double euclidianDistance(int i, int j)
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{
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double xDiff = absolute(V[i].x - V[j].x);
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double yDiff = absolute(V[i].y - V[j].y);
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return sqrt((xDiff*xDiff)+(yDiff*yDiff));
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}
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double absolute(double n)
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{
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return (n < 0) ? -n : n;
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}
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void heapify()
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{
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int shiftdowns_required = (nC/2)-1;
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for (int i = shiftdowns_required; i >= 0; i--)
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{
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shiftdown(i);
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};
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}
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void shiftdown(int i)
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{
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int child = (i * 2) + 1; // left child
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if (child < nC) // has at least one child
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{
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if (child < nC - 1) // has both children
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{
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// if right child smaller
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if (
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D[C[child]]+euclidianDistance(C[child], dst) >
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D[C[child + 1]]+euclidianDistance(C[child+1], dst))
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child++; // pick right child
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}
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if (
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D[C[i]]+euclidianDistance(C[i], dst)
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> D[C[child]]+euclidianDistance(C[child], dst))
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{
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swap(i, child);
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shiftdown(child);
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}
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}
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}
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void shiftup(int i)
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{
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if (i == 0)
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return;
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int parent = (i - 1) / 2;
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if (D[C[parent]]+euclidianDistance(C[parent], dst) >
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D[C[i]]+euclidianDistance(C[i], dst))
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{
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swap(parent, i);
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shiftup(parent);
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}
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}
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void swap(int i, int j)
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{
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int tmp = C[i];
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C[i] = C[j];
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C[j] = tmp;
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}
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