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Submission #400959

# Submission time Handle Problem Language Result Execution time Memory
400959 2021-05-08T22:21:33 Z Hegdahl The Xana coup (BOI21_xanadu) C++17
100 / 100
 90 ms 32560 KB 
#include <bits/stdc++.h>
#define ar array

using namespace std;
using ll = long long;

const ll INF = 1e9;

const int mxN = 1e5;
vector<int> g[mxN];
int a[mxN];

// 0b(pressed)(state)
ar<ll, 4> solve(int cur, int prv) {
  int kid_cnt = 0;
  for (int nxt : g[cur]) {
    if (nxt == prv) continue;
    ++kid_cnt;
  }
  if (!kid_cnt) {
    ar<ll, 4> ret {INF, INF, INF, INF};
    if (a[cur]) {
      ret[0b01] = 0;
      ret[0b10] = 1;
    } else {
      ret[0b00] = 0;
      ret[0b11] = 1;
    }

    /*
    cerr << cur << '\n';
    cerr << kid_cnt << '\n';
    for (int s = 0; s < 1<<2; ++s)
      cerr << bitset<2>(s) << ' ' << ret[s] << '\n';
    cerr << '\n'; */

    return ret;
  }

  vector<ll> kid_costs[4];
  for (int nxt : g[cur]) {
    if (nxt == prv) continue;
    auto r = solve(nxt, cur);

    for (int s = 0; s < 1<<2; ++s)
      kid_costs[s].push_back(r[s]);
  }

  /*
  for (int s = 0; s < 1<<2; ++s) {
    cerr << bitset<2>(s) << ": ";
    for (int i = 0; i < kid_cnt; ++i)
      cerr << kid_costs[s][i] << ' ';
    cerr << '\n';
  } // */

  ar<ll, 4> ret {INF, INF, INF, INF};

  // not pressed
  // can only take 0b00 or 0b10

  vector<int> idxs(kid_cnt);
  iota(idxs.begin(), idxs.end(), 0);
  sort(idxs.begin(), idxs.end(), [&](int i, int j) {
      return kid_costs[0b010][i]-kid_costs[0b00][i]
      < kid_costs[0b010][j]-kid_costs[0b00][j];
      });

  ll s0x = 0;
  for (int i = 0; i < kid_cnt; ++i)
    s0x += kid_costs[0b00][i];

  ret[0b00 ^ a[cur]] = min(ret[0b00 ^ a[cur]], s0x);
  for (int swp = 0; swp < kid_cnt; ++swp) {
    s0x -= kid_costs[0b00][idxs[swp]];
    s0x += kid_costs[0b10][idxs[swp]];

    int msk = 0b00 ^ (a[cur]^((swp+1)&1));
    //cerr << "s0x " << bitset<2>(msk) << ' ' << swp << ' ' << s0x << '\n';
    ret[msk] = min(ret[msk], s0x);
  }

  // pressed
  // can only take 0b01 or 0b11

  sort(idxs.begin(), idxs.end(), [&](int i, int j) {
      return kid_costs[0b011][i]-kid_costs[0b01][i]
      < kid_costs[0b011][j]-kid_costs[0b01][j];
      });

  ll s1x = 1;
  for (int i = 0; i < kid_cnt; ++i)
    s1x += kid_costs[0b01][i];

  ret[0b11 ^ a[cur]] = min(ret[0b11 ^ a[cur]], s1x);
  for (int swp = 0; swp < kid_cnt; ++swp) {
    s1x -= kid_costs[0b01][idxs[swp]];
    s1x += kid_costs[0b11][idxs[swp]];

    int msk = 0b11 ^ (a[cur]^((swp+1)&1));

    //cerr << "s1x " << bitset<2>(msk) << ' ' << swp << ' ' << s1x << '\n';
    ret[msk] = min(ret[msk], s1x);
  }

  //cerr << cur << '\n';
  //cerr << kid_cnt << '\n';
  /*
  for (int s = 0; s < 1<<2; ++s)
    cerr << bitset<2>(s) << ' ' << ret[s] << '\n';
  cerr << '\n'; // */

  return ret;
}

int main() {
  ios::sync_with_stdio(0);cin.tie(0);

  int n; cin >> n;
  for (int nn = 0; nn < n-1; ++nn) {
    int i, j; cin >> i >> j; --i, --j;
    g[i].push_back(j);
    g[j].push_back(i);
  }

  for (int i = 0; i < n; ++i)
    cin >> a[i];

