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Submission #1024671

# Submission time Handle Problem Language Result Execution time Memory
1024671 2024-07-16T09:05:26 Z NeroZein Graph (BOI20_graph) C++17
100 / 100
 453 ms 43084 KB 
#include "bits/stdc++.h"
using namespace std;
#define int long long

#ifdef Nero
#include "Deb.h"
#else
#define debug(...)
#endif

const int N = 1e5 + 5;
const int INF = 1e15 + 9;

int val[N];
bool vis[N];
bool vis2[N];
bool color[N];
stack<int> stk;
vector<int> component;
vector<int> odd_cycle;
vector<pair<int, int>> g[N];

bool check_not_bipartite(int v, int c) {
  if (vis[v]) {
    if (color[v] != c && odd_cycle.empty()) {
      odd_cycle.push_back(v);
      while (true) {
        int x = stk.top();
        stk.pop();
        odd_cycle.push_back(x); 
        if (x == v) {
          break; 
        }
      }
      return true;
    }
    return false; 
  }
  vis[v] = true; 
  stk.push(v);
  color[v] = c; 
  component.push_back(v); 
  bool ret = false; 
  for (auto [u, w] : g[v]) {
    ret |= check_not_bipartite(u, c ^ 1); 
  }
  if (!stk.empty() && stk.top() == v) {
    stk.pop();    
  }
  return ret; 
}

int assign(int v, int c) {
  if (vis2[v]) {
    if (val[v] != c) {
      return INF;
    }
    return 0;
  }
  vis2[v] = true;
  val[v] = c;
  int ret = abs(c); 
  for (auto [u, w] : g[v]) {
    ret += assign(u, w - c);
    ret = min(ret, INF);
  }
  return ret; 
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, m;
  cin >> n >> m;
  map<pair<int, int>, int> mp;
  for (int i = 0; i < m; ++i) {
    int u, v, w;
    cin >> u >> v >> w;
    w *= 2;
    if (u > v) swap(u, v);
    if (!mp.count({u, v})) {
      mp[{u, v}] = w;
      g[u].push_back({v, w});
      g[v].push_back({u, w});
    }
    if (mp[{u, v}] != w) {
      cout << "NO" << '\n';
      return 0; 
    }
  }
  for (int i = 1; i <= n; ++i) {
    if (vis[i]) {
      continue; 
    }
    while (!stk.empty()) stk.pop();
    bool not_bipartite = check_not_bipartite(i, 0); 
    if (not_bipartite) {
      int sum = 0;
      for (int j = 1; j < (int) odd_cycle.size(); ++j) {
        int u = odd_cycle[j - 1], v = odd_cycle[j];
        if (u > v) swap(u, v);
        sum += mp[{u, v}] * (j % 2 ? 1 : -1);
      }
      int rt = odd_cycle[0];
      int x = assign(rt, sum / 2);
      if (x == INF) {
        cout << "NO" << '\n';
        return 0; 
      }
      odd_cycle.clear();
    } else {
      int l = -3e5, r = 3e5;
      while (r - l > 10) {
        int ml = l + (r - l) / 3;
        int mr = r - (r - l) / 3;
        int tmp = assign(i, ml);
        for (int v : component) {
          vis2[v] = false; 
        }
        int tmp2 = assign(i, mr);
        for (int v : component) {
          vis2[v] = false; 
        }
        if (tmp < tmp2) {
          r = mr;
        } else {
          l = ml;
        }
      }
      int mn = INF, uv = -1;
      for (int tval = l; tval <= r; tval++) {
        int tmp = assign(i, tval);
        if (tmp < mn) {
          mn = tmp;
          uv = tval;
        }
        for (int v : component) {
          vis2[v] = 0;
        }
      }
      if (uv == -1) {
        cout << "NO" << '\n';
        return 0; 
      }
      assign(i, uv); 
    }
    component.clear();
  }
  for (auto [e, w] : mp) {
    if (val[e.first] + val[e.second] != w) {
      cout << "NO" << '\n';
      return 0; 
    }
  }
  cout << "YES" << '\n';
  for (int i = 1; i <= n; ++i) {
    cout << (val[i] / 2.0) << ' ';
  }
  return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2648 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 1 ms 2652 KB answer = YES
6 Correct 1 ms 2652 KB answer = YES
7 Correct 1 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2652 KB answer = NO
10 Correct 1 ms 2824 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2652 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2648 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 1 ms 2652 KB answer = YES
6 Correct 1 ms 2652 KB answer = YES
7 Correct 1 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2652 KB answer = NO
10 Correct 1 ms 2824 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2652 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO
24 Correct 1 ms 2648 KB answer = YES
25 Correct 1 ms 2652 KB answer = YES
26 Correct 1 ms 2652 KB answer = YES
27 Correct 1 ms 2652 KB answer = YES
28 Correct 1 ms 2652 KB answer = YES
29 Correct 1 ms 2652 KB answer = YES
30 Correct 1 ms 2652 KB answer = NO
31 Correct 1 ms 2652 KB answer = YES
32 Correct 1 ms 2652 KB answer = YES
33 Correct 1 ms 2740 KB answer = YES
34 Correct 1 ms 2652 KB answer = YES
35 Correct 1 ms 2652 KB answer = YES
36 Correct 1 ms 2652 KB answer = YES

