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Submission #709103

# Submission time Handle Problem Language Result Execution time Memory
709103 2023-03-13T06:18:32 Z null_awe Graph (BOI20_graph) C++14
100 / 100
 285 ms 12800 KB 
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define pii pair<int, int>

const double EPS = 0.000001;

struct line {

  int m, b;

  line() {}

  line(int m, int b) : m(m), b(b) {}

  double combine(line other) {
    int mm = m - other.m, bb = other.b - b;
    if (mm == 0 && bb) {
      cout << "NO\n";
      exit(0);
    }
    if (mm == 0) return INT_MAX;
    return (double) bb / mm;
  }
};

int n, m;
vector<vector<pii>> adj;
vector<line> lines;
vector<bool> vis;
vector<double> all;

void solve(int fv) {
  if (vis[fv]) return;
  lines[fv] = line(1, 0);
  queue<int> q;
  vector<int> has;
  vis[fv] = true, q.push(fv), has.push_back(fv);
  double ans = INT_MAX;
  while (q.size()) {
    int v = q.front(); q.pop();
    for (pii p : adj[v]) {
      int u = p.first, c = p.second;
      line change(-lines[v].m, c - lines[v].b);
      if (!vis[u]) {
        vis[u] = true, q.push(u), has.push_back(u);
        lines[u] = change;
      } else {
        double comb = lines[u].combine(change);
        if (ans > INT_MAX - 1) ans = comb;
      }
    }
  }
  if (ans > INT_MAX - 1) {
    vector<pii> values;
    vector<int> orig;
    int ind = 0;
    for (int v : has) {
      line l = lines[v];
      values.push_back({-l.b / l.m, ind++});
      orig.push_back(-l.b / l.m);
    }
    vector<pii> negs(values.size());
    for (int i = 0; i < values.size(); ++i) negs[i] = {-values[i].first, i};
    sort(values.begin(), values.end());
    sort(negs.begin(), negs.end());
    vector<ll> arr(values.size());
    vector<int> pos, neg;
    for (int v : has) {
      line l = lines[v];
      if (l.m > 0) pos.push_back(-l.b);
      else neg.push_back(-l.b);
    }
    sort(pos.begin(), pos.end());
    sort(neg.begin(), neg.end());
    vector<ll> pp(pos.size() + 1), pn(neg.size() + 1);
    for (int i = 0; i < pos.size(); ++i) pp[i + 1] = pp[i] - pos[i];
    for (int i = 0; i < neg.size(); ++i) pn[i + 1] = pn[i] - neg[i];
    int pi = 0, ni = 0;
    for (pii p : values) {
      int num = p.first;
      while (pi < pos.size() && pos[pi] < num) ++pi;
      arr[p.second] = pp[pi] + (ll) num * pi - (pp[(int) pos.size()] - pp[pi]) - (ll) num * ((int) pos.size() - pi);
    }
    for (pii p : negs) {
      int num = p.first;
      while (ni < neg.size() && neg[ni] < num) ++ni;
      arr[p.second] += pn[ni] + (ll) num * ni - (pn[(int) neg.size()] - pn[ni]) - (ll) num * ((int) neg.size() - ni);
    }
    ll mn = LLONG_MAX;
    for (int i = 0; i < values.size(); ++i) {
      if (arr[i] < mn) mn = arr[i], ans = orig[i];
    }
  }
  for (int v : has) vis[v] = false;
  all[fv] = ans;
  q = queue<int>();
  vis[fv] = true, q.push(fv);
  while (q.size()) {
    int v = q.front(); q.pop();
    for (pii p : adj[v]) {
      int u = p.first, c = p.second;
      if (vis[u]) continue;
      vis[u] = true, q.push(u);
      all[u] = c - all[v];
    }
  }
}

int main() {
  cin >> n >> m;
  adj.resize(n);
  for (int i = 0; i < m; ++i) {
    int a, b, c; cin >> a >> b >> c; --a, --b;
    adj[a].push_back({b, c}), adj[b].push_back({a, c});
  }
  lines = vector<line>(n);
  vis = vector<bool>(n);
  all.resize(n);
  for (int i = 0; i < n; ++i) solve(i);
  for (int v = 0; v < n; ++v) {
    for (pii p : adj[v]) {
      if (abs(all[v] + all[p.first] - p.second) > EPS) {
        cout << "NO\n";
        return 0;
      }
    }
  }
  cout << "YES\n";
  for (double val : all) cout << val << ' ';
  cout << '\n';
  return 0;
}

