Submission #927831

#	Time	Username	Problem	Language	Result	Execution time	Memory
927831		TranGiaHuy1508	Alice, Bob, and Circuit (APIO23_abc)	C++17	54 / 100	76 ms	11344 KiB

abc

#include <bits/stdc++.h>
#include "abc.h"

// 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

// Aliases
const int BIT_LENGTH = 16;
const int LOGN = 5;
using u16 = unsigned short;

namespace {
	struct GateOutput {
		int operation;
		int op0, op1;

		GateOutput(int _op, int _op0, int _op1):
				operation(_op), op0(_op0), op1(_op1) {
		}
	};

	int gate_index;
	std::vector<GateOutput> outputs;
}

struct LogicGate {
	int idx;
	int operation;

	LogicGate() {}
	LogicGate(int _idx) : idx(_idx) {
	}
	LogicGate(int _op, const LogicGate _op0, const LogicGate _op1) :
			idx(gate_index++), operation(_op) {
		outputs.emplace_back(operation, _op0.idx, _op1.idx);
	}
};

namespace {
	std::vector<LogicGate> input_gates;
	LogicGate zerobit, onebit;
}

template <int LEN>
struct Number {
	std::array<LogicGate, LEN> digits;

	Number() {}
	Number(std::vector<LogicGate> _digits){
		for (int i = 0; i < LEN; i++) digits[i] = _digits[i];
	}

	// Cost: 74 operations
	Number operator + (const Number &B) {
		const Number A = *this;
		Number result;

		int shifted = 0;
		for (int i = 0; i < LEN; i++){
			if (B.digits[i].idx == zerobit.idx){
				result.digits[i] = A.digits[i];
				shifted++;
			}
			else break;
		}

		LogicGate carry = zerobit;
		for (int i = shifted; i < LEN; i++){
			LogicGate D(OP_XOR, A.digits[i], B.digits[i]);
		
			if (i == LEN - 1){
				LogicGate new_digit(OP_XOR, D, carry);
				result.digits[i] = new_digit;
				continue;
			}

			LogicGate CR(OP_AND, A.digits[i], B.digits[i]);

			if (i == shifted){
				result.digits[i] = D;
				carry = CR;
				continue;
			}

			LogicGate new_digit(OP_XOR, D, carry);
			LogicGate carry2(OP_AND, carry, D);
			LogicGate new_carry(OP_OR, CR, carry2);

			result.digits[i] = new_digit;
			carry = new_carry;
		}

		return result;
	}

	// Cost: 16 operations
	Number operator & (const LogicGate gate){
		const Number A = *this;
		Number result;

		for (int i = 0; i < LEN; i++){
			if (A.digits[i].idx == zerobit.idx){
				result.digits[i] = A.digits[i];
				continue;
			}
			LogicGate new_digit(OP_AND, A.digits[i], gate);
			result.digits[i] = new_digit;
		}

		return result;
	}

	// Cost: 16 operations
	Number operator | (const Number B){
		const Number A = *this;
		Number result;

		for (int i = 0; i < LEN; i++){
			if (A.digits[i].idx == onebit.idx){
				result.digits[i] = onebit;
				continue;
			}
			if (A.digits[i].idx == zerobit.idx){
				result.digits[i] = B.digits[i];
				continue;
			}
			if (B.digits[i].idx == onebit.idx){
				result.digits[i] = onebit;
				continue;
			}
			if (B.digits[i].idx == zerobit.idx){
				result.digits[i] = A.digits[i];
				continue;
			}

			LogicGate new_digit(OP_OR, A.digits[i], B.digits[i]);
			result.digits[i] = new_digit;
		}

		return result;
	}

	// Cost: 0 operation
	Number operator << (int shift) {
		const Number A = *this;
		Number result;

		for (int i = 0; i < BIT_LENGTH; i++){
			int j = i - shift;
			if (j < 0) result.digits[i] = zerobit;
			else result.digits[i] = A.digits[j];
		}

		return result;
	}

	// Cost: 723 operations
	Number operator * (const Number &B) {
		const Number A = *this;
		Number result(std::vector<LogicGate>(LEN, zerobit));
		Number current = A;

		for (int i = 0; i < LEN; i++){
			result = result + (current & B.digits[i]);
			current = current << 1;
		}

		return result;
	}
};

// Cost: 2 operations
void initialize(const int la, const int lb){
	gate_index = la + lb;
	for (int i = 0; i < la + lb; i++){
		LogicGate inp(i);
		input_gates.push_back(inp);
	}

	zerobit = LogicGate(OP_ZERO, input_gates[0], input_gates[1]);
	onebit = LogicGate(OP_ONE, input_gates[0], input_gates[1]);
}

int print_output(
	const int la,
    const int lb,
    int operations[],
    int operands[][2],
    int outputs_circuit[][16],
	std::vector<Number<BIT_LENGTH>> res
){
	int crr = la + lb;

	for (auto gate_output: outputs){
		operations[crr] = gate_output.operation;
		operands[crr][0] = gate_output.op0;
		operands[crr][1] = gate_output.op1;
		crr++;
	}