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2648 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 1 ms 2652 KB answer = YES
6 Correct 1 ms 2652 KB answer = YES
7 Correct 1 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2652 KB answer = NO
10 Correct 1 ms 2824 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2652 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO
24 Correct 1 ms 2648 KB answer = YES
25 Correct 1 ms 2652 KB answer = YES
26 Correct 1 ms 2652 KB answer = YES
27 Correct 1 ms 2652 KB answer = YES
28 Correct 1 ms 2652 KB answer = YES
29 Correct 1 ms 2652 KB answer = YES
30 Correct 1 ms 2652 KB answer = NO
31 Correct 1 ms 2652 KB answer = YES
32 Correct 1 ms 2652 KB answer = YES
33 Correct 1 ms 2740 KB answer = YES
34 Correct 1 ms 2652 KB answer = YES
35 Correct 1 ms 2652 KB answer = YES
36 Correct 1 ms 2652 KB answer = YES
37 Correct 1 ms 2652 KB answer = YES
38 Correct 1 ms 2652 KB answer = YES
39 Correct 2 ms 2908 KB answer = YES
40 Correct 1 ms 2908 KB answer = YES
41 Correct 2 ms 2908 KB answer = NO
42 Correct 3 ms 2908 KB answer = YES
43 Correct 2 ms 2908 KB answer = YES
44 Correct 2 ms 2908 KB answer = YES
45 Correct 2 ms 2908 KB answer = YES
46 Correct 1 ms 2652 KB answer = YES
47 Correct 2 ms 3160 KB answer = YES
48 Correct 1 ms 2908 KB answer = YES

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2648 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 1 ms 2652 KB answer = YES
6 Correct 1 ms 2652 KB answer = YES
7 Correct 1 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2652 KB answer = NO
10 Correct 1 ms 2824 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2652 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO
24 Correct 1 ms 2648 KB answer = YES
25 Correct 1 ms 2652 KB answer = YES
26 Correct 1 ms 2652 KB answer = YES
27 Correct 1 ms 2652 KB answer = YES
28 Correct 1 ms 2652 KB answer = YES
29 Correct 1 ms 2652 KB answer = YES
30 Correct 1 ms 2652 KB answer = NO
31 Correct 1 ms 2652 KB answer = YES
32 Correct 1 ms 2652 KB answer = YES
33 Correct 1 ms 2740 KB answer = YES
34 Correct 1 ms 2652 KB answer = YES
35 Correct 1 ms 2652 KB answer = YES
36 Correct 1 ms 2652 KB answer = YES
37 Correct 1 ms 2652 KB answer = YES
38 Correct 1 ms 2652 KB answer = YES
39 Correct 2 ms 2908 KB answer = YES
40 Correct 1 ms 2908 KB answer = YES
41 Correct 2 ms 2908 KB answer = NO
42 Correct 3 ms 2908 KB answer = YES
43 Correct 2 ms 2908 KB answer = YES
44 Correct 2 ms 2908 KB answer = YES
45 Correct 2 ms 2908 KB answer = YES
46 Correct 1 ms 2652 KB answer = YES
47 Correct 2 ms 3160 KB answer = YES
48 Correct 1 ms 2908 KB answer = YES
49 Correct 24 ms 4292 KB answer = YES
50 Correct 10 ms 4700 KB answer = YES
51 Correct 21 ms 4700 KB answer = YES
52 Correct 19 ms 4952 KB answer = NO
53 Correct 2 ms 2908 KB answer = YES
54 Correct 4 ms 3164 KB answer = YES
55 Correct 11 ms 3416 KB answer = YES
56 Correct 23 ms 4188 KB answer = YES
57 Correct 17 ms 3928 KB answer = YES
58 Correct 17 ms 3928 KB answer = YES
59 Correct 9 ms 3932 KB answer = YES
60 Correct 22 ms 4184 KB answer = YES
61 Correct 5 ms 3420 KB answer = YES
62 Correct 9 ms 4188 KB answer = NO
63 Correct 182 ms 24900 KB answer = YES
64 Correct 157 ms 24656 KB answer = NO
65 Correct 178 ms 24656 KB answer = YES
66 Correct 4 ms 2908 KB answer = YES

