제출 #125114

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
125114		NMAC427	Islands (IOI08_islands)	C++17	27 / 100	685 ms	131072 KiB

islands

// https://oj.uz/problem/view/IOI08_islands

#include <bits/stdc++.h>
#define int int64_t
#define ff first
#define ss second

using namespace std;

int N;

vector<pair<int, int>> to;
vector<vector<int>> from;
vector<bool> inCycle;

pair<int, int> dfsSolve(int v) {
	int max1 = 0;
	int max2 = 0;

	int maxInternal = 0; // Maximum internal path;

	for (const int child: from[v]) {
		if (inCycle[child]) continue;  // Check here because we want to be able to pass in a node of the cycle

		auto childDFS = dfsSolve(child);
		childDFS.ff += to[child].ss;

		if (childDFS.ff >= max1) {
			max2 = max1;
			max1 = childDFS.ff;
		} else if (childDFS.ff > max2) {
			max2 = childDFS.ff;
		}

		maxInternal = max(maxInternal, childDFS.ss);
	}

	maxInternal = max(maxInternal, max1 + max2);

	return {max1, maxInternal};
}

signed main() {

	#ifndef __APPLE__
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	#endif

	cin >> N;

	to.resize(N);
	from.resize(N);

	for (int i = 0; i < N; i++) {
		cin >> to[i].ff >> to[i].ss;
		to[i].ff -= 1;

		from[to[i].ff].push_back(i);
	}


	// Generate inCycle Vector
	inCycle.assign(N, false);
	vector<bool> visited (N, false);

	for (int i = 0; i < N; i++) {
		if (visited[i]) continue;

		vector<int> cycle;
		int next = i;

		while (true) {
			visited[next] = true;
			cycle.push_back(next);

			if (visited[to[next].ff]) {
				bool __inCycle = false;
				for (int v: cycle)  {
					if (to[next].ff == v) __inCycle = true;
					if (__inCycle) inCycle[v] = true;
				}

				break;
			} else {
				next = to[next].ff;
			}
		}
	}


	// Solve
	int ans = 0;

	for (int i = 0; i < N; i++) {
		if (!inCycle[i]) continue;

		int compAns = 0;

		vector<int> cycle;
		vector<int> dfsV;
		vector<int> prefixSum = {0};
		int next = i;

		do {
			auto dfs = dfsSolve(next);
			compAns = max(compAns, dfs.ss);  // Internal Path

			cycle.push_back(next);
			dfsV.push_back(dfs.ff);
			prefixSum.push_back(prefixSum.back() + to[next].ss);
			next = to[next].ff;
		} while (next != i);

		for (int v: cycle) {
			inCycle[v] = false;  // Don't visit same component twice
		}

		// int _compAns = compAns;


		// int tmm = dfsV[0] - prefixSum[0];
		// int tp = dfsV[0] + prefixSum[0];

		// for(int i = 1; i < cycle.size(); i++) {
		// 	compAns = max(compAns, dfsV[i] + prefixSum[i] + tmm);
		// 	compAns = max(compAns, dfsV[i] - prefixSum[i] + tp + prefixSum.back());
		// 	tmm = max(tmm, dfsV[i] - prefixSum[i]);
		// 	tp = max(tp, dfsV[i] + prefixSum[i]);
		// }

		// int __compAns = compAns;
		// compAns = _compAns;


		int leftPtr = 0;
		int rightPtr = 1;
		int diameter = cycle.size();
		int prefix = dfsV[0] + to[i].ss;

		while (leftPtr < diameter && rightPtr < diameter * 2) {

			if (leftPtr == (rightPtr % diameter)) {
				prefix -= dfsV[leftPtr];
				prefix -= to[cycle[leftPtr]].ss;
				leftPtr++;
			}

			compAns = max(compAns, prefix + dfsV[rightPtr % diameter]);

			if (prefix <= dfsV[rightPtr % diameter]) {
				prefix  = dfsV[rightPtr % diameter];
				leftPtr = rightPtr % diameter;
			}
			
			prefix   += to[cycle[rightPtr % diameter]].ss;
			rightPtr += 1;
		}

		// assert(compAns == __compAns);

		ans += compAns;
	}

	cout << ans << "\n";

	return 0;
}

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