Submission #749760

#	Time	Username	Problem	Language	Result	Execution time	Memory
749760		SanguineChameleon	Alice, Bob, and Circuit (APIO23_abc)	C++17	100 / 100	681 ms	291364 KiB

abc

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

// you may find the definitions useful
const int OP_ZERO    = 0;  // f(OP_ZERO,    x0, x1) = 0
const int OP_NOR     = 1;  // f(OP_NOR,     x0, x1) = !(x0 || x1)
const int OP_GREATER = 2;  // f(OP_GREATER, x0, x1) = (x0 > x1)
const int OP_NOT_X1  = 3;  // f(OP_NOT_X1,  x0, x1) = !x1
const int OP_LESS    = 4;  // f(OP_LESS,    x0, x1) = (x0 < x1)
const int OP_NOT_X0  = 5;  // f(OP_NOT_X0,  x0, x1) = !x0
const int OP_XOR     = 6;  // f(OP_XOR,     x0, x1) = (x0 ^ x1)
const int OP_NAND    = 7;  // f(OP_NAND,    x0, x1) = !(x0 && x1)
const int OP_AND     = 8;  // f(OP_AND,     x0, x1) = (x0 && x1)
const int OP_EQUAL   = 9;  // f(OP_EQUAL,   x0, x1) = (x0 == x1)
const int OP_X0      = 10; // f(OP_X0,      x0, x1) = x0
const int OP_GEQ     = 11; // f(OP_GEQ,     x0, x1) = (x0 >= x1)
const int OP_X1      = 12; // f(OP_X1,      x0, x1) = x1
const int OP_LEQ     = 13; // f(OP_LEQ,     x0, x1) = (x0 <= x1)
const int OP_OR      = 14; // f(OP_OR,      x0, x1) = (x0 || x1)
const int OP_ONE     = 15; // f(OP_ONE,     x0, x1) = 1

int encode(string s) {
	int res = 0;
	for (auto c: s) {
		res = res * 26 + (c - 'a');
	}
	int pw = 1;
	for (int i = 1; i <= (int)s.size() - 1; i++) {
		pw = pw * 26;
		res += pw;
	}
	return res;
}

vector<int> build(vector<int> a) {
	int n = a.size();
	if (n <= 1) {
		return vector<int>();
	}
	vector<int> pos(n);
	for (int i = 0; i < n; i++) {
		pos[a[i]] = i;
	}
	vector<vector<pair<int, int>>> adj(n);
	vector<int> swap1(n / 2, -1);
	vector<int> swap2(n / 2, -1);
	for (int i = 0; i < n / 2; i++) {
		int x = pos[i];
		int y = pos[n / 2 + i];
		if (n % 2 == 1 && (x == n - 1 || y == n - 1)) {
			continue;
		}
		int u = (x < n / 2 ? x : x - n / 2);
		int v = (y < n / 2 ? y : y - n / 2);
		int w = (x < n / 2) ^ (y < n / 2) ^ 1;
		adj[u].emplace_back(v, w);
		adj[v].emplace_back(u, w);
	}
	if (n % 2 == 1 && pos[n - 1] != n - 1) {
		int cur = (pos[n - 1] < n / 2 ? pos[n - 1] : pos[n - 1] - n / 2);
		swap1[cur] = (pos[n - 1] < n / 2);
		while (true) {
			bool found = false;
			for (auto e: adj[cur]) {
				int nxt = e.first;
				int w = e.second;
				if (swap1[nxt] == -1) {
					swap1[nxt] = swap1[cur] ^ w;
					cur = nxt;
					found = true;
					break;
				}
			}
			if (!found) {
				break;
			}
		}
	}
	for (int i = 0; i < n / 2; i++) {
		if (swap1[i] == -1) {
			int cur = i;
			swap1[cur] = 0;
			while (true) {
				bool found = false;
				for (auto e: adj[cur]) {
					int nxt = e.first;
					int w = e.second;
					if (swap1[nxt] == -1) {
						swap1[nxt] = swap1[cur] ^ w;
						cur = nxt;
						found = true;
						break;
					}
				}
				if (!found) {
					break;
				}
			}
		}
	}
	vector<int> al(a.begin(), a.begin() + n / 2);
	vector<int> ar(a.begin() + n / 2, a.end());
	for (int i = 0; i < n / 2; i++) {
		if (swap1[i]) {
			swap(al[i], ar[i]);
		}
	}
	for (int i = 0; i < n / 2; i++) {
		if (al[i] < n / 2) {
			swap2[al[i]] = 0;
		}
		else {
			al[i] -= n / 2;
			swap2[al[i]] = 1;
		}
	}
	for (int i = 0; i < n - n / 2; i++) {
		if (ar[i] >= n / 2) {
			ar[i] -= n / 2;
		}
	}
	vector<int> fl = build(al);
	vector<int> fr = build(ar);
	vector<int> res(swap1.begin(), swap1.end());
	res.insert(res.end(), fl.begin(), fl.end());
	res.insert(res.end(), fr.begin(), fr.end());
	res.insert(res.end(), swap2.begin(), swap2.end());
	return res;
}

