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- #include <algorithm>
- #include <iostream>
- #include <array>
- #include <vector>
- using namespace std;
- #define int long long
- #pragma comment(linker,"/STACK:1000000000,1000000000")
- const long long INF = 1e9 + 7;
- const int MAXN = 2e5 + 10;
- const int N = 1e5 + 10;
- const int M1 = 1e9 + 123;
- const int M2 = 1e9 + 321;
- const int P1 = 22811;
- const int P2 = 22699;
- array<int, MAXN> power1, power2;
- void init_pow() {
- power1[0] = 1;
- power2[0] = 1;
- for (int i = 1; i < MAXN; ++i) {
- power1[i] = (power1[i - 1] * P1) % M1;
- power2[i] = (power2[i - 1] * P2) % M2;
- }
- }
- void build_hash(string& s, vector<pair<int, int>>& h) {
- int n = s.size();
- h.resize(n + 1);
- h[0].first = 0;
- h[0].second = 0;
- for (int i = 0; i < n; ++i) {
- h[i + 1].first = (h[i].first + (s[i] - 'a' + 1) * power1[i]) % M1;
- h[i + 1].second = (h[i].second + (s[i] - 'a' + 1) * power2[i]) % M2;
- }
- }
- pair<int, int> get_hash(vector<pair<int, int>>& h, int pos, int len, int mx_pow = 0) {
- int h1 = h[pos + len].first - h[pos].first;
- int h2 = h[pos + len].second - h[pos].second;
- if (h1 < 0) {
- h1 += M1;
- }
- if (h2 < 0) {
- h2 += M2;
- }
- if (mx_pow != 0) {
- h1 = h1 * power1[mx_pow - (pos + len - 1)] % M1;
- h2 = h2 * power2[mx_pow - (pos - + len - 1)] % M2;
- }
- return make_pair(h1, h2);
- }
- bool is_equal(vector<pair<int, int>>& h_l, vector<pair<int, int>>& h_r, int start1, int start2, int len) {
- pair<int, int> d_l, d_r;
- d_l.first = ((h_l[start1 + len].first - h_l[start1].first + M1) * power1[start2]) % M1;
- d_l.second = ((h_l[start1 + len].second - h_l[start1].second + M2) * power2[start2]) % M2;
- d_r.first = ((h_r[start2 + len].first - h_r[start2].first + M1) * power1[start1]) % M1;
- d_r.second = ((h_r[start2 + len].second - h_r[start2].second + M2) * power2[start1]) % M2;
- return d_l == d_r;
- }
- signed main() {
- ios_base::sync_with_stdio(false);
- cin.tie(nullptr);
- cout.tie(nullptr);
- int n;
- cin >> n;
- string a, b;
- cin >> a >> b;
- vector<pair<int, int>> h_a, h_b;
- init_pow();
- build_hash(a, h_a);
- build_hash(b, h_b);
- int l = 0, r = n + 1;
- vector<pair<int, int>> segs;
- int ans_pos;
- while (r - l > 1) {
- int mid = (r + l) / 2;
- segs.clear();
- for (int i = 0; i + mid <= n; ++i) {
- segs.emplace_back(get_hash(h_a, i, mid, n));
- }
- int pos = -1;
- sort(segs.begin(), segs.end());
- for (int i = 0; i + mid <= n; ++i) {
- if (binary_search(segs.begin(), segs.end(), get_hash(h_b, i, mid, n))) {
- pos = i;
- break;
- }
- }
- if (pos >= 0) {
- l = mid;
- ans_pos = pos;
- } else {
- r = mid;
- }
- }
- cout << b.substr(ans_pos, l) << '\n';
- }
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