✅ hashing

submissions/ICPC/2020-2021 ACM-ICPC Brazil Subregional Programming Contest/C. Concatenating Teams(2).cpp

@@ -0,0 +1,145 @@
+/*
+	To a string not beculiar a few things must happen:
+	Looking to a string Ai from A:
+		- let P be some prefix of A
+		- and S be the rest of string
+		- so Ai = P + S
+		- then P must be a string in A
+		- S must be a prefix of some string in B
+		in a way that if there is a Bj in B such 
+		that Bj = S + S', and S' also belongs to B
+			- because than we will have two concatenated strings 
+			generated by different strings, these are:
+				Ai + S' = P + Bj
+			- so Ai, P, S', and Bj are non peculiar
+*/
+#include <bits/stdc++.h>
+using namespace std;
+
+using ull = unsigned long long;
+
+const int MAXN(1'000'000);
+
+const ull P = 31;
+ull p[MAXN + 1];
+void precompute() {
+	p[0] = 1;
+	for (int i = 1; i <= MAXN; i++)
+	 p[i] = (P * p[i - 1]);
+}
+
+struct Hash {
+	int n;
+	vector<ull> h;
+	// vector<ull> hi;
+	Hash() {}
+
+	Hash(const string& s) : n(s.size()), h(n) /*, hi(n) */ {
+		h[0] = s[0];
+		for (int i = 1; i < n; i++)
+			h[i] = (s[i] + h[i - 1] * P);
+
+
+		// hi[n - 1] = s[n - 1];
+		// for (int i = n - 2; i >= 0; i--)
+		// 	hi[i] = (s[i] + hi[i + 1] * P);
+	}
+
+	ull query(int l, int r) {
+		ull hash = (h[r] - (l ? h[l - 1] * p[r - l + 1] : 0));
+		return hash;
+	}
+
+	// ull query_inv(int l, int r) {
+	// 	ull hash = (hi[l] - (r + 1 < n ? hi[r + 1] * p[r - l + 1] : 0));
+	// 	return hash;
+	// }
+};
+
+pair<int,int> solve(vector<string>& as, vector<string>& bs) {
+	// string it self, it's complement, and if belong to bs
+	using t = tuple<ull, ull, bool>;
+	map<ull, vector<t>> by_S;
+
+	vector<Hash> hash_as;
+	set<ull> hashes_as;
+	for (auto &ai : as) {
+		Hash hash_ai = Hash(ai);
+		hash_as.push_back(hash_ai);
+		hashes_as.emplace(hash_ai.query(0, hash_ai.n-1));
+	}
+
+	for (auto &hash_ai : hash_as) {
+		int n = hash_ai.n;
+		auto full = hash_ai.query(0,n-1);
+		for (int i = 0; i < n - 1; i++) {
+			auto pref = hash_ai.query(0, i);
+			auto suff = hash_ai.query(i+1, n-1);
+			if (hashes_as.count(pref)) {
+				by_S[suff].push_back({full,pref, 0});
+			}
+		}
+	}
+
+	// save every hash from Bs
+	set<ull> bs_full_hashes;
+	vector<Hash> bs_hashes;
+	for (auto &bi : bs) {
+		Hash bi_hash = Hash(bi);
+		bs_hashes.emplace_back(bi_hash);
+		bs_full_hashes.emplace(bi_hash.query(0, (int)bi.size()-1));
+	}
+
+	// See which S are valid
+	set<ull> allowed_S;
+	for (auto &bi_hash : bs_hashes) {
+		int n = bi_hash.n;
+		for (int i = 0; i < n -1; i++) {
+			auto pref = bi_hash.query(0, i);
+			auto suff = bi_hash.query(i+1, n-1);
+			if (bs_full_hashes.count(suff)) {
+				if (by_S[pref].size() >= 1) {
+					allowed_S.emplace(pref);
+					by_S[pref].push_back({bi_hash.query(0, n-1), suff, 1});
+				}
+			}
+
+		}
+	}
+
+	// just mark every one as unpeculiar
+	set<ull> bad_a, bad_b;
+	for (auto &[key, triplets] : by_S) {
+		if (allowed_S.count(key) == 0) continue;
+
+		for (auto &[a, b, c ] : triplets) {
+			if (c == 0) {
+				bad_a.emplace(a);
+				bad_a.emplace(b);
+			}
+			else {
+				bad_b.emplace(a);
+				bad_b.emplace(b);
+			}
+		}
+	}
+	return {as.size() - bad_a.size(), bs.size() - bad_b.size()};
+}
+
+int32_t main() {
+	ios_base::sync_with_stdio(0);
+	cin.tie(0);
+	precompute();
+
+	int m, n;
+	cin >> m >> n;
+	vector<string> as(m), bs(n);
+	for (auto& ai : as) cin >> ai;
+	for (auto& bi : bs) cin >> bi;
+
+	auto [ansa, ansb] = solve(as, bs);
+
+	cout << ansa << ' ' << ansb << '\n';
+}
+
+// AC, hashing