int calc(int n) {
	if (n <= 1) {
		return 0;
	}
	return calc(n / 2) + calc(n - n / 2) + (n / 2) * 2;
}

// Alice
int // returns la
alice(
	/*  in */ const int n,
	/*  in */ const char names[][5],
	/*  in */ const unsigned short numbers[],
	/* out */ bool outputs_alice[]
) {
	vector<pair<int, int>> order(n);
	for (int i = 0; i < n; i++) {
		order[i] = make_pair(encode(names[i]), i);
	}
	sort(order.begin(), order.end());
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < 19; j++) {
			outputs_alice[i * 35 + j] = (order[i].first >> j) & 1;
		}
		for (int j = 0; j < 16; j++) {
			outputs_alice[i * 35 + 19 + j] = (numbers[order[i].second] >> j) & 1;
		}
	}
	vector<int> perm(n);
	for (int i = 0; i < n; i++) {
		perm[i] = order[i].second;
	}
	vector<int> flag = build(perm);
	int sz = flag.size();
	for (int i = 0; i < sz; i++) {
		outputs_alice[n * 35 + i] = flag[i];
	}
	return n * 35 + sz;
}


// Bob
int // returns lb
bob(
	/*  in */ const int m,
	/*  in */ const char senders[][5],
	/*  in */ const char recipients[][5],
	/* out */ bool outputs_bob[]
) {
	vector<pair<int, int>> order1(m);
	for (int i = 0; i < m; i++) {
		order1[i] = make_pair(encode(recipients[i]), encode(senders[i]));
	}
	sort(order1.begin(), order1.end());
	vector<pair<pair<int, int>, int>> order2(m);
	for (int i = 0; i < m; i++) {
		order2[i] = make_pair(make_pair(order1[i].second, order1[i].first), i);
	}
	sort(order2.begin(), order2.end());
	for (int i = 0; i < m; i++) {
		for (int j = 0; j < 19; j++) {
			outputs_bob[i * 38 + j] = (order2[i].first.first >> j) & 1;
		}
		for (int j = 0; j < 19; j++) {
			outputs_bob[i * 38 + 19 + j] = (order2[i].first.second >> j) & 1;
		}
	}
	vector<int> perm(m);
	for (int i = 0; i < m; i++) {
		perm[i] = order2[i].second;
	}
	vector<int> flag = build(perm);
	int sz = flag.size();
	for (int i = 0; i < sz; i++) {
		outputs_bob[m * 38 + i] = flag[i];
	}
	return m * 38 + sz;
}

int *operations;
int (*operands)[2];
int ZERO_GATE;
int ONE_GATE;
int gate_cnt;

