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bin_heap.cpp
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bin_heap.cpp
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/*
* bin_heap.cpp
*
* Created on: 7 Oct 2021
* Author: mndx
*/
#include <iostream>
#include <math.h>
#include <vector>
#include "memory.hpp"
#include "user_types.hpp"
Heap::Heap(int size) {
heap_size = size;
A = new node*[size+1];
heap_ref = new node*[size+1];
element_map = new int[size+1];
size_array = size + 1;
element_map[0] = 0;
for(int i = 1; i <= heap_size; ++i) {
element_map[i] = i;
A[i] = new node;
A[i]->pi = NULL;
}
}
Heap::~Heap() {
delete [] A;
delete [] heap_ref;
delete [] element_map;
}
int Heap::parent(int i) {
return i/2;
}
int Heap::left(int i) {
return 2*i;
}
int Heap::right(int i) {
return 2*i + 1;
}
node* Heap::get_heap_element(int node_index) {
return heap_ref[node_index];
}
int Heap::get_heap_index(int node_index) {
int index_in_heap = element_map[node_index];
return index_in_heap;
}
int Heap::get_root_index() {
return A[1]->index;
}
void Heap::min_heapify(node* A[], int i) {
int l, r, smallest;
l = Heap::left(i);
r = Heap::right(i);
if(l < heap_size + 1 && A[l]->key < A[i]->key) {
smallest = l;
}
else {
smallest = i;
}
if(r < heap_size + 1 && A[r]->key < A[smallest]->key) {
smallest = r;
}
if(smallest != i) {
node* dummy;
dummy = A[i];
element_map[A[smallest]->index] = i;
element_map[A[i]->index] = smallest;
A[i] = A[smallest];
A[smallest] = dummy;
Heap::min_heapify(A, smallest);
}
}
void Heap::build_min_heap() {
for(int i = heap_size/2; i > 0; --i) {
Heap::min_heapify(A, i);
}
}
void Heap::set_heap(node* B[]) {
for(int i = 1; i < heap_size + 1; ++i) {
A[i] = B[i];
heap_ref[i] = A[i];
}
}
int Heap::get_heap_size() {
return heap_size;
}
node* Heap::heap_extract_min() {
if(heap_size < 1) {
std::cout << "heap size is less than 1" << std::endl;
}
node* min = A[1];
element_map[A[heap_size]->index] = 1;
A[1] = A[heap_size];
heap_size = heap_size - 1;
Heap::min_heapify(A, 1);
return min;
}
void Heap::heap_decrease_key(int index, double key) {
if(key > A[index]->key) {
printf("new key is larger than current key\n");
}
else {
A[index]->key = key;
while(index > 1 && A[parent(index)]->key > A[index]->key) {
element_map[A[index]->index] = parent(index);
element_map[A[parent(index)]->index] = index;
node* dummy = A[index];
A[index] = A[parent(index)];
A[parent(index)] = dummy;
index = parent(index);
}
}
}
void relax(node* u, node* v, int** w, Heap* heap) {
int index_in_heap = heap->get_heap_index(v->index);
if(v->key > u->key + w[u->index][v->index]) {
int weight = u->key + w[u->index][v->index];
heap->heap_decrease_key(index_in_heap, weight);
v->pi = u;
}
}
int map_index2(int n, int index, int s) {
int r;
if(index >= s) { r = index - s + 1; }
else { r = n - s + index + 1; }
return r;
}
int map_inverse2(int n, int index, int s) {
int r;
r = s + index - 1;
if(r > n) {
r = r - n;
}
return r;
}
void set_weight_and_heap_refs(int size_graph,
std::vector< std::vector<int> > &edges,
int s,
Heap& min_heap,
int** weight_mat,
node** node_refs) {
//Initialize node references
for(int i = 1; i < size_graph + 1; ++i) {
node_refs[i] = new node;
node_refs[i]->key = INF;
node_refs[i]->pi = NULL;
node_refs[i]->index = i;
node_refs[i]->index_og = map_inverse2(size_graph, i, s);
}
//Initializing start vertex
node_refs[1]->key = 0;
//Set and build heap
min_heap.set_heap(node_refs);
min_heap.build_min_heap();
//Set weight matrix
int num_edges = (int) edges.size();
for(int i = 0; i < num_edges; ++i) {
int start_index = edges[i][0];
int end_index = edges[i][1];
int weight = edges[i][2];
int start = map_index2(size_graph, start_index, s);
int end = map_index2(size_graph, end_index, s);
node_refs[start]->adj_nodes.push_back(end);
node_refs[end]->adj_nodes.push_back(start);
weight_mat[start][end] = weight;
weight_mat[end][start] = weight;
}
//Traverse edges again to pick minimum weights
for(int i = 0; i < num_edges; ++i) {
int start_index = edges[i][0];
int end_index = edges[i][1];
int weight = edges[i][2];
int start = map_index2(size_graph, start_index, s);
int end = map_index2(size_graph, end_index, s);
if(weight_mat[start][end] >= weight) {
weight_mat[start][end] = weight;
weight_mat[end][start] = weight;
}
}
}
void dijkstra(Heap* min_heap, int** weight_mat) {
//Perform Dijkstra's algorithm
int heap_size = min_heap->get_heap_size();
while(heap_size > 0) {
node* u = min_heap->heap_extract_min();
heap_size = min_heap->get_heap_size();
int num_adj_nodes = (int) u->adj_nodes.size();
for(int i = 0; i < num_adj_nodes; ++i) {
int it = u->adj_nodes[i];
node* v = min_heap->get_heap_element(it);
relax(u, v, weight_mat, min_heap);
}
}
}
void reorder_results_bin(int n, int s, node** node_refs, std::vector<int>& results) {
for(int i = 1; i <= n; ++i) {
int index = map_index2(n, i, s);
if(node_refs[index]->index_og != s) {
int key = node_refs[index]->key;
if(key == INF) { key = -1; }
results.push_back(key);
}
}
}
std::vector<int> shortest_reach2(int n, std::vector< std::vector<int> > &edges, int s) {
std::vector<int> results;
//Initialize weight and adjacency matrices and binary min heap
Heap min_heap(n);
node** node_refs = new node*[n + 1];
int** weight_mat = int2D(n + 1);
//Populate weight matrix and initialize heap and heap references
set_weight_and_heap_refs(n, edges, s, min_heap, weight_mat, node_refs);
//Perform Dijkstra's algorithm
dijkstra(&min_heap, weight_mat);
//Reorder results
reorder_results_bin(n, s, node_refs, results);
//Deallocate memory
free_int2D(weight_mat, n + 1);
free_node_ref_bin(node_refs, n + 1);
return results;
}