Submission #387730

#	Time	Username	Problem	Language	Result	Execution time	Memory
387730		8e7	Cheerleaders (info1cup20_cheerleaders)	C++14	100 / 100	1560 ms	10180 KiB

cheerleaders

//Challenge: Accepted
#include <iostream>
#include <algorithm>
#include <vector>
#include <utility>
#define ll long long
#define maxn 150005
#define pii pair<int, int>
#define ff first
#define ss second
#define io ios_base::sync_with_stdio(0);cin.tie(0);
using namespace std;
//#include <bits/extc++.h>
//using namespace __gnu_pbds;
//template<class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
//find by order, order of key
int a[maxn];

int bit[maxn], shift[17][maxn];
void modify(int ind, int val) {
	for (;ind < maxn;ind += ind & (-ind)) bit[ind] += val;
}
int query(int ind) {
	int ret = 0;
	for (;ind > 0;ind -= ind & (-ind)) ret += bit[ind];
	return ret;
}

ll solve(int pos, int type, int n) {
	ll ret = 0;
	type = n - 1 - type;
	int dif = (pos - type + n) % n;
	//cout << "   " << dif << endl;
	for (int i = 0;i < (1<<(n - 1 - type));i++) {
		for (int j = 0;j < (1<<type);j++) {
			int ind = shift[dif][(i<<(type+1)) + j];
			//cout << ind << endl;
			modify(a[ind], 1);
		}
		for (int j = 0;j < (1<<type);j++) {
			int ind = shift[dif][(i<<(type+1)) + (1<<type) + j];
			//cout << " " << ind << endl;
			ret += query(a[ind]);
		}
		for (int j = 0;j < (1<<type);j++) {
			int ind = shift[dif][(i<<(type+1)) + j];
			modify(a[ind], -1);
		}
	}
	return ret;
}
int main() {
	io

	int n;
	cin >> n;
	for (int i = 0;i < (1<<n);i++) {
		cin >> a[i], a[i]++;
		shift[0][i] = i;
		int tmp = i;
		//cout << tmp << " ";
		for (int j = 1;j < n;j++) {
			//cout << (tmp & (1<<(n - 1))) << endl;
			int b = (tmp & (1<<(n - 1))) ? 1 : 0;
			tmp -= (tmp & (1<<(n - 1)));
			tmp = (tmp<<1) + b;
			shift[j][i] = tmp;
			//cout << shift[j][i] << " ";
		}
		//cout << endl;
	}
	/*
	int op;
	while (cin >> op) {
		if (op == 1) {
			for (int i = 0;i < (1<<(n - 1));i++) swap(a[i], a[i + (1<<(n - 1))]);
		} else {
			int b[1<<n];
			for (int i = 0;i < (1<<n);i += 2) b[i / 2] = a[i];
			for (int i = 1;i < (1<<n);i += 2) b[i / 2 + (1<<(n - 1))] = a[i];
			for (int i = 0;i < (1<<n);i++) a[i] = b[i];
		}
		for (int i = 0;i < (1<<n);i++) cout << a[i] << " ";
		cout << endl;
	}
	*/
	ll best = 0;
	int bind = 0, bp = 0;
	for (int p = 0;p < n;p++) { //position of the highest bit is p
		ll val = 0;
		int num = 0;
		for (int t = 0;t < n;t++) {
			ll z = solve((p - t + n) % n, t, n);
			ll o = (1LL<<t) * (1LL<<(n - 1 - t)) * (1LL<<(n - 1 - t)) - z;
			//cout << t << " " << z << " " << o << endl;
			val += max(z, o);
			num<<=1;
			if (o > z) {
				num += 1;
			}
		}
		//cout << p << " " << num << " " << val << endl;
		if (val > best) {
			best = val;
			bind = num, bp = p;
		}
	}
	//cout << best << endl;
	int tot = 1<<n;
	cout << (ll)tot * (tot - 1) / 2 - best << "\n";

	if (n) {
		bind = shift[(bp + 1) % n][bind];
		cout << 2;
		for (int i = 0;i < n;i++) {
			if (bind & (1<<i)) cout << 1;
			cout << 2;
		}
		for (int i = 0;i < bp;i++) cout << 2;
		cout << endl;
	}

}
/*
2
0 3 1 2

3
2 3 7 6 1 4 5 0

4
1 4 8 5 3 6 12 13 10 11 2 9 14 0 15 7
 */

• Subtask 1: 16 / 16
• Subtask 2: 10 / 10
• Subtask 3: 25 / 25
• Subtask 4: 21 / 21
• Subtask 5: 28 / 28