int gate(int op, int x, int y) {
	operations[gate_cnt] = op;
	operands[gate_cnt][0] = x;
	operands[gate_cnt][1] = y;
	return gate_cnt++;
}

pair<int, int> add(int x, int y, int z) {
	int sum1 = gate(OP_XOR, x, y);
	int rem1 = gate(OP_AND, x, y);
	int sum2 = gate(OP_XOR, sum1, z);
	int rem2 = gate(OP_AND, sum1, z);
	return make_pair(sum2, gate(OP_OR, rem1, rem2));
}

vector<int> add(vector<int> num1, vector<int> num2) {
	vector<int> res(16);
	int rem = ZERO_GATE;
	for (int i = 0; i < 16; i++) {
		auto p = add(num1[i], num2[i], rem);
		res[i] = p.first;
		rem = p.second;
	}
	return res;
}

vector<int> mul(vector<int> num, int x) {
	vector<int> res(16);
	for (int i = 0; i < 16; i++) {
		res[i] = gate(OP_AND, num[i], x);
	}
	return res;
}

vector<int> mul_flip(vector<int> num, int x) {
	vector<int> res(16);
	for (int i = 0; i < 16; i++) {
		res[i] = gate(OP_GREATER, num[i], x);
	}
	return res;
}

vector<int> _xor(vector<int> num1, vector<int> num2) {
	vector<int> res(16);
	for (int i = 0; i < 16; i++) {
		res[i] = gate(OP_XOR, num1[i], num2[i]);
	}
	return res;
}

struct event {
	int type;
	bool fake;
	vector<int> name1, name2, val;

	event(): type(-1), fake(true) {};
};

vector<event> events;
vector<pair<int, int>> swaps;
vector<int> flag;

void build(int lt, int rt) {
	int n = rt - lt + 1;
	if (n <= 1) {
		return;
	}
	for (int i = 0; i < n / 2; i++) {
		swaps.emplace_back(lt + i, lt + n / 2 + i);
	}
	build(lt, lt + n / 2 - 1);
	build(lt + n / 2, rt);
	for (int i = 0; i < n / 2; i++) {
		swaps.emplace_back(lt + i, lt + n / 2 + i);
	}
}

void swap(int &x, int &y, int f) {
	int z = gate(OP_AND, gate(OP_XOR, x, y), f);
	x = gate(OP_XOR, x, z);
	y = gate(OP_XOR, y, z);
}

int comp(int x, int y) {
	if (events[y].fake) {
		return ZERO_GATE;
	}
	if (events[x].fake) {
		return ONE_GATE;
	}
	int equal = ONE_GATE;
	int res = ZERO_GATE;
	for (int i = 18; i >= 0; i--) {
		res = gate(OP_OR, res, gate(OP_AND, equal, gate(OP_GREATER, events[x].name1[i], events[y].name1[i])));
		equal = gate(OP_AND, equal, gate(OP_EQUAL, events[x].name1[i], events[y].name1[i]));
	}
	res = gate(OP_OR, res, gate(OP_AND, equal, gate(OP_GREATER, events[x].type, events[y].type)));
	equal = gate(OP_AND, equal, gate(OP_EQUAL, events[x].type, events[y].type));
	return res;
}

void shuffle() {
	int sz = swaps.size();
	for (int i = 0; i < sz; i++) {
		int x = swaps[i].first;
		int y = swaps[i].second;
		if (flag[i] == -1) {
			flag[i] = comp(x, y);
		}
		if (flag[i] == ZERO_GATE) {
			continue;
		}
		if (flag[i] == ONE_GATE) {
			swap(events[x], events[y]);
			continue;
		}
		for (int j = 0; j < 19; j++) {
			swap(events[x].name1[j], events[y].name1[j], flag[i]);
			swap(events[x].name2[j], events[y].name2[j], flag[i]);
		}
		for (int j = 0; j < 16; j++) {
			swap(events[x].val[j], events[y].val[j], flag[i]);
		}
		swap(events[x].type, events[y].type, flag[i]);
	}
}

void merge(int x, int y, int step) {
	if (x + step == y) {
		swaps.emplace_back(x, y);
		return;
	}
	merge(x, y, step * 2);
	merge(x + step, y + step, step * 2);
	x += step;
	while (x + step < 2048) {
		swaps.emplace_back(x, x + step);
		x += step * 2;
	}
}

