heap sort

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<string,int> psi;
typedef priority_queue<int> pqmax;
typedef priority_queue<int,vector<int>,greater<int>> pqmin;
typedef unordered_map<int,int> mii;
typedef unordered_map<long long,long long> mll;
typedef unordered_map<string,int> msi;
typedef unordered_map<char,int> mci;
typedef unordered_set<int> si;
typedef unordered_set<long long> sll;
typedef unordered_set<string> ss;
typedef unordered_set<char> sc;
typedef map<int,int> ormii;
typedef map<long long,long long> ormll;
typedef map<string,int> ormsi;
typedef map<char,int> ormci;
typedef set<int> orsi;
typedef set<long long> orsll;
typedef set<string> orss;
typedef set<char> orsc;
typedef vector<int> vi;
typedef vector<string> vs;
typedef vector<char> vc;
typedef vector<ll> vll;
typedef vector<vector<int>> vvi;
typedef vector<vector<string>> vvs;
typedef vector<vector<ll>> vvll;

#define FOR(i, a, b) for (auto i=a; i<=(b); i++)
#define FORd(i,b,a) for (int i =b; i >= a; i--)
#define sortinc(v)  sort(v.begin(),v.end())
#define sortdec(v)  sort(v.rbegin(),v.rend())
#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define pob pop_back
#define pf push_front
#define pof pop_front
#define fi first
#define se second
#define ins insert

const int MOD = 1000000007;
void Heapify(vi &v,int n,int i)
{
    int l=2*i+1,r=2*i+2,largest=i;
    if(l<n&&v[l]>largest) largest=l;
    if(r<n&&v[r]>largest) largest=r;
    if(largest!=i) swap(v[i],v[largest]);
}
void HS(vi &v,int n)
{
    //building heap for the internal unordered_set
    FORd(i,(n/2)-1,0)
    Heapify(v,n,i);
    //so now max element is at top of heap
    FORd(i,n-1,0)
    {
        swap(v[i],v[0]);
        Heapify(v,i,0);
    }
}
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int tc=1;
    //cin>>tc;
    FOR(w,1,tc)
    {
       vi v={4,2,1,9};
       int n=sz(v);
       HS(v,n);
       FOR(i,0,n-1)
       cout<<v[i]<<" ";
    }
    return 0;
}