Dijksta's Algorithm not finding path in Adjacency Matrix - c++

Question

For some reason when I run dijkstra's algorithm on my randomly generated matrix it does not find paths between all the nodes even though it's clear that it's a connected graph. I've printed out the graphs and they always follow this form
0--2--3
| | |
4--5--6
| | |
7--8--9
Right now I'm only working with a 3*3 matrix and am trying to get that to work properly. The below code makes a adjacency matrix with 9 nodes and randomly generates a number between 1 and 3 to represent the weights of edges. I use 4 for infinity.
source is hard coded to 0 and numOfVertices 9
#include<iostream>
#include <time.h>
#include <math.h>
#define INFINITY 4
#define V 9
using namespace std;
class Dijkstra{
private:
int predecessor[20],distance[20];
bool mark[20];
int source;
int destination;
int numOfVertices;
char gameMode;
public:
int adjMatrix[9][9];
void read();
void initialize();
void setSource(int k);
int getClosestUnmarkedNode();
void calculateDistance();
void output();
int randomEdge();
int randomNode();
void printPath(int);
};
void Dijkstra::read(){
numOfVertices = 4;
for(int i = 0; i < numOfVertices;i++){
for(int j = 0; j < numOfVertices;j++){
if(i == j)
adjMatrix[i][j] = 0;
else if(j >= i){
if(j == i + 1 || j == i - 1 || j == i + sqrt((double)numOfVertices)|| j == i - sqrt((double)numOfVertices))
adjMatrix[i][j] = randomEdge();
else
adjMatrix[i][j] = 4;
if((i % ((int)sqrt((double)numOfVertices)) == ((int)sqrt((double)numOfVertices)) - 1) && j == i + 1)
adjMatrix[i][j] = 4;
}
else
adjMatrix[i][j] = adjMatrix[j][i];
cout<<adjMatrix[i][j]<< " ";
}
cout<< "\n";
}
source = 0;
}
void Dijkstra::initialize(){
for(int i=0;i<numOfVertices;i++) {
mark[i] = false;
predecessor[i] = -1;
distance[i] = INFINITY;
}
distance[source]= 0;
}
int Dijkstra::getClosestUnmarkedNode(){
int minDistance = INFINITY;
int closestUnmarkedNode = 0;
for(int i=0;i<numOfVertices;i++) {
if((!mark[i]) && ( minDistance >= distance[i])) {
minDistance = distance[i];
closestUnmarkedNode = i;
}
}
return closestUnmarkedNode;
}
void Dijkstra::calculateDistance(){
initialize();
int minDistance = INFINITY;
int closestUnmarkedNode;
int count = 0;
while(count < numOfVertices) {
closestUnmarkedNode = getClosestUnmarkedNode();
mark[closestUnmarkedNode] = true;
for(int i=0;i<numOfVertices;i++) {
if((!mark[i]) && (adjMatrix[closestUnmarkedNode][i]>0) ) {
if(distance[i] > distance[closestUnmarkedNode]+adjMatrix[closestUnmarkedNode][i]) {
distance[i] = distance[closestUnmarkedNode]+adjMatrix[closestUnmarkedNode][i];
predecessor[i] = closestUnmarkedNode;
}
}
}
count++;
}
}
void Dijkstra::printPath(int node){
if(node == source)
cout<<node<<"..";
else if(predecessor[node] == -1)
cout<<"No path from "<<source<<"to "<<node<<endl;
else {
printPath(predecessor[node]);
cout<<node<<"..";
}
}
void Dijkstra::output(){
for(int i=0;i<numOfVertices;i++) {
if(i == source)
cout<<source<<".."<<source;
else
printPath(i);
cout<<"->"<<distance[i]<<endl;
}
}
int Dijkstra::randomEdge(){
return rand() % 3 + 1;
}
void Dijkstra::setSource(int k){
source = k;
}
int main(int argc, char** argv){
Dijkstra G;
G.read();
G.calculateDistance();
G.output();
int k;
cin>> k;
exit(0);
}

Answer 1

You are using 4 to represent infinite distance... but 4 is a distance that is easy to reach along a valid path. This code rejects any path with a total distance >=4, because every node starts out with a distance at most 4 (i.e. unreachable) from the source.