// Circuit
int // returns l
circuit(
	/*  in */ const int la,
	/*  in */ const int lb,
	/* out */ int _operations[],
	/* out */ int _operands[][2],
	/* out */ int outputs_circuit[][16]
) {
	operations = _operations;
	operands = _operands;
	gate_cnt = la + lb;
	ZERO_GATE = gate(OP_ZERO, 0, 0);
	ONE_GATE = gate(OP_ONE, 0, 0);
	int n = 0;
	while (n * 35 + calc(n) < la) {
		n++;
	}
	int m = 0;
	while (m * 38 + calc(m) < lb) {
		m++;
	}
	events.resize(2048);
	for (int i = 0; i < n; i++) {
		events[i].name1.resize(19);
		events[i].name2.resize(19);
		events[i].val.resize(16);
		for (int j = 0; j < 19; j++) {
			events[i].name1[j] = i * 35 + j;
			events[i].name2[j] = i * 35 + j;
		}
		for (int j = 0; j < 16; j++) {
			events[i].val[j] = i * 35 + 19 + j;
		}
		events[i].type = ZERO_GATE;
		events[i].fake = false;
	}
	for (int i = 0; i < m; i++) {
		events[1024 + i].name1.resize(19);
		events[1024 + i].name2.resize(19);
		events[1024 + i].val.resize(16, ZERO_GATE);
		for (int j = 0; j < 19; j++) {
			events[1024 + i].name1[j] = la + i * 38 + j;
			events[1024 + i].name2[j] = la + i * 38 + 19 + j;
		}
		events[1024 + i].type = ONE_GATE;
		events[1024 + i].fake = false;
	}
	merge(0, 1024, 1);
	flag.resize(swaps.size(), -1);
	shuffle();
	vector<int> cur(16, ZERO_GATE);
	for (int i = 0; i < n + m; i++) {
		cur = _xor(cur, mul_flip(_xor(cur, events[i].val), events[i].type));
		events[i].val = cur;
		swap(events[i].name1, events[i].name2);
	}
	reverse(swaps.begin(), swaps.end());
	reverse(flag.begin(), flag.end());
	shuffle();
	swaps.clear();
	flag.clear();
	build(1024, 1024 + m - 1);
	flag.resize(swaps.size());
	for (int i = 0; i < (int)flag.size(); i++) {
		flag[i] = la + m * 38 + i;
	}
	shuffle();
	swaps.clear();
	flag.clear();
	merge(0, 1024, 1);
	flag.resize(swaps.size(), -1);
	shuffle();
	cur.clear();
	cur.resize(16, ZERO_GATE);
	for (int i = n + m - 1; i >= 0; i--) {
		swap(cur, events[i].val);
		cur = mul(add(cur, events[i].val), events[i].type);
	}
	reverse(swaps.begin(), swaps.end());
	reverse(flag.begin(), flag.end());
	shuffle();
	swaps.clear();
	flag.clear();
	build(0, n - 1);
	flag.resize(swaps.size());
	for (int i = 0; i < (int)flag.size(); i++) {
		flag[i] = n * 35 + i;
	}
	shuffle();
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < 16; j++) {
			outputs_circuit[i][j] = events[i].val[j];
		}
	}
	return gate_cnt;
}

• Subtask 1: 4 / 4
• Subtask 2: 4 / 4
• Subtask 3: 4 / 4
• Subtask 4: 24 / 24
• Subtask 5: 24 / 24
• Subtask 6: 6 / 6
• Subtask 7: 18 / 18
• Subtask 8: 10 / 10
• Subtask 9: 6 / 6