Submission #265561

#	Time	Username	Problem	Language	Result	Execution time	Memory
265561		square1001	Palindromes (APIO14_palindrome)	C++14	47 / 100	1086 ms	79200 KiB

palindrome

// APIO 2014 Problem 1 - Palindromes

#include <tuple>
#include <string>
#include <vector>
#include <iostream>
#include <algorithm>
#include <functional>
#include <unordered_set>
using namespace std;
int N; unordered_set<int> s1[600009], s2[600009];
tuple<long long, int, int, int> solve(int l, int r, vector<int> &lcp, vector<pair<int, int> > &trait) {
	// returns = (answer, store-pos, ct1, ct2)
	int baselen = trait[l].second;
	for(int i = l; i < r - 1; ++i) {
		baselen = min(baselen, lcp[i]);
	}
	if(r - l == 1) {
		if(trait[l].first == 1) s1[l].insert(trait[l].second);
		if(trait[l].first == 2) s2[l].insert(trait[l].second);
		return make_tuple(1LL, l, 0, 0);
	}
	long long ans = 0;
	vector<tuple<int, int, int> > g;
	int pre = l;
	for(int i = l; i < r; ++i) {
		if(i == r - 1 || lcp[i] == baselen) {
			tuple<long long, int, int, int> res = solve(pre, i + 1, lcp, trait);
			ans = max(ans, get<0>(res));
			pre = i + 1;
			g.push_back(make_tuple(get<1>(res), get<2>(res), get<3>(res)));
		}
	}
	int mxpos = -1, mxsize = 0;
	for(int i = 0; i < g.size(); ++i) {
		int sz = s1[get<0>(g[i])].size() + s2[get<0>(g[i])].size();
		if(mxsize < sz) {
			mxsize = sz;
			mxpos = i;
		}
	}
	int p = get<0>(g[mxpos]);
	int ct1 = get<1>(g[mxpos]) * 2, ct2 = get<2>(g[mxpos]) * 2;
	for(int i = 0; i < g.size(); ++i) {
		if(i == mxpos) continue;
		for(int j : s1[get<0>(g[i])]) {
			if(s2[p].find(N - j) != s2[p].end()) ++ct1;
			if(s2[p].find(N - j + 1) != s2[p].end()) ++ct2;
		}
		for(int j : s2[get<0>(g[i])]) {
			if(s1[p].find(N - j) != s1[p].end()) ++ct1;
			if(s1[p].find(N - j + 1) != s1[p].end()) ++ct2;
		}
	}
	for(int i = 0; i < g.size(); ++i) {
		if(i == mxpos) continue;
		for(int j : s1[get<0>(g[i])]) {
			s1[p].insert(j);
		}
		for(int j : s2[get<0>(g[i])]) {
			s2[p].insert(j);
		}
	}
	for(int i = 0; i < g.size(); ++i) {
		if(i == mxpos) continue;
		for(int j : s1[get<0>(g[i])]) {
			if(s2[p].find(N - j) != s2[p].end()) ++ct1;
			if(s2[p].find(N - j + 1) != s2[p].end()) ++ct2;
		}
		for(int j : s2[get<0>(g[i])]) {
			if(s1[p].find(N - j) != s1[p].end()) ++ct1;
			if(s1[p].find(N - j + 1) != s1[p].end()) ++ct2;
		}
	}
	ct1 /= 2; ct2 /= 2;
	ans = max(ans, 1LL * (baselen * 2) * ct1);
	ans = max(ans, 1LL * (baselen * 2 - 1) * ct2);
	return make_tuple(ans, p, ct1, ct2);
}
int main() {
	// step #1. read input
	string S;
	cin >> S;
	N = S.size();
	// step #2. construct suffix array of T = S + "#" + rev(S)
	string RS = S;
	reverse(RS.begin(), RS.end());
	string T = S + "#" + RS;
	vector<int> sa_inv(2 * N + 1);
	for(int i = 0; i < 2 * N + 1; ++i) {
		sa_inv[i] = int(T[i]);
	}
	for(int i = 1; i < 2 * N + 1; i *= 2) {
		vector<pair<int, int> > nseq(2 * N + 1);
		for(int j = 0; j < 2 * N + 1; ++j) {
			nseq[j] = make_pair(sa_inv[j], j + i < 2 * N + 1 ? sa_inv[j + i] : -1);
		}
		vector<pair<int, int> > sseq(nseq);
		sort(sseq.begin(), sseq.end());
		sseq.erase(unique(sseq.begin(), sseq.end()), sseq.end());
		for(int j = 0; j < 2 * N + 1; ++j) {
			sa_inv[j] = lower_bound(sseq.begin(), sseq.end(), nseq[j]) - sseq.begin();
		}
	}
	vector<int> sa(2 * N + 1);
	for(int i = 0; i < 2 * N + 1; ++i) {
		sa[sa_inv[i]] = i;
	}
	// step #3. construct rolling-hash table and rolling-hash function
	const int mod = 469762049;
	const int base = 311;
	vector<int> pw(2 * N + 2), h(2 * N + 2);
	pw[0] = 1;
	for(int i = 0; i < 2 * N + 1; ++i) {
		pw[i + 1] = 1LL * pw[i] * base % mod;
		h[i + 1] = (1LL * h[i] * base + T[i]) % mod;
	}
	function<int(int, int)> gethash = [&](int l, int r) {
		return (h[r] - 1LL * h[l] * pw[r - l] % mod + mod) % mod;
	};
	// step #4. calculate LCP
	vector<int> lcp(2 * N);
	for(int i = 0; i < 2 * N; ++i) {
		int l = 0, r = (2 * N + 1) - max(sa[i], sa[i + 1]) + 1;
		while(r - l > 1) {
			int m = (l + r) >> 1;
			if(gethash(sa[i], sa[i] + m) == gethash(sa[i + 1], sa[i + 1] + m)) l = m;
			else r = m;
		}
		lcp[i] = l;
	}
	// step #5. calculate types and lengths of elements in suffix array
	vector<pair<int, int> > trait(2 * N + 1);
	for(int i = 0; i < 2 * N + 1; ++i) {
		if(sa[i] == N) trait[i] = make_pair(0, -1);
		else if(sa[i] < N) trait[i] = make_pair(1, N - sa[i]);
		else trait[i] = make_pair(2, (2 * N + 1) - sa[i]);
	}
	// step #6. calculate the answer
	tuple<long long, int, int, int> ans = solve(1, 2 * N + 1, lcp, trait);
	// step #7. print the answer
	cout << get<0>(ans) << endl;
	return 0;
}

Compilation message (stderr)

palindrome.cpp: In function 'std::tuple<long long int, int, int, int> solve(int, int, std::vector<int>&, std::vector<std::pair<int, int> >&)':
palindrome.cpp:35:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::tuple<int, int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   35 |  for(int i = 0; i < g.size(); ++i) {
      |                 ~~^~~~~~~~~~
palindrome.cpp:44:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::tuple<int, int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   44 |  for(int i = 0; i < g.size(); ++i) {
      |                 ~~^~~~~~~~~~
palindrome.cpp:55:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::tuple<int, int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   55 |  for(int i = 0; i < g.size(); ++i) {
      |                 ~~^~~~~~~~~~
palindrome.cpp:64:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::tuple<int, int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   64 |  for(int i = 0; i < g.size(); ++i) {
      |                 ~~^~~~~~~~~~

• Subtask 1: 8 / 8
• Subtask 2: 15 / 15
• Subtask 3: 24 / 24
• Subtask 4: 0 / 26
• Subtask 5: 0 / 27