  auto ans_ar = solve(0, -1);
  ll ans = min(ans_ar[0b00], ans_ar[0b10]);
  if (ans > n) {
    cout << "impossible\n";
    return 0;
  }
  cout << ans << '\n';
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2672 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2672 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2672 KB Output is correct
7 Correct 2 ms 2668 KB Output is correct
8 Correct 2 ms 2636 KB Output is correct
9 Correct 2 ms 2672 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 3 ms 2636 KB Output is correct
12 Correct 2 ms 2636 KB Output is correct
13 Correct 2 ms 2636 KB Output is correct
14 Correct 2 ms 2636 KB Output is correct
15 Correct 3 ms 2676 KB Output is correct
16 Correct 2 ms 2668 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 85 ms 32360 KB Output is correct
2 Correct 90 ms 31956 KB Output is correct
3 Correct 84 ms 32560 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 83 ms 32376 KB Output is correct
2 Correct 81 ms 31940 KB Output is correct
3 Correct 85 ms 32472 KB Output is correct
4 Correct 66 ms 7048 KB Output is correct
5 Correct 77 ms 7436 KB Output is correct
6 Correct 71 ms 7492 KB Output is correct
7 Correct 2 ms 2636 KB Output is correct
8 Correct 23 ms 4460 KB Output is correct
9 Correct 71 ms 7688 KB Output is correct
10 Correct 72 ms 7824 KB Output is correct
11 Correct 83 ms 10004 KB Output is correct
12 Correct 76 ms 10356 KB Output is correct
13 Correct 70 ms 7108 KB Output is correct
14 Correct 76 ms 7516 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2672 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2672 KB Output is correct
7 Correct 2 ms 2668 KB Output is correct
8 Correct 2 ms 2636 KB Output is correct
9 Correct 2 ms 2672 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 3 ms 2636 KB Output is correct
12 Correct 2 ms 2636 KB Output is correct
13 Correct 2 ms 2636 KB Output is correct
14 Correct 2 ms 2636 KB Output is correct
15 Correct 3 ms 2676 KB Output is correct
16 Correct 2 ms 2668 KB Output is correct
17 Correct 85 ms 32360 KB Output is correct
18 Correct 90 ms 31956 KB Output is correct
19 Correct 84 ms 32560 KB Output is correct
20 Correct 83 ms 32376 KB Output is correct
21 Correct 81 ms 31940 KB Output is correct
22 Correct 85 ms 32472 KB Output is correct
23 Correct 66 ms 7048 KB Output is correct
24 Correct 77 ms 7436 KB Output is correct
25 Correct 71 ms 7492 KB Output is correct
26 Correct 2 ms 2636 KB Output is correct
27 Correct 23 ms 4460 KB Output is correct
28 Correct 71 ms 7688 KB Output is correct
29 Correct 72 ms 7824 KB Output is correct
30 Correct 83 ms 10004 KB Output is correct
31 Correct 76 ms 10356 KB Output is correct
32 Correct 70 ms 7108 KB Output is correct
33 Correct 76 ms 7516 KB Output is correct
34 Correct 2 ms 2636 KB Output is correct
35 Correct 2 ms 2636 KB Output is correct
36 Correct 2 ms 2636 KB Output is correct
37 Correct 2 ms 2636 KB Output is correct
38 Correct 2 ms 2636 KB Output is correct
39 Correct 2 ms 2636 KB Output is correct
40 Correct 2 ms 2636 KB Output is correct
41 Correct 2 ms 2636 KB Output is correct
42 Correct 3 ms 2676 KB Output is correct
43 Correct 2 ms 2636 KB Output is correct
44 Correct 2 ms 2636 KB Output is correct
45 Correct 82 ms 32368 KB Output is correct
46 Correct 83 ms 32036 KB Output is correct
47 Correct 87 ms 32452 KB Output is correct
48 Correct 73 ms 7084 KB Output is correct
49 Correct 82 ms 7352 KB Output is correct
50 Correct 74 ms 7484 KB Output is correct
51 Correct 3 ms 2680 KB Output is correct
52 Correct 23 ms 4428 KB Output is correct
53 Correct 73 ms 7628 KB Output is correct
54 Correct 76 ms 7760 KB Output is correct
55 Correct 79 ms 9924 KB Output is correct
56 Correct 76 ms 10368 KB Output is correct
57 Correct 66 ms 7112 KB Output is correct
58 Correct 72 ms 7508 KB Output is correct
59 Correct 23 ms 4340 KB Output is correct
60 Correct 67 ms 7108 KB Output is correct
61 Correct 74 ms 7620 KB Output is correct
62 Correct 74 ms 7748 KB Output is correct
63 Correct 76 ms 7800 KB Output is correct
64 Correct 72 ms 7672 KB Output is correct
65 Correct 58 ms 8008 KB Output is correct
66 Correct 57 ms 8004 KB Output is correct
67 Correct 55 ms 11444 KB Output is correct
68 Correct 58 ms 11420 KB Output is correct
69 Correct 55 ms 11416 KB Output is correct
70 Correct 54 ms 11404 KB Output is correct