Compilation message

Graph.cpp: In function 'void solve(int)':
Graph.cpp:65:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   65 |     for (int i = 0; i < values.size(); ++i) negs[i] = {-values[i].first, i};
      |                     ~~^~~~~~~~~~~~~~~
Graph.cpp:78:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   78 |     for (int i = 0; i < pos.size(); ++i) pp[i + 1] = pp[i] - pos[i];
      |                     ~~^~~~~~~~~~~~
Graph.cpp:79:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   79 |     for (int i = 0; i < neg.size(); ++i) pn[i + 1] = pn[i] - neg[i];
      |                     ~~^~~~~~~~~~~~
Graph.cpp:83:17: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   83 |       while (pi < pos.size() && pos[pi] < num) ++pi;
      |              ~~~^~~~~~~~~~~~
Graph.cpp:88:17: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   88 |       while (ni < neg.size() && neg[ni] < num) ++ni;
      |              ~~~^~~~~~~~~~~~
Graph.cpp:92:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   92 |     for (int i = 0; i < values.size(); ++i) {
      |                     ~~^~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB answer = YES
2 Correct 0 ms 304 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 1 ms 212 KB answer = YES
6 Correct 1 ms 212 KB answer = YES
7 Correct 1 ms 212 KB answer = YES
8 Correct 1 ms 212 KB answer = YES
9 Correct 1 ms 212 KB answer = NO
10 Correct 1 ms 212 KB answer = YES
11 Correct 0 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 212 KB answer = YES
14 Correct 1 ms 212 KB answer = YES
15 Correct 1 ms 212 KB answer = YES
16 Correct 1 ms 212 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 212 KB answer = YES
19 Correct 1 ms 212 KB answer = YES
20 Correct 1 ms 212 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB answer = YES
2 Correct 0 ms 304 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 1 ms 212 KB answer = YES
6 Correct 1 ms 212 KB answer = YES
7 Correct 1 ms 212 KB answer = YES
8 Correct 1 ms 212 KB answer = YES
9 Correct 1 ms 212 KB answer = NO
10 Correct 1 ms 212 KB answer = YES
11 Correct 0 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 212 KB answer = YES
14 Correct 1 ms 212 KB answer = YES
15 Correct 1 ms 212 KB answer = YES
16 Correct 1 ms 212 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 212 KB answer = YES
19 Correct 1 ms 212 KB answer = YES
20 Correct 1 ms 212 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO
24 Correct 1 ms 300 KB answer = YES
25 Correct 1 ms 300 KB answer = YES
26 Correct 1 ms 212 KB answer = YES
27 Correct 1 ms 212 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 296 KB answer = YES
30 Correct 1 ms 300 KB answer = NO
31 Correct 1 ms 212 KB answer = YES
32 Correct 1 ms 212 KB answer = YES
33 Correct 1 ms 212 KB answer = YES
34 Correct 1 ms 212 KB answer = YES
35 Correct 1 ms 212 KB answer = YES
36 Correct 1 ms 300 KB answer = YES

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB answer = YES
2 Correct 0 ms 304 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 1 ms 212 KB answer = YES
6 Correct 1 ms 212 KB answer = YES
7 Correct 1 ms 212 KB answer = YES
8 Correct 1 ms 212 KB answer = YES
9 Correct 1 ms 212 KB answer = NO
10 Correct 1 ms 212 KB answer = YES
11 Correct 0 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 212 KB answer = YES
14 Correct 1 ms 212 KB answer = YES
15 Correct 1 ms 212 KB answer = YES
16 Correct 1 ms 212 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 212 KB answer = YES
19 Correct 1 ms 212 KB answer = YES
20 Correct 1 ms 212 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO
24 Correct 1 ms 300 KB answer = YES
25 Correct 1 ms 300 KB answer = YES
26 Correct 1 ms 212 KB answer = YES
27 Correct 1 ms 212 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 296 KB answer = YES
30 Correct 1 ms 300 KB answer = NO
31 Correct 1 ms 212 KB answer = YES
32 Correct 1 ms 212 KB answer = YES
33 Correct 1 ms 212 KB answer = YES
34 Correct 1 ms 212 KB answer = YES
35 Correct 1 ms 212 KB answer = YES
36 Correct 1 ms 300 KB answer = YES
37 Correct 1 ms 212 KB answer = YES
38 Correct 1 ms 212 KB answer = YES
39 Correct 1 ms 340 KB answer = YES
40 Correct 1 ms 308 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 2 ms 340 KB answer = YES
43 Correct 2 ms 340 KB answer = YES
44 Correct 2 ms 340 KB answer = YES
45 Correct 2 ms 340 KB answer = YES
46 Correct 1 ms 340 KB answer = YES
47 Correct 2 ms 340 KB answer = YES
48 Correct 3 ms 340 KB answer = YES

