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Submission #530265

# Submission time Handle Problem Language Result Execution time Memory
530265 2022-02-24T22:34:13 Z Alex_tz307 Lampice (COCI19_lampice) C++17
42 / 110
 5000 ms 39680 KB 
#include <bits/stdc++.h>

using namespace std;

const int kN = 5e4;
const int mod = 1e9 + 9;
const int base = 29;
const int kM = (1 << 25) - 1;
string s;
vector<uint16_t> g[1 + kN];
uint16_t sz[1 + kN];
int p[1 + kN], h1[1 + kN], h2[1 + kN];
vector<uint16_t> centroids, nodes;
bitset<1 + kN> vis;
bitset<1 + kM> filter;
unordered_map<int, uint16_t> preffixes[kN];

void addSelf(int &x, const int &y) {
  x += y;
  if (x >= mod) {
    x -= mod;
  }
}

int add(int x, const int &y) {
  addSelf(x, y);
  return x;
}

void multSelf(int &x, const int &y) {
  x = (int64_t)x * y % mod;
}

int mult(int x, const int &y) {
  multSelf(x, y);
  return x;
}

void precalc() {
  p[0] = 1;
  for (int i = 1; i <= kN; ++i) {
    p[i] = mult(p[i - 1], base);
  }
}

void findSize(int u, int par) {
  sz[u] = 1;
  for (int v : g[u]) {
    if (!vis[v] && v != par) {
      findSize(v, u);
      sz[u] += sz[v];
    }
  }
}

int findCentroid(int u, int par, int n) {
  for (int v : g[u]) {
    if (!vis[v] && v != par && sz[v] > n / 2) {
      return findCentroid(v, u, n);
    }
  }
  return u;
}

void dfs1(int u, int par, int depth) {
  h1[u] = add(mult(h1[par], base), s[u] - 'a' + 1);
  h2[u] = add(h2[par], mult(p[depth], s[u] - 'a' + 1));
  preffixes[depth + 1][h1[u]] += 1;
  filter[h1[u] & kM] = true;
  for (int v : g[u]) {
    if (!vis[v] && v != par) {
      dfs1(v, u, depth + 1);
    }
  }
}

void modifyPaths(int u, int par, int depth, int t) {
  preffixes[depth][h1[u]] += t;
  for (int v : g[u]) {
    if (!vis[v] && v != par) {
      modifyPaths(v, u, depth + 1, t);
    }
  }
}

bool dfs2(int u, int par, int depth, int len) {
  if (depth == len) {
    return h1[u] == h2[u];
  }
  nodes.emplace_back(u);
  int d = len - depth + 1;
  if (d <= depth) {
    int split = nodes[nodes.size() - d];
    if (h1[split] == h2[split]) {
      split = nodes[nodes.size() - d - 1];
      int hsh = add(h1[u], mod - mult(p[d], h1[split]));
      if (filter[hsh & kM] && preffixes[d][hsh] > 0) {
        return true;
      }
    }
  }
  for (int v : g[u]) {
    if (!vis[v] && v != par && dfs2(v, u, depth + 1, len)) {
      return true;
    }
  }
  nodes.pop_back();
  return false;
}

void build(int u) {
  findSize(u, 0);
  int c = findCentroid(u, 0, sz[u]);
  centroids.emplace_back(c);
  vis[c] = true;
  for (int v : g[c]) {
    if (!vis[v]) {
      build(v);
    }
  }
}

bool solve(int u, int len) {
  for (int c : centroids) {
    dfs1(c, 0, 0);
    for (int v : g[c]) {
      if (!vis[v]) {
        modifyPaths(v, c, 2, -1);
        nodes.clear();
        nodes.emplace_back(0);
        nodes.emplace_back(c);
        if (dfs2(v, c, 2, len)) {
          modifyPaths(v, c, 2, 1);
          modifyPaths(c, 0, 1, -1);
          return true;
        }
        modifyPaths(v, c, 2, 1);
      }
    }
    modifyPaths(c, 0, 1, -1);
    vis[c] = true;
  }
  return false;
}

bool check(int n, int len) {
  bool ret = solve(1, len);
  for (int v = 1; v <= n; ++v) {
    vis[v] = false;
  }
  return ret;
}

void testCase() {
  int n;
  cin >> n >> s;
  s = '$' + s;
  bool ok2 = false;
  for (int i = 1; i < n; ++i) {
    int u, v;
    cin >> u >> v;
    g[u].emplace_back(v);
    g[v].emplace_back(u);
    if (s[u] == s[v]) {
      ok2 = true;
    }
  }
  build(1);
  for (int v = 1; v <= n; ++v) {
    vis[v] = false;
  }
  int l = 1, r = (n - 1) / 2, ans1 = 1;
  while (l <= r) {
    int mid = (l + r) / 2;
    if (check(n, 2 * mid + 1)) {
      ans1 = 2 * mid + 1;
      l = mid + 1;
    } else {
      r = mid - 1;
    }
  }
  int ans2 = 0;
  l = 2, r = n / 2;
  while (l <= r) {
    int mid = (l + r) / 2;
    if (check(n, 2 * mid)) {
      ans2 = 2 * mid;
      l = mid + 1;
    } else {
      r = mid - 1;
    }
  }
  cout << max({1 + ok2, ans1, ans2}) << '\n';
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  precalc();
  int tests = 1;
  for (int tc = 0; tc < tests; ++tc) {
    testCase();
  }
  return 0;
}

Subtask #1
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 4556 KB Output is correct
2 Correct 10 ms 5008 KB Output is correct
3 Correct 36 ms 8456 KB Output is correct
4 Correct 56 ms 8004 KB Output is correct
5 Correct 3 ms 4428 KB Output is correct
6 Correct 3 ms 4428 KB Output is correct
7 Correct 3 ms 4428 KB Output is correct

Subtask #2
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 4359 ms 33528 KB Output is correct
2 Correct 3100 ms 33588 KB Output is correct
3 Correct 1697 ms 29212 KB Output is correct
4 Correct 2104 ms 30608 KB Output is correct
5 Correct 4120 ms 39680 KB Output is correct
6 Correct 203 ms 18244 KB Output is correct

Subtask #3
0 / 31.0

# Verdict Execution time Memory Grader output
1 Execution timed out 5070 ms 31812 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #4
0 / 37.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 4556 KB Output is correct
2 Correct 10 ms 5008 KB Output is correct
3 Correct 36 ms 8456 KB Output is correct
4 Correct 56 ms 8004 KB Output is correct
5 Correct 3 ms 4428 KB Output is correct
6 Correct 3 ms 4428 KB Output is correct
7 Correct 3 ms 4428 KB Output is correct
8 Correct 4359 ms 33528 KB Output is correct
9 Correct 3100 ms 33588 KB Output is correct
10 Correct 1697 ms 29212 KB Output is correct
11 Correct 2104 ms 30608 KB Output is correct
12 Correct 4120 ms 39680 KB Output is correct
13 Correct 203 ms 18244 KB Output is correct
14 Execution timed out 5070 ms 31812 KB Time limit exceeded
15 Halted 0 ms 0 KB -