oj.uz

Submission #980090

# Submission time Handle Problem Language Result Execution time Memory
980090 2024-05-11T22:59:26 Z asdfgrace Event Hopping (BOI22_events) C++17
35 / 100
 1022 ms 15452 KB 
#include <bits/stdc++.h>
using namespace std;

#define dbg(x) //x
#define prt(x) dbg(cerr << x)
#define pv(x) dbg(cerr << #x << " = " << x << '\n')
#define pv2(x) dbg(cerr << #x << " = " << x.first << ',' << x.second << '\n')
#define parr(x) dbg(prt(#x << " = { "); for (auto y : x) prt(y << ' '); prt("}\n");)
#define parr2(x) dbg(prt(#x << " = { "); for (auto [y, z] : x) prt(y << ',' << z << "  "); prt("}\n");)
#define parr2d(x) dbg(prt(#x << ":\n"); for (auto arr : x) {parr(arr);} prt('\n'));
#define parr2d2(x) dbg(prt(#x << ":\n"); for (auto arr : x) {parr2(arr);} prt('\n'));

const int inf = 2e9 + 5;

/*
o(n^2):
for (each event)
add edge from this one to every range that contains it
and basically
you want to find the shortest path from i to j
note - if e[i] = e[j], there will be cycles in the graph
but these aren't that useful unless you want to jump directly from i to j
so we will be dealing with a dag here
so you wouldn't want to switch from anything with the same end
so e[i] must strictly increase
note that if no contained pairs
and you do have a CONTIGIOUS range of indices that you can hop to next
how to solve in n^2?
precomputing answers?
just get all the edges
maybe run n dijkstra? is this different bc dag?
for (cur node)
for (next node)
if (reachable)
for (each node)
dist[node][next] = min(dist[node][next], dist[node][cur] + 1)
or maybe just run a dijkstra if you have all the edges and n <= 1000 and q <= 100
greedy?
if you CANNOT reach the dest from here, you should go to the latest ending event
so that it starts before the dest ends
what about when does it end
if it ends before the dest ends that's fine
it has to end after the dest starts
it cannot end after the dest ends
NOTE: while we must have s[j] <= e[i] we don't have to maximize or minimize it
then we want to pick the maximum possible e[j] <= e[d]
so we can make like a pref max for end values based on start values have to be less
than or equal to whatever
but that won't factor in the "e[j] <= e[d]"
but that's a good reformulation
given max start, what is max e[j] <= e[d]?
we should be able to do queries offline then
so that for each query
we make some new values valid
*/

struct SegTree {
  int n;
  vector<int> st;
  
  SegTree (int x) {
    n = x;
    st.resize(2 * n, 0);
  }
  
  void upd(int k, int x) {
    k += n;
    st[k] = x;
    for (k /= 2; k >= 1; k /= 2) {
      st[k] = max(st[k * 2], st[k * 2 + 1]);
    }
  }
  
  int quer(int l, int r) {
    l += n; r += n;
    int res = 0;
    while (r >= l && l >= 1) {
      if (l % 2 == 1) res = max(res, st[l++]);
      if (r % 2 == 0) res = max(res, st[r--]);
      l /= 2; r /= 2;
    }
    return res;
  }
};

