1747 - Pyramid Array.cpp

/*
Problem Name: Pyramid Array
Problem Link: https://cses.fi/problemset/task/1747
Author: Sachin Srivastava (mrsac7)
*/
#include<bits/stdc++.h>
using namespace std;
 
#define int long long
#define endl '\n'
 
const int mxN = 200005;
int bit[mxN];
void upd(int k) {
    for (; k < mxN; k += k&-k)
        bit[k] += 1;
}
int qry(int k) {
    int sm = 0;
    for (; k > 0; k -= k&-k)
        sm += bit[k];
    return sm;
}
 
signed main(){
    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    #ifdef LOCAL
    freopen("input.txt", "r" , stdin);
    freopen("output.txt", "w", stdout);
    #endif
    
    int n; cin>>n;
    int a[n];
    //index compression
    map<int,int> mp;
    vector<int> v;
    for (int i = 0; i < n; i++) {
        cin>>a[i];
        v.push_back(a[i]);
    }
    sort(v.begin(), v.end());
    int ct = 0;
    for (auto i: v)
        mp[i] = ++ct;
 
    int inv[n] = {0};
    for (int i = n-1; i >= 0; i--) {
        inv[i] = qry(ct) - qry(mp[a[i]]);
        upd(mp[a[i]]);
    }
    memset(bit, 0, sizeof bit);
    int ans = 0;
    //position of element is decided by the number of inversions
    //i.e. whether inversions are less on left or right
    for (int i = 0; i < n; i++) {
        int x = qry(ct) - qry(mp[a[i]]);
        upd(mp[a[i]]);
        ans += min(x, inv[i]);
    }
    cout<<ans;
}