oj.uz

Submission #995392

# Submission time Handle Problem Language Result Execution time Memory
995392 2024-06-09T02:48:17 Z asdfgrace Stranded Far From Home (BOI22_island) C++17
20 / 100
 206 ms 33432 KB 
#include <bits/stdc++.h>
using namespace std;

#define dbg(x) //x
#define prt(x) dbg(cerr << x)
#define pv(x) prt(#x << " = " << x << '\n')
#define parr(x) dbg(prt(#x << " = "); for (auto y : x) prt(y << ' '); prt('\n'));
#define parr2d(x) dbg(prt(#x << " = \n"); for (auto y : x) {parr(y)}; prt('\n'));

/*
which ties are possible?
a can convince b if sum(a) > sum(b)
note that nodes are weighted
note that the tie with the strictly least number can't be 1 in the end
one with strictly most can be 1 in the end
how to greedily make 1 the largest?
dfs from the node
and keep adding the smallest adj greedily
and make sure that the size of this color's comp is greater than any other color's comp

subtask 1: brute force
subtask 2: tree; every node's parent has greater value than self
you can always get everything in your own subtree
go to the root
and for every node on the path to the root
you also absorb the parent
and everything else in the parent's subtree - note that that is guaranteed to be possible
if you've already absorbed the parent
this dp cond is checkable as you go up the tree
(this node's subtree sum >= parent's value?)
all the values to the root have to be true
for a node to work
subtask 3: just some weird stuff with set ig
*/

int main() {
  ios::sync_with_stdio(0); cin.tie(0);
  int n, m;
  cin >> n >> m;
  vector<long long> s(n);
  for (int i = 0; i < n; i++) {
    cin >> s[i];
  }
  bool inc = false;
  for (int i = 0; i < n - 1; i++) {
    if (s[i + 1] > s[i]) {
      inc = true;
    }
  }
  bool dif1 = true;
  vector<vector<int>> edges(n);
  for (int i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    x--; y--;
    pv(x); pv(y); pv(abs(x - y));
    if (abs(x - y) > 1) dif1 = false;
    edges[x].push_back(y);
    edges[y].push_back(x);
  }
  pv(dif1);
  if (n <= 2000 && m <= 2000) {
    for (int i = 0; i < n; i++) {
      vector<bool> vis(n, false);
      vis[i] = true;
      priority_queue<array<long long, 2>> que;
      que.push({-s[i], i});
      bool ok = true;
      long long tot = s[i];
      while (que.size()) {
        long long sz = -que.top()[0], node = que.top()[1];
        que.pop();
        if (sz > tot) {
          ok = false;
          break;
        }
        if (node != i) {
          tot += sz;
        }
        for (auto next : edges[node]) {
          if (!vis[next]) {
            vis[next] = true;
            que.push({-s[next], next});
          }
        }
      }
      cout << (ok ? 1 : 0);
    }
    cout << '\n';
  } else if (m == n - 1 && !inc) {
    vector<bool> ok(n, true);
    vector<long long> sum = s;
    function<void(int, int)> dfs1 = [&] (int node, int par) {
      for (auto next : edges[node]) {
        if (next != par) {
          dfs1(next, node);
          sum[node] += sum[next];
        }
      }
    };
    dfs1(0, 0);
    function<void(int, int)> dfs2 = [&] (int node, int par) {
      if (node != 0) {
        ok[node] = ok[par];
        if (s[par] > sum[node]) {
          ok[node] = false;
        }
      }
      for (auto next : edges[node]) {
        if (next != par) {
          dfs2(next, node);
        }
      }
    };
    dfs2(0, 0);
    for (int i = 0; i < n; i++) {
      cout << (ok[i] ? 1 : 0);
    }
    cout << '\n';
  } else if (dif1) {
    /*
    sum(l + 1, r - 1) < both a[l] and a[r]
    so for each l find the min r so that sum(l + 1, r - 1) >= a[l]
    for each r find the max l so that sum(l + 1, r - 1) >= a[r]
    if mxl[r] <= l && mnr[l] >= r, they work probably
    so probably find the l with the max mnr
    or just an increasing seq of them that you can binary search
    so you have n ranges of invalid elems
    probably use set to remove all the elems
    
