Submission #882831

#	Time	Username	Problem	Language	Result	Execution time	Memory
882831		MilosMilutinovic	Chorus (JOI23_chorus)	C++14	100 / 100	5729 ms	71900 KiB

chorus

#include <bits/stdc++.h>
 
using namespace std;
 
struct line {
  long long k, n;
  int f;
  void init() {
    k = 0;
    n = (long long) 1e18;
    f = 0;
  }
  long long val(long long x) {
    return k * x + n;
  }
};
 
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  vector<int> a, b;
  for (int i = 0; i < 2 * n; i++) {
    if (s[i] == 'A') {
      a.push_back(i);
    } else {
      b.push_back(i);
    }
  }
  vector<int> ia(2 * n);
  for (int i = 0; i < n; i++) {
    ia[a[i]] = i + 1;
  }
  vector<long long> pref(2 * n);
  for (int i = 0; i < 2 * n; i++) {
    if (i > 0) {
      pref[i] = pref[i - 1];
    }
    pref[i] += (s[i] == 'A' ? 1 : 0);
  }
  vector<int> ib(2 * n);
  for (int i = 0; i < n; i++) {
    ib[b[i]] = pref[b[i]];
  }
  for (int i = 0; i < n; i++) {
    if (i > 0) {
      pref[i] = pref[i - 1];
    } else {
      pref[i] = 0;
    }
    pref[i] += ib[b[i]];
  }
  deque<line> hull;
  auto Update = [&](line c) {
    while ((int) hull.size() >= 2) {
      line a = hull.rbegin()[1];
      line b = hull.back();
      long long x_ab = (b.n - a.n) * 1LL * (a.k - c.k);
      long long x_ac = (c.n - a.n) * 1LL * (a.k - b.k);
      if (x_ab > x_ac || (x_ab == x_ac && b.f >= c.f)) {
        hull.pop_back();
      } else {
        break;
      }
    }
    hull.push_back(c);
  };
  auto Query = [&](int x) {
    while ((int) hull.size() >= 2 && (hull.front().val(x) > hull[1].val(x) || 
                                     (hull.front().val(x) == hull[1].val(x) && hull.front().f >= hull[1].f))) {
      hull.pop_front();
    }
    return make_pair(hull.front().val(x), hull.front().f);
  };
  auto Solve = [&](long long mid) {
    const long long inf = (long long) 1e18;
    vector<pair<long long, int>> dp(n + 1, {inf, 0});
    dp[0] = {0, 0};
    int ptr = -1;
    multiset<pair<long long, int>> st;
    hull.clear();
    for (int i = 0; i < n; i++) {
      st.insert(dp[i]);
      while (ptr + 1 <= i && ia[a[i]] >= ib[b[ptr + 1]]) {
        ptr += 1;
        line cur;
        cur.k = -ptr;
        cur.n = dp[ptr].first + (ptr == 0 ? 0 : pref[ptr - 1]) + mid;
        cur.f = dp[ptr].second;
        Update(cur);
        st.erase(st.find(dp[ptr]));
      }
      if (!st.empty()) {
        pair<long long, int> val = *st.begin();
        dp[i + 1] = min(dp[i + 1], {val.first + mid, val.second + 1});
      }
      if (ptr != -1) {
        pair<long long, int> val = Query(ia[a[i]]);
        dp[i + 1] = min(dp[i + 1], {val.first + ia[a[i]] * 1LL * (ptr + 1) - pref[ptr], val.second + 1});
      }
    }
    return dp[n];
  };
  long long low = 0, high = 1e12, p = 0;
  while (low <= high) {
    long long mid = low + high >> 1;
    pair<long long, int> res = Solve(mid);
    if (res.second <= k) {
      p = mid;
      high = mid - 1;
    } else {
      low = mid + 1;
    }
  }
  pair<long long, int> res = Solve(p);
  cout << res.first - p * k << '\n';
  return 0;
}

Compilation message (stderr)

chorus.cpp: In function 'int main()':
chorus.cpp:109:25: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  109 |     long long mid = low + high >> 1;
      |                     ~~~~^~~~~~

• Subtask 1: 16 / 16
• Subtask 2: 24 / 24
• Subtask 3: 21 / 21
• Subtask 4: 26 / 26
• Subtask 5: 13 / 13