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FastSIRUsingHeaps.c
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FastSIRUsingHeaps.c
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#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <stdbool.h>
#define MAX_TIME 300
#define TAU 0.5
#define GAMMA 0.2
#define MAX_NODES 10000
#define MAX_EDGES 300
#define INITIAL_INFECTED 1
/*The program takes 30 minutes to run when 10000 and 3000 are used, and even longer when INITIAL_INFECTED is made large*/
/*The following global variables are declared
-An adjaceny matrix consisting of booleans
-Arrays keeping a record of the S,I and R values
-The number of susceptible,infected and recovered people
-An integer holding the day number
*/
bool adjGraph[MAX_NODES][MAX_NODES];
int S[MAX_TIME],I[MAX_TIME],R[MAX_TIME];
int susceptible,infected,recovered;
int day=1;int heap_size=0;
/*The following structs will be used:
-graph_node: Contains all the relevant information about the node of the graph
-node: The node of the priority queue
-queue: Head of the priority queue
-data: Linked list node for the neighbours of a graph node
-list: Head of the above linked list node
*/
typedef struct graph_node
{
char status;
int index,pred_inf_time,rec_time;
}graph_node;
typedef struct node
{
int time,action;//0 action is recover, 1 is transmit
graph_node u;
}node;
// typedef struct queue
// {
// int size;
// node *head;
// }queue;
typedef struct data
{
int index;
struct data *next;
}data;
typedef struct list
{
data *head;
}list;
node queue[MAX_NODES*MAX_NODES];
void swap(node *a, node *b)
{
node temp = *b;
*b = *a;
*a = temp;
}
/*Function to insert into the linked list containing the neigbours of a graph node*/
void insert(list *l, int index)
{
data *element=(data *)malloc(sizeof(data));
element->index=index;element->next=NULL;
if(l->head==NULL) l->head=element;//If list is empty
else//Insert at end
{
for(data *ptr=l->head;ptr!=NULL;ptr=ptr->next)
{
if(ptr->next==NULL)
{
ptr->next=element;
break;
}
}
}
}
/*Toss a coin with a probability p of landing heads*/
int coinToss(float p)
{
int num=10*p;
int x=rand()%(10);
if(x<num) return 1;//Heads
else return 0;//Tails
}
/*Find the minima of 3 numbers*/
int minima(int x,int y,int z)
{
if(x<y&&x<z) return x;
else if(y<x&&y<z) return y;
else return z;
}
/*Generates a random adjaceny matrix*/
void generateMatrix(int V, bool adjMatrix[V][V],list array[V])
{
for(int i=0;i<V;i++){
int limit=0;
//Lines 102 to 116 randomise the graph formation. Line 118 makes the matrix symmetric
for(int j=i;j<V;j++){
if(i==0)
{
if(!coinToss(0.5)&&limit<MAX_EDGES&&i!=j)
{
adjMatrix[i][j]=true;
limit++;
}
}
else if(!coinToss(0.5)&&limit<MAX_EDGES/2&&i!=j)
{
adjMatrix[i][j]=true;
limit++;
}
else adjMatrix[i][j]=false;
adjMatrix[j][i]=adjMatrix[i][j];
//If the vertex is a neighbour to another vertex, record it in the neighbour linked list
if(adjMatrix[i][j])
{
insert(&array[i],j);
}
}
}
}
/*The graph nodes are maintained in an array. This function initialises the graph*/
void generateGraph(int V, graph_node Graph[V])
{
for(int i=0;i<V;i++){
Graph[i].index=i;
Graph[i].status='S';
Graph[i].pred_inf_time=MAX_TIME+69;
Graph[i].rec_time=0;
}
}
/*Creates a new event in the priority queue*/
node newNode(int time, int action, graph_node u)
{
node new;
new.time=time;new.action=action;new.u=u;
return new;
}
void heapify(node array[], int heap_size, int i) {
//printf("here1\n");
if (heap_size == 1)
{
printf("Single element in the heap");
}
else
{
// Find the largest among root, left child and right child
int smallest = i;
int l = 2 * i + 1;
int r = 2 * i + 2;
if (l < heap_size && array[l].time < array[smallest].time) smallest = l;
if (r < heap_size && array[r].time < array[smallest].time) smallest = r;
// Swap and continue heapifying if root is not largest
if (smallest!=i)
{
swap(&array[i], &array[smallest]);
heapify(array, heap_size, smallest);
}
}
}
/*Inserts a new event in the priority queue*/
void eventInsert(node array[], int time, int action, graph_node u)
{
//printf("here2\n");
node newEvent=newNode(time,action,u);
if (heap_size == 0)
{
array[0] = newEvent;
heap_size += 1;
