Usage of vector push_back with pair - c++

Question

I was looking at the implementation of Prim's Algorithim on geeksforgeeks.org and tried to implement the function on practice mode. I looked at how the input was received and I saw this:
#include<bits/stdc++.h>
using namespace std;
const int MAX = 1e4 + 5;
int spanningTree(vector <pair<int,int> > g[], int n);
int main()
{
int t ;
cin>>t;
while(t--)
{
vector <pair<int,int> > adj[MAX];
int n,e;
int w, mC;
cin >> n>> e;
for(int i = 0;i < e;++i)
{
int x,y;
cin >> x >> y >> w;
adj[x].push_back({w, y});
adj[y].push_back({w, x});
}
mC= spanningTree(adj, MAX);
cout << mC << endl;
}
return 0;
}
I'm having a lot of trouble understanding how they're using vector. I've never seen the passing of a vector in a similar way to an array: vector <pair<int,int> > g[].
I looked at the STD implementation of vector and couldn't find anything about passing a vector this way, or constructing a vector with vector <pair<int,int> > adj[MAX];.
Lastly, I am very confused about what the following code does:
adj[x].push_back({w, y});
adj[y].push_back({w, x});
I tried implementing it myself:
#include <iostream>
#include <vector>
#include <utility>
#include <string>
using namespace std;
int main()
{
vector< pair<string, int> > vec[2];
vec[0].push_back({"One", 1});
vec[1].push_back({"Two", 2});
for(int x = 0; x < 2; ++x){
cout << vec[x].first << ", " << vec[x].second << endl;
}
return 0;
}
But I get an error class 'std::vector< pair<string, int> >' has no member named ‘first’.
If I could have some help understanding how vector is being used here, I would really appreciate it. I looked at multiple StackOverflow posts already, including vector::push_back vs vector::operator[].
The link to the original problem is here

Answer 1

I've never seen the passing of a vector in a similar way to an array: vector <pair<int,int> > g[]
It is an array! An array of vectors.
The problem with your code is that you have two vectors, both with a single element, and your loop only pulls out the vectors... not their single element.
Your version would be:
#include <iostream>
#include <vector>
#include <utility>
#include <string>
using namespace std;
int main()
{
vector< pair<string, int> > vec[2];
vec[0].push_back({"One", 1});
vec[1].push_back({"Two", 2});
for(int x = 0; x < 2; ++x){
cout << vec[x][0].first << ", " << vec[x][0].second << endl;
}
return 0;
}
All I added was [0] (index into each vector).
Of course such an example is of questionable practicality. In such a situation it would seem that you want one vector with two elements, and no arrays in sight.
To be honest, I'm not wild about the original code, either. Mixing arrays and vectors is a recipe for confusion (hyello); they could have used "2D vectors" or, better, a 1D vector with 2D indexes laid on top of it. That would then have much better cache locality as well.

Answer 2

Its' a C-style array of vectors, really nothing magic here.
int spanningTree(vector <pair<int,int> > g[], int n);
Maybe you have seen something like that before:
int foo( int array[], int n);
In their code, the elements of the array are not ints but std::vectors. Why they mix plain arrays and std::vector I cannot tell you.
In your example, you need to first use operator[] to access an element before you can access its .first and .second, or use front to get the first element:
for(int x = 0; x < 2; ++x){
cout << vec[x].front().first << ", " << vec[x].front().second << endl;
}