    implies that if we start in [6, 6] we can't escape to the left OR right
    */
    vector<long long> ps = s;
    for (int i = 1; i < n; i++) {
      ps[i] += ps[i - 1];
    }
    vector<int> mxl(n), mnr(n);
    for (int i = 1; i < n; i++) {
      if (i > 0) mxl[i] = upper_bound(ps.begin(), ps.end(), ps[i - 1] - s[i]) - ps.begin();
      if (i < n - 1) mnr[i] = lower_bound(ps.begin(), ps.end(), ps[i + 1] + s[i]) - ps.begin();
    }
    vector<int> ord(n);
    iota(ord.begin(), ord.end(), 0);
    sort(ord.begin(), ord.end(), [&] (int x, int y) {
      return mxl[x] > mxl[y];
    });
    int ptr = n - 1;
    vector<array<int, 2>> arr, bad;
    array<int, 2> tmp;
    for (int i = 0; i < n; i++) {
      pv(i); pv(ord[i]);
      while (ptr >= mxl[ord[i]]) {
        while (arr.size() && -arr.back()[0] <= mnr[ptr]) arr.pop_back();
        arr.push_back({-mnr[ptr], ptr});
        ptr--;
      }
      parr2d(arr);
      // GOAL: find the first >= i
      // ACTUAL GOAL: find the last <= -i
      tmp = {-mxl[ord[i]], (int) 1e9};
      int lb = upper_bound(arr.begin(), arr.end(), tmp) - arr.begin() - 1;
      if (lb != -1 && arr[lb][1] < ord[i] - 1) {
        bad.push_back({arr[lb][1] + 1, ord[i ] - 1});
        parr(bad.back());
      }
    }
    for (int i = n - 1; i > 0; i--) {
      if (s[i] > ps[i - 1]) {
        bad.push_back({0, i - 1});
        break;
      }
    }
    for (int i = 0; i < n - 1; i++) {
      if (s[i] > ps[n - 1] - ps[i]) {
        bad.push_back({i + 1, n - 1});
        break;
      }
    }
    parr2d(bad);
    set<int> st;
    for (int i = 0; i < n; i++) {
      st.insert(i);
    }
    for (auto [l, r] : bad) {
      auto it = st.lower_bound(l);
      while (it != st.end() && *it <= r) {
        st.erase(it);
        it = st.lower_bound(l);
      }
    }
    parr(mxl); parr(mnr); parr(ord);
    for (int i = 0; i < n; i++) {
      cout << (st.count(i) ? 1 : 0);
    }
    cout << '\n';
  }
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 135 ms 604 KB Output is correct
5 Correct 115 ms 604 KB Output is correct
6 Correct 199 ms 576 KB Output is correct
7 Correct 133 ms 600 KB Output is correct
8 Correct 92 ms 348 KB Output is correct
9 Correct 206 ms 616 KB Output is correct
10 Correct 47 ms 600 KB Output is correct
11 Correct 45 ms 604 KB Output is correct
12 Correct 42 ms 600 KB Output is correct
13 Correct 82 ms 604 KB Output is correct
14 Correct 85 ms 604 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 108 ms 22100 KB Output is correct
4 Correct 74 ms 22100 KB Output is correct
5 Correct 91 ms 14412 KB Output is correct
6 Correct 84 ms 14664 KB Output is correct
7 Correct 84 ms 14676 KB Output is correct
8 Correct 84 ms 14668 KB Output is correct
9 Correct 72 ms 14672 KB Output is correct
10 Correct 62 ms 15304 KB Output is correct
11 Correct 54 ms 15336 KB Output is correct
12 Correct 80 ms 14928 KB Output is correct
13 Correct 83 ms 33432 KB Output is correct
14 Correct 81 ms 33364 KB Output is correct
15 Correct 96 ms 33364 KB Output is correct
16 Correct 75 ms 32940 KB Output is correct

Subtask #3
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Incorrect 147 ms 27828 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #4
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Incorrect 77 ms 12852 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #5
0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 135 ms 604 KB Output is correct
5 Correct 115 ms 604 KB Output is correct
6 Correct 199 ms 576 KB Output is correct
7 Correct 133 ms 600 KB Output is correct
8 Correct 92 ms 348 KB Output is correct
9 Correct 206 ms 616 KB Output is correct
10 Correct 47 ms 600 KB Output is correct
11 Correct 45 ms 604 KB Output is correct
12 Correct 42 ms 600 KB Output is correct
13 Correct 82 ms 604 KB Output is correct
14 Correct 85 ms 604 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 344 KB Output is correct
17 Correct 108 ms 22100 KB Output is correct
18 Correct 74 ms 22100 KB Output is correct
19 Correct 91 ms 14412 KB Output is correct
20 Correct 84 ms 14664 KB Output is correct
21 Correct 84 ms 14676 KB Output is correct
22 Correct 84 ms 14668 KB Output is correct
23 Correct 72 ms 14672 KB Output is correct
24 Correct 62 ms 15304 KB Output is correct
25 Correct 54 ms 15336 KB Output is correct
26 Correct 80 ms 14928 KB Output is correct
27 Correct 83 ms 33432 KB Output is correct
28 Correct 81 ms 33364 KB Output is correct
29 Correct 96 ms 33364 KB Output is correct
30 Correct 75 ms 32940 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Incorrect 147 ms 27828 KB Output isn't correct
33 Halted 0 ms 0 KB -