Implementing Dijkstra's algorithm with C++ STL - stl

Question

I have implemented the Dijkstra's algorithm as follows
#include <iostream>
#include <bits/stdc++.h>
#include<cstdio>
#define ll long long int
#define mod 1000000007
#define pi 3.141592653589793
#define f first
#define s second
#define pb push_back
#define pf push_front
#define pob pop_back
#define pof pop_front
#define vfor(e, a) for (vector<ll> :: iterator e = a.begin(); e != a.end(); e++)
#define vfind(a, e) find(a.begin(), a.end(), e)
#define forr(i, n) for (ll i = 0; i < n; i++)
#define rfor(i, n) for (ll i = n - 1; i >= 0; i--)
#define fors(i, b, e, steps) for(ll i = b; i < e; i += steps)
#define rfors(i, e, b, steps) for(ll i = e; i > b; i -= steps)
#define mp make_pair
using namespace std;
void up(pair<ll, ll> a[], ll n, ll i, ll indArray[]) {
ll ind = (i - 1) / 2;
while (ind >= 0 && a[ind].s > a[i].s) {
swap(a[ind], a[i]);
indArray[a[ind].f] = ind;
indArray[a[i].f] = i;
i = ind;
ind = (i - 1) / 2;
}
}
void down(pair<ll, ll> a[], ll n, ll i, ll indArray[]) {
ll left = 2 * i + 1;
ll right = 2 * i + 2;
ll m = a[i].s;
ll ind = i;
if (left < n && a[left].s < m) {
ind = left;
m = a[left].s;
}
if (right < n && a[right].s < m) {
ind = right;
}
if (ind != i) {
swap(a[i], a[ind]);
indArray[a[i].f] = i;
indArray[a[ind].f] = ind;
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
// cout << setprecision(10);
ll n, m;
cin >> n >> m;
vector<pair<ll, ll>> a[n];
forr(i, m) {
ll u, v, w;
cin >> u >> v >> w;
a[u].pb(mp(v, w));
a[v].pb(mp(u, w));
}
ll parent[n];
parent[0] = -1;
pair<ll, ll> dist[n];
forr(i, n) {
dist[i] = mp(i, INT_MAX);
}
dist[0].s = 0;
ll ind[n];
iota(ind, ind + n, 0);
ll ans[n];
ans[0] = 0;
bool visited[n];
fill(visited, visited + n, false);
ll size = n;
forr(i, n) {
ll u = dist[0].f;
visited[u] = true;
ll d1 = dist[0].s;
ans[u] = dist[0].s;
swap(dist[0], dist[size - 1]);
size--;
down(dist, size, 0, ind);
for (auto e : a[u]) {
if (visited[e.f]){
continue;
}
ll v = e.f;
ll j = ind[v];
if (dist[j].s > d1 + e.s) {
dist[j].s = d1 + e.s;
up(dist, size, j, ind);
parent[v] = u;
}
}
}
stack<ll> st;
forr(i, n) {
ll j = i;
while (j != -1) {
st.push(j);
j = parent[j];
}
while (!st.empty()) {
cout << st.top() << "->";
st.pop();
}
cout << " Path length is " << ans[i];
cout << '\n';
}
}
This implementation is correct and giving correct output.
As it can be seen every time I select the node with lowest key value(distance from source) and then I update the keys on all the adjacent nodes of the selected node. After updating the keys of the adjacent nodes I am calling the 'up' function as to maintain the min heap properties. But priority queue is present in the c++ stl. How can I use them to avoid the functions up and down.
The thing is I need to be able to find the index of the node-key pair in the mean heap whose key needs to be updated. Here in this code I have used a seperate ind array which is updated every time the min heap is updated.
But how to make use of c++ stl

Answer 1

Like you implied, we cannot random-access efficiently with std::priority_queue. For this case I would suggest that you use std::set. It is not actually a heap but a balanced binary search tree. However it works the desired way you wanted. find, insert and erase methods are all O(log n) so you can insert/erase/update a value with desired time since update can be done with erase-then-insert. And accessing minimum is O(1).
You may refer to this reference implementation like the exact way I mentioned. With your adjacency list, the time complexity is O(E log V) where E is number of edges, V is number of vertices.
And please note that
With default comparator, std::set::begin() method returns the min element if non-empty
In this code, it puts the distance as first and index as second. By doing so, the set elements are sorted with distance in ascending order
% I did not look into the implementation of up and down of your code in detail.