	for (int i = 0; i < (int)res.size(); i++){
		for (int j = 0; j < BIT_LENGTH; j++){
			outputs_circuit[i][j] = res[i].digits[j].idx;
		}
	}

	return crr;
}

// Alice
int alice(
	const int n,
    const char raw_names[][5],
    const u16 numbers[],
    bool outputs_alice[]
) {
	std::vector<std::string> names(n);
	for (int i = 0; i < n; i++){
		names[i] = std::string(raw_names[i]);
	}

	std::vector<std::pair<std::string, int>> vec(n);
	for (int i = 0; i < n; i++){
		vec[i] = {names[i], i};
	}

	std::sort(vec.begin(), vec.end());
	std::vector<int> position(n);

	for (int i = 0; i < n; i++){
		position[vec[i].second] = i;
	}
	int crr = 0;

	// Send numbers
	for (int i = 0; i < n; i++){
		u16 num = numbers[vec[i].second];
		for (int j = 0; j < BIT_LENGTH; j++){
			outputs_alice[crr++] = (num >> j) & 1;
		}
	}

	// Send permutation
	for (int i = 0; i < n; i++){
		for (int j = 0; j < LOGN; j++){
			outputs_alice[crr++] = (position[i] >> j) & 1;
		}
	}

	return crr;
}


// Bob
int bob(
    const int m,
    const char senders[][5],
    const char recipients[][5],
    bool outputs_bob[]
) {
	std::vector<std::string> names;

	for (int i = 0; i < m; i++){
		names.push_back(std::string(senders[i]));
		names.push_back(std::string(recipients[i]));
	}

	std::sort(names.begin(), names.end());
	names.resize(std::unique(names.begin(), names.end()) - names.begin());

	int n = names.size();

	std::map<std::string, int> mp;
	for (int i = 0; i < n; i++){
		mp[names[i]] = i;
	}

	std::vector<std::vector<int>> matrix(n, std::vector<int>(n));

	for (int i = 0; i < m; i++){
		std::string str1 = std::string(senders[i]);
		std::string str2 = std::string(recipients[i]);

		int p1 = mp[str1], p2 = mp[str2];
		matrix[p1][p2]++;
	}

	int crr = 0;
	for (int i = 0; i < n; i++){
		for (int j = 0; j < n; j++){
			for (int c = 0; c < 1; c++){
				outputs_bob[crr++] = (matrix[i][j] >> c) & 1;
			}
		}
	}

	return crr;
}


// Circuit
int circuit(
    const int la,
    const int lb,
    int operations[],
    int operands[][2],
    int outputs_circuit[][16]
) {
	initialize(la, lb);

	int n = sqrtl(lb);
	std::vector<Number<BIT_LENGTH>> ans(n);

	for (int i = 0; i < n; i++){
		ans[i] = Number<BIT_LENGTH>(std::vector(BIT_LENGTH, zerobit));
	}

	std::vector<Number<BIT_LENGTH>> nums(n);
	for (int i = 0; i < n; i++){
		std::vector<LogicGate> bits(BIT_LENGTH);
		for (int j = 0; j < BIT_LENGTH; j++){
			bits[j] = input_gates[i * BIT_LENGTH + j];
		}
		nums[i] = Number<BIT_LENGTH>(bits);
	}

	for (int i = 0; i < n; i++){
		for (int j = 0; j < n; j++){
			LogicGate cnt = input_gates[i * n + j + la];
			ans[j] = ans[j] + (nums[i] & cnt);
		}
	}

	std::vector<Number<LOGN>> perm(n);
	for (int i = 0; i < n; i++){
		std::vector<LogicGate> bits(LOGN);
		for (int j = 0; j < LOGN; j++){
			bits[j] = input_gates[n * BIT_LENGTH + i * LOGN + j];
		}
		perm[i] = Number<LOGN>(bits);
	}

	std::vector<Number<LOGN>> lst(n);
	for (int i = 0; i < n; i++){
		std::vector<LogicGate> bits(LOGN);
		for (int j = 0; j < LOGN; j++){
			bits[j] = ((i >> j) & 1) ? onebit : zerobit;
		}
		lst[i] = Number<LOGN>(bits);
	}

	std::vector<Number<BIT_LENGTH>> final(n);
	for (int i = 0; i < n; i++){
		final[i] = Number<BIT_LENGTH>(std::vector<LogicGate>(BIT_LENGTH, zerobit));
	}

	for (int i = 0; i < n; i++){
		for (int j = 0; j < n; j++){
			LogicGate x = onebit;
			for (int b = 0; b < LOGN; b++){
				LogicGate chk(OP_EQUAL, perm[i].digits[b], lst[j].digits[b]);
				x = LogicGate(OP_AND, x, chk);
			}
			Number<BIT_LENGTH> crrnum = ans[j] & x;
			final[i] = final[i] | crrnum;
		}
	}

	return print_output(la, lb, operations, operands, outputs_circuit, final);
}

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• Subtask 2: 0 / 4
• Subtask 3: 0 / 4
• Subtask 4: 24 / 24
• Subtask 5: 24 / 24
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