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB answer = YES
2 Correct 0 ms 304 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 1 ms 212 KB answer = YES
6 Correct 1 ms 212 KB answer = YES
7 Correct 1 ms 212 KB answer = YES
8 Correct 1 ms 212 KB answer = YES
9 Correct 1 ms 212 KB answer = NO
10 Correct 1 ms 212 KB answer = YES
11 Correct 0 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 212 KB answer = YES
14 Correct 1 ms 212 KB answer = YES
15 Correct 1 ms 212 KB answer = YES
16 Correct 1 ms 212 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 212 KB answer = YES
19 Correct 1 ms 212 KB answer = YES
20 Correct 1 ms 212 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO
24 Correct 1 ms 300 KB answer = YES
25 Correct 1 ms 300 KB answer = YES
26 Correct 1 ms 212 KB answer = YES
27 Correct 1 ms 212 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 296 KB answer = YES
30 Correct 1 ms 300 KB answer = NO
31 Correct 1 ms 212 KB answer = YES
32 Correct 1 ms 212 KB answer = YES
33 Correct 1 ms 212 KB answer = YES
34 Correct 1 ms 212 KB answer = YES
35 Correct 1 ms 212 KB answer = YES
36 Correct 1 ms 300 KB answer = YES
37 Correct 1 ms 212 KB answer = YES
38 Correct 1 ms 212 KB answer = YES
39 Correct 1 ms 340 KB answer = YES
40 Correct 1 ms 308 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 2 ms 340 KB answer = YES
43 Correct 2 ms 340 KB answer = YES
44 Correct 2 ms 340 KB answer = YES
45 Correct 2 ms 340 KB answer = YES
46 Correct 1 ms 340 KB answer = YES
47 Correct 2 ms 340 KB answer = YES
48 Correct 3 ms 340 KB answer = YES
49 Correct 18 ms 1748 KB answer = YES
50 Correct 14 ms 1200 KB answer = YES
51 Correct 15 ms 1592 KB answer = YES
52 Correct 8 ms 1076 KB answer = NO
53 Correct 2 ms 340 KB answer = YES
54 Correct 4 ms 596 KB answer = YES
55 Correct 7 ms 980 KB answer = YES
56 Correct 14 ms 1620 KB answer = YES
57 Correct 15 ms 1252 KB answer = YES
58 Correct 16 ms 1340 KB answer = YES
59 Correct 14 ms 1080 KB answer = YES
60 Correct 14 ms 1460 KB answer = YES
61 Correct 7 ms 724 KB answer = YES
62 Correct 131 ms 6068 KB answer = NO
63 Correct 153 ms 6256 KB answer = YES
64 Correct 140 ms 6284 KB answer = NO
65 Correct 147 ms 6208 KB answer = YES
66 Correct 3 ms 516 KB answer = YES