int main() {
  ios::sync_with_stdio(0); cin.tie(0);
  int n, q;
  cin >> n >> q;
  vector<array<int, 3>> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i][0] >> a[i][1];
    a[i][2] = i;
  }
  sort(a.begin(), a.end(), [&] (array<int, 3> x, array<int, 3> y) {
    return x[1] < y[1] || (x[1] == y[1] && x[0] < y[0]);
  });
  parr2d(a);
  vector<int> at(n);
  for (int i = 0; i < n; i++) {
    at[a[i][2]] = i;
  }
  if (q <= 100) {
    vector<array<int, 3>> quer(q);
    for (int i = 0; i < q; i++) {
      cin >> quer[i][0] >> quer[i][1];
      quer[i][0]--; quer[i][1]--;
      quer[i][0] = at[quer[i][0]];
      quer[i][1] = at[quer[i][1]];
      quer[i][2] = i;
    }
    sort(quer.begin(), quer.end(), [&] (array<int, 3> x, array<int, 3> y) {
      return x[1] < y[1];
    });
    parr2d(quer);
    vector<int> ans(q, -1);
    SegTree pmx(n);
    vector<int> s(n);
    for (int i = 0; i < n; i++) {
      s[i] = a[i][0];
    }
    sort(s.begin(), s.end());
    vector<int> ords(n);
    iota(ords.begin(), ords.end(), 0);
    sort(ords.begin(), ords.end(), [&] (int x, int y) {
      return a[x][0] < a[y][0];
    });
    vector<int> ats(n);
    for (int i = 0 ; i < n; i++) {
      ats[ords[i]] = i;
    }
    int j = 0;
    for (int i = 0; i < q; i++) {
      if (a[quer[i][0]][1] > a[quer[i][1]][1]) continue;
      for (; j < n && a[j][1] <= a[quer[i][1]][1]; j++) {
        pmx.upd(ats[j], a[j][1]);
      }
      if (quer[i][0] == quer[i][1]) {ans[quer[i][2]] = 0; continue;}
      int rb = a[quer[i][0]][1], res = 0;
      while (rb < a[quer[i][1]][0]) { // if rb < a[quer[i][1]][0], then you can't go to whatever the end is
        int k = upper_bound(s.begin(), s.end(), rb) - s.begin() - 1;
        int mx = pmx.quer(0, k);
        if (mx == rb) {
          res = -2;
          break;
        }
        rb = mx;
        res++;
      }
      res++;
      ans[quer[i][2]] = res;
    }
    for (int i = 0; i < q; i++) {
      if (ans[i] == -1) {
        cout << "impossible\n";
      } else {
        cout << ans[i] << '\n';
      }
    }
  } else {
    /*
    binary lifting probably?
    where are you going
    the thing on the right with lowest left value, hope it's this
    except you can have some annoying 2-cycles or smth
    so maybe calc dist to nearest 2cyc
    */
    vector<int> to(n, n);
    int mnl = inf, ind = n;
    for (int i = n - 1; i >= 0; i--) {
      if (mnl <= a[i][1]) {
        to[i] = ind;
      }
      if (a[i][0] < mnl) {
        mnl = a[i][0];
        ind = i;
      }
    }
    vector<bool> cyc(n, false);
    for (int i = 1; i < n; i++) {
      if (a[i][1] == a[i - 1][1]) {
        pv(i);
        to[i - 1] = i;
        to[i] = i - 1;
        cyc[i - 1] = cyc[i] = true;
        if (i > 2) assert(a[i - 2][1] != a[i][1]);
      }
    }
    vector<vector<int>> lift(n, vector<int>(20, 0));
    for (int i = 0; i < n; i++) {
      lift[i][0] = to[i];
    }
    for (int j = 1; j < 20; j++) {
      for (int i = 0; i < n; i++) {
        lift[i][j] = (lift[i][j - 1] == n ? n : lift[lift[i][j - 1]][j - 1]);
      }
    }
    parr(to);
    while (q--) {
      int l, r;
      cin >> l >> r;
      l--; r--;
      l = at[l]; r = at[r];
      int ans = 0;
      for (int j = 19; j >= 0; j--) {
        if (lift[l][j] < n && !cyc[lift[l][j]] && lift[l][j] <= r) {
          l = lift[l][j];
          ans += (1 << j);
        }
      }
      if (cyc[r]) {
        for (int i = 0; i < 2; i++) {
          l = to[l];
          ans++;
          if (l == r) break;
        }
      }
      if (l != r) {
        cout << "impossible\n";
      } else {
        cout << ans << '\n';
      }
    }
  }
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 64 ms 14904 KB Output is correct
3 Correct 76 ms 14672 KB Output is correct
4 Correct 63 ms 14504 KB Output is correct
5 Correct 62 ms 14676 KB Output is correct
6 Correct 59 ms 14772 KB Output is correct
7 Correct 63 ms 14676 KB Output is correct
8 Correct 53 ms 15180 KB Output is correct
9 Correct 62 ms 15184 KB Output is correct
10 Correct 75 ms 14932 KB Output is correct
11 Correct 79 ms 14928 KB Output is correct
12 Correct 58 ms 15452 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 8 ms 492 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 344 KB Output is correct
9 Correct 0 ms 348 KB Output is correct

Subtask #3
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 8 ms 492 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 344 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 344 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 7 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 2 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Incorrect 21 ms 2152 KB Output isn't correct
20 Halted 0 ms 0 KB -

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 8 ms 492 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 344 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 8 ms 348 KB Output is correct
13 Correct 1 ms 344 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 1022 ms 4180 KB Output is correct
20 Correct 223 ms 3924 KB Output is correct
21 Correct 40 ms 3956 KB Output is correct
22 Correct 96 ms 3932 KB Output is correct
23 Correct 30 ms 3920 KB Output is correct
24 Correct 35 ms 3920 KB Output is correct
25 Correct 21 ms 3932 KB Output is correct

Subtask #5
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 63 ms 14692 KB Output is correct
2 Correct 60 ms 14676 KB Output is correct
3 Correct 64 ms 14680 KB Output is correct
4 Correct 52 ms 15020 KB Output is correct
5 Correct 80 ms 15108 KB Output is correct
6 Incorrect 93 ms 14780 KB Output isn't correct
7 Halted 0 ms 0 KB -

Subtask #6
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 64 ms 14904 KB Output is correct
3 Correct 76 ms 14672 KB Output is correct
4 Correct 63 ms 14504 KB Output is correct
5 Correct 62 ms 14676 KB Output is correct
6 Correct 59 ms 14772 KB Output is correct
7 Correct 63 ms 14676 KB Output is correct
8 Correct 53 ms 15180 KB Output is correct
9 Correct 62 ms 15184 KB Output is correct
10 Correct 75 ms 14932 KB Output is correct
11 Correct 79 ms 14928 KB Output is correct
12 Correct 58 ms 15452 KB Output is correct
13 Correct 1 ms 344 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 8 ms 492 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 344 KB Output is correct
23 Correct 0 ms 348 KB Output is correct
24 Correct 7 ms 348 KB Output is correct
25 Correct 1 ms 348 KB Output is correct
26 Correct 2 ms 348 KB Output is correct
27 Correct 1 ms 348 KB Output is correct
28 Correct 1 ms 348 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Incorrect 21 ms 2152 KB Output isn't correct
32 Halted 0 ms 0 KB -