Submission #438650

#	Time	Username	Problem	Language	Result	Execution time	Memory
438650		fleimgruber	Dungeons Game (IOI21_dungeons)	C++17	63 / 100	2937 ms	737400 KiB

dungeons

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

using namespace std;

const int MAX_N = 400001;
const int MAX_LOG = 25; // 2^24 > 10^7

int n, s[MAX_N], p[MAX_N], w[MAX_N], l[MAX_N];

// MLE for other subtasks. probably requires smarter jump pointers
struct Subtask1345 {
	// dp[i][j][k] = we're at i, simulate for 2^j steps and
	// win against an opponent if strength < 2^k (we don't gain strength)
	struct {
		int end; // where do we end up at?
		long long gained; // total strength gained on the path
		// max(sum(gained) - opponent) along the simulation,
		// for all opponents we lose against
		long long max;
	} dp[50001][MAX_LOG][MAX_LOG];

	Subtask1345() {
		for (int j = 0; j < MAX_LOG; j++)
			for (int i = 0; i <= n; i++)
				for (int k = 0; k < MAX_LOG; k++) {
					auto& x = dp[i][j][k];
					if (j == 0)
						if (i == n) {
							x.end = n;
							x.gained = x.max = 0;
						} else if (s[i] < (1 << k)) { // we win
							x.end = w[i];
							x.gained = s[i];
							x.max = LLONG_MIN;
						} else {
							x.end = l[i];
							x.gained = p[i];
							// 1 step behind (we didn't gain 'gained' yet)
							x.max = -s[i];
						}
					else {
						auto& a = dp[i][j - 1][k];
						auto& b = dp[a.end][j - 1][k];
						x.end = b.end;
						x.gained = a.gained + b.gained;
						x.max = max(a.max, a.gained + b.max);
					}
				}
	}

	long long simulate(int at, int s_init) {
		long long strength = s_init;
		int k = 0;
		auto advance_k = [&] { // msb
			if (strength >= (1 << 24))
				k = 24;
			else
				while ((1 << (k + 1)) <= strength)
					k++;
		};
		// find first time our dp takes the wrong turn. once this
		// happens, the msb will change => happens only log(something)
		// times at this vertex we win:
		//	strength + gained - opponent >= 0
		// => strength + dp.max >= 0
		// but dp loses (dp.max is only calculated for losing edges)
		auto wrong_turn = [&](int i, int j, int k) {
			return strength + dp[i][j][k].max >= 0;
		};
		while (at != n) {
			advance_k();
			// jump to point where msb changes
			for (int j = MAX_LOG - 1; j >= 0; j--)
				if (!wrong_turn(at, j, k)) { // doesn't change => jump
					auto& x = dp[at][j][k];
					at = x.end;
					strength += x.gained;
				} // else it changes, so don't jump forward
			// now wrong_turn(at, 0, k) holds, so we win
			strength += s[at];
			at = w[at];
		}
		return strength;
	}
};

// because p[i] = s[i], every time we lose, our strength doubles
// lots of copy-pasta
struct Subtask2 {
	struct {
		int end;
		long long gained;
		long long min; // min(sum(gained) - opponent)
	} dp[MAX_N][MAX_LOG];

	Subtask2() {
		for (int j = 0; j < MAX_LOG; j++)
			for (int i = 0; i <= n; i++) {
				auto& x = dp[i][j];
				if (j == 0)
					if (i == n) {
						x.end = n;
						x.gained = x.min = 0;
					} else {
						x.end = w[i];
						x.gained = s[i];
						x.min = -s[i];
					}
				else {
					auto& a = dp[i][j - 1];
					auto& b = dp[a.end][j - 1];
					x.end = b.end;
					x.gained = a.gained + b.gained;
					x.min = min(a.min, a.gained + b.min);
				}
			}
	}

	long long simulate(int at, int s_init) {
		long long strength = 0;
		auto lose = [&](int i, int j) {
			return strength + dp[i][j].min < 0;
		};
		while (at != n) {
			// jump until we lose
			for (int j = MAX_LOG - 1; j >= 0; j--)
				if (!lose(at, j)) {
					auto& x = dp[at][j];
					at = x.end;
					strength += x.gained;
				}
			// lose (if we're at the end, this adds 0)
			strength += p[at]; // = s[at] > strength
			at = l[at];
		}
		return strength;
	}
};

optional<Subtask1345> sub1345;
optional<Subtask2> sub2;

void init(int n_, vector<int> s_, vector<int> p_,
		vector<int> w_, vector<int> l_) {
	n = n_;
	copy_n(s_.begin(), n, s);
	copy_n(p_.begin(), n, p);
	copy_n(w_.begin(), n, w);
	copy_n(l_.begin(), n, l);
	w[n] = l[n] = n;
	if (n > 50000)
		sub2.emplace();
	else
		sub1345.emplace();
}

long long simulate(int at, int s_init) {
	return n > 50000 ? sub2->simulate(at, s_init) :
		sub1345->simulate(at, s_init);
}

• Subtask 1: 11 / 11
• Subtask 2: 0 / 26
• Subtask 3: 13 / 13
• Subtask 4: 12 / 12
• Subtask 5: 27 / 27
• Subtask 6: 0 / 11