Subtask #5
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2648 KB answer = YES
2 Correct 1 ms 2652 KB answer = YES
3 Correct 1 ms 2652 KB answer = YES
4 Correct 1 ms 2652 KB answer = NO
5 Correct 1 ms 2652 KB answer = YES
6 Correct 1 ms 2652 KB answer = YES
7 Correct 1 ms 2652 KB answer = YES
8 Correct 1 ms 2652 KB answer = YES
9 Correct 1 ms 2652 KB answer = NO
10 Correct 1 ms 2824 KB answer = YES
11 Correct 1 ms 2652 KB answer = YES
12 Correct 1 ms 2652 KB answer = NO
13 Correct 1 ms 2652 KB answer = YES
14 Correct 1 ms 2652 KB answer = YES
15 Correct 1 ms 2652 KB answer = YES
16 Correct 1 ms 2652 KB answer = YES
17 Correct 1 ms 2652 KB answer = YES
18 Correct 1 ms 2652 KB answer = YES
19 Correct 1 ms 2652 KB answer = YES
20 Correct 1 ms 2652 KB answer = YES
21 Correct 1 ms 2652 KB answer = YES
22 Correct 1 ms 2652 KB answer = NO
23 Correct 1 ms 2652 KB answer = NO
24 Correct 1 ms 2648 KB answer = YES
25 Correct 1 ms 2652 KB answer = YES
26 Correct 1 ms 2652 KB answer = YES
27 Correct 1 ms 2652 KB answer = YES
28 Correct 1 ms 2652 KB answer = YES
29 Correct 1 ms 2652 KB answer = YES
30 Correct 1 ms 2652 KB answer = NO
31 Correct 1 ms 2652 KB answer = YES
32 Correct 1 ms 2652 KB answer = YES
33 Correct 1 ms 2740 KB answer = YES
34 Correct 1 ms 2652 KB answer = YES
35 Correct 1 ms 2652 KB answer = YES
36 Correct 1 ms 2652 KB answer = YES
37 Correct 1 ms 2652 KB answer = YES
38 Correct 1 ms 2652 KB answer = YES
39 Correct 2 ms 2908 KB answer = YES
40 Correct 1 ms 2908 KB answer = YES
41 Correct 2 ms 2908 KB answer = NO
42 Correct 3 ms 2908 KB answer = YES
43 Correct 2 ms 2908 KB answer = YES
44 Correct 2 ms 2908 KB answer = YES
45 Correct 2 ms 2908 KB answer = YES
46 Correct 1 ms 2652 KB answer = YES
47 Correct 2 ms 3160 KB answer = YES
48 Correct 1 ms 2908 KB answer = YES
49 Correct 24 ms 4292 KB answer = YES
50 Correct 10 ms 4700 KB answer = YES
51 Correct 21 ms 4700 KB answer = YES
52 Correct 19 ms 4952 KB answer = NO
53 Correct 2 ms 2908 KB answer = YES
54 Correct 4 ms 3164 KB answer = YES
55 Correct 11 ms 3416 KB answer = YES
56 Correct 23 ms 4188 KB answer = YES
57 Correct 17 ms 3928 KB answer = YES
58 Correct 17 ms 3928 KB answer = YES
59 Correct 9 ms 3932 KB answer = YES
60 Correct 22 ms 4184 KB answer = YES
61 Correct 5 ms 3420 KB answer = YES
62 Correct 9 ms 4188 KB answer = NO
63 Correct 182 ms 24900 KB answer = YES
64 Correct 157 ms 24656 KB answer = NO
65 Correct 178 ms 24656 KB answer = YES
66 Correct 4 ms 2908 KB answer = YES
67 Correct 158 ms 26096 KB answer = YES
68 Correct 151 ms 26028 KB answer = YES
69 Correct 88 ms 26696 KB answer = YES
70 Correct 148 ms 43084 KB answer = YES
71 Correct 86 ms 26948 KB answer = YES
72 Correct 327 ms 16188 KB answer = YES
73 Correct 107 ms 16328 KB answer = YES
74 Correct 71 ms 16456 KB answer = YES
75 Correct 151 ms 16216 KB answer = NO
76 Correct 29 ms 4440 KB answer = YES
77 Correct 66 ms 6104 KB answer = YES
78 Correct 114 ms 8652 KB answer = YES
79 Correct 260 ms 14280 KB answer = YES
80 Correct 181 ms 16588 KB answer = YES
81 Correct 89 ms 21136 KB answer = NO
82 Correct 125 ms 25672 KB answer = YES
83 Correct 142 ms 27148 KB answer = YES
84 Correct 442 ms 26188 KB answer = YES
85 Correct 158 ms 27328 KB answer = YES
86 Correct 92 ms 28232 KB answer = YES
87 Correct 197 ms 19904 KB answer = NO
88 Correct 179 ms 22088 KB answer = YES
89 Correct 119 ms 16468 KB answer = YES
90 Correct 113 ms 16464 KB answer = YES
91 Correct 124 ms 16724 KB answer = YES
92 Correct 53 ms 10352 KB answer = YES
93 Correct 58 ms 10188 KB answer = YES
94 Correct 453 ms 27212 KB answer = NO
95 Correct 61 ms 16212 KB answer = NO
96 Correct 250 ms 36544 KB answer = YES
97 Correct 151 ms 26976 KB answer = NO