}
else
{
array[heap_size] = newEvent;
heap_size += 1;
for (int i = heap_size / 2 - 1; i >= 0; i--)
{
heapify(array, heap_size, i);
}
}
}
/*Delete the front of the queue*/
void eventDelete(node array[], int num) {
//printf("here3\n");
int i;
for (i = 0; i < heap_size; i++)
{
if (num == array[i].time) break;
}
swap(&array[i], &array[heap_size - 1]);
heap_size -= 1;
for (int i = heap_size / 2 - 1; i >= 0; i--)
{
heapify(array, heap_size, i);
}
}
/*Extracts front of the queue*/
node extractMin(node array[])
{
//printf("here4\n");
node temp=array[0];
swap(&array[0], &array[heap_size - 1]);
heap_size -= 1;
for (int i = heap_size / 2 - 1; i >= 0; i--) {
heapify(array, heap_size, i);
}
return temp;
}
/*Generating the inital number of infected people*/
void initialInfected(int V,graph_node Graph[V])
{
for(int i=0;i<INITIAL_INFECTED;i++)
{
eventInsert(queue,0,1,Graph[i]);
Graph[i].pred_inf_time=0;
}
}
/*Recovery of a node*/
void process_rec_SIR(int V,graph_node Graph[V],graph_node u)
{
//printf("here5\n");
recovered++;infected--;
int x=u.index;
Graph[x].status='R';
u.status='R';
}
/*Transmit to a node*/
void find_trans_SIR(node array[],int time,graph_node source,graph_node *target)
{
//printf("here6\n");
//If the node is susceptible
if(target->status=='S')
{
//Calculate the recovery time
int inf_time=time;
do{
inf_time++;
}while(!coinToss(TAU));
//Check if the node can get infected
if(inf_time<minima(source.rec_time,target->pred_inf_time,MAX_TIME))
{
graph_node temp=*target;
eventInsert(array,inf_time,1,temp);
target->pred_inf_time=inf_time;
}
}
}
/*Transfer the virus to other nodes*/
void process_trans_SIR(int V,graph_node Graph[V],bool adjMatrix[V][V],node arrayQ[],graph_node u,int time,list array[V])
{
//printf("here7\n");
susceptible--;infected++;
int x=u.index;
//Calculate the recovery time for the source node
int recovery=time;
do{
recovery++;
}while(!coinToss(GAMMA));
u.rec_time=recovery;
Graph[x].rec_time=recovery;
Graph[x].status='I';
//If the node can recover
if(Graph[x].rec_time<MAX_TIME)
{
graph_node temp=Graph[x];
eventInsert(arrayQ,recovery,0,temp);
}
//Traverse the neighbour linked list
data *ptr=array[x].head;
while(ptr)
{
int i=ptr->index;
//Transfer the virus to the neighbour
find_trans_SIR(arrayQ,time,u,&Graph[i]);
ptr=ptr->next;
}
}
/*Simulate the epidemic*/
void fast_SIR(int V,graph_node Graph[V],bool adjMatrix[V][V],list array[V])
{
susceptible=V;infected=0;recovered=0;
S[0]=V;I[0]=0;R[0]=0;
//Create the queue of initially infected people
initialInfected(V,Graph);
//While queue is not empty
while(heap_size>0)
{
//Update S,I,R according to the day
while(day<queue[0].time)
{
S[day]=susceptible;
I[day]=infected;
R[day]=recovered;
day++;
}
//If the earliest event is a transmit event
if(queue[0].action==1)
{
//If the node is susceptible
if(queue[0].u.status=='S'&&susceptible>0&&infected<MAX_NODES)
{
process_trans_SIR(V,Graph,adjMatrix,queue,queue[0].u,queue[0].time,array);
}
}
//If the event is recovery
else if(recovered<MAX_NODES&&infected>0)
{
process_rec_SIR(V,Graph,queue[0].u);
}
extractMin(queue);
}
}
int main()
{
srand(time(NULL));
int V=MAX_NODES;
//Graph array
graph_node Graph[V];
//Array of linked lists(of neighbours)
list array[V];
for(int i=0;i<V;i++)
{
(array[i].head)=NULL;
}
/*Initialise all the required data structures*/
generateMatrix(V,adjGraph,array);
printf("\nAdjacency Matrix generated\n");
generateGraph(V,Graph);
printf("Graph generated\n\n");
/*Start the simulation*/
fast_SIR(V,Graph,adjGraph,array);
/*The epidemic is considered done when all infected patients have been cured*/
int i;
for (i=0;i<MAX_TIME; ++i){
if(I[i]==0&&I[i+1]==0) break;
}
i++;
//Updating the lists
if(i>1) S[i-1]=S[i-2];
else if(i) S[i-1]--;
R[i-1]=R[i-2]+1;
/*The epidemic is considered done when all infected patients have been cured*/
printf("The epidemic is simulated for a population of %d.On day 0, %d person/people get infected\n",MAX_NODES,INITIAL_INFECTED);
for(int j=0;j<i;j++)
{
printf("Day %d\n", j);
printf("S: %d\n", S[j]);
printf("I: %d\n", I[j]);
printf("R: %d\n", R[j]);
printf("\n");
}
printf("The epidemic ends after %d days\n", i-1);
printf("\n");
}