Subtask #5
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB answer = YES
2 Correct 0 ms 304 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 212 KB answer = NO
5 Correct 1 ms 212 KB answer = YES
6 Correct 1 ms 212 KB answer = YES
7 Correct 1 ms 212 KB answer = YES
8 Correct 1 ms 212 KB answer = YES
9 Correct 1 ms 212 KB answer = NO
10 Correct 1 ms 212 KB answer = YES
11 Correct 0 ms 212 KB answer = YES
12 Correct 1 ms 212 KB answer = NO
13 Correct 1 ms 212 KB answer = YES
14 Correct 1 ms 212 KB answer = YES
15 Correct 1 ms 212 KB answer = YES
16 Correct 1 ms 212 KB answer = YES
17 Correct 1 ms 212 KB answer = YES
18 Correct 1 ms 212 KB answer = YES
19 Correct 1 ms 212 KB answer = YES
20 Correct 1 ms 212 KB answer = YES
21 Correct 1 ms 212 KB answer = YES
22 Correct 1 ms 212 KB answer = NO
23 Correct 1 ms 212 KB answer = NO
24 Correct 1 ms 300 KB answer = YES
25 Correct 1 ms 300 KB answer = YES
26 Correct 1 ms 212 KB answer = YES
27 Correct 1 ms 212 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 296 KB answer = YES
30 Correct 1 ms 300 KB answer = NO
31 Correct 1 ms 212 KB answer = YES
32 Correct 1 ms 212 KB answer = YES
33 Correct 1 ms 212 KB answer = YES
34 Correct 1 ms 212 KB answer = YES
35 Correct 1 ms 212 KB answer = YES
36 Correct 1 ms 300 KB answer = YES
37 Correct 1 ms 212 KB answer = YES
38 Correct 1 ms 212 KB answer = YES
39 Correct 1 ms 340 KB answer = YES
40 Correct 1 ms 308 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 2 ms 340 KB answer = YES
43 Correct 2 ms 340 KB answer = YES
44 Correct 2 ms 340 KB answer = YES
45 Correct 2 ms 340 KB answer = YES
46 Correct 1 ms 340 KB answer = YES
47 Correct 2 ms 340 KB answer = YES
48 Correct 3 ms 340 KB answer = YES
49 Correct 18 ms 1748 KB answer = YES
50 Correct 14 ms 1200 KB answer = YES
51 Correct 15 ms 1592 KB answer = YES
52 Correct 8 ms 1076 KB answer = NO
53 Correct 2 ms 340 KB answer = YES
54 Correct 4 ms 596 KB answer = YES
55 Correct 7 ms 980 KB answer = YES
56 Correct 14 ms 1620 KB answer = YES
57 Correct 15 ms 1252 KB answer = YES
58 Correct 16 ms 1340 KB answer = YES
59 Correct 14 ms 1080 KB answer = YES
60 Correct 14 ms 1460 KB answer = YES
61 Correct 7 ms 724 KB answer = YES
62 Correct 131 ms 6068 KB answer = NO
63 Correct 153 ms 6256 KB answer = YES
64 Correct 140 ms 6284 KB answer = NO
65 Correct 147 ms 6208 KB answer = YES
66 Correct 3 ms 516 KB answer = YES
67 Correct 144 ms 12456 KB answer = YES
68 Correct 161 ms 12588 KB answer = YES
69 Correct 120 ms 8388 KB answer = YES
70 Correct 196 ms 11648 KB answer = YES
71 Correct 122 ms 8416 KB answer = YES
72 Correct 173 ms 12800 KB answer = YES
73 Correct 144 ms 9024 KB answer = YES
74 Correct 82 ms 5740 KB answer = YES
75 Correct 50 ms 5684 KB answer = NO
76 Correct 16 ms 1908 KB answer = YES
77 Correct 41 ms 3528 KB answer = YES
78 Correct 65 ms 5924 KB answer = YES
79 Correct 139 ms 11084 KB answer = YES
80 Correct 96 ms 8180 KB answer = YES
81 Correct 91 ms 8012 KB answer = NO
82 Correct 152 ms 8416 KB answer = YES
83 Correct 167 ms 8468 KB answer = YES
84 Correct 205 ms 12432 KB answer = YES
85 Correct 144 ms 12368 KB answer = YES
86 Correct 126 ms 8248 KB answer = YES
87 Correct 110 ms 7988 KB answer = NO
88 Correct 152 ms 8416 KB answer = YES
89 Correct 136 ms 8072 KB answer = YES
90 Correct 151 ms 8100 KB answer = YES
91 Correct 153 ms 8068 KB answer = YES
92 Correct 67 ms 4940 KB answer = YES
93 Correct 70 ms 4828 KB answer = YES
94 Correct 93 ms 8400 KB answer = NO
95 Correct 106 ms 7736 KB answer = NO
96 Correct 285 ms 11492 KB answer = YES
97 Correct 76 ms 7880 KB answer = NO