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Submission #709101

# Submission time Handle Problem Language Result Execution time Memory
709101 2023-03-13T06:17:22 Z null_awe Graph (BOI20_graph) C++14
100 / 100
 292 ms 13944 KB 
#include <iostream>
#include <vector>
#include <queue>
#include <climits>
#include <algorithm>
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) {
    // make this part faster please:
    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 (int num : arr) cout << num << ' ';
    // cout << '\n';
    for (pii p : negs) {
      int num = p.first;
      while (ni < neg.size() && neg[ni] < num) ++ni;
      // cout << pn[ni] << ' ';
      // cout << num * ni << ' ';
      // cout << pn[neg.size()] - pn[ni] << ' ';
      // cout << num * ((int) neg.size() - ni) << '\n';
      arr[p.second] += pn[ni] + (ll) num * ni - (pn[(int) neg.size()] - pn[ni]) - (ll) num * ((int) neg.size() - ni);
    }

    // for (int num : orig) cout << num << ' ';
    // cout << '\n';
    // for (int num : arr) cout << num << ' ';
    // cout << '\n';

    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:70:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   70 |     for (int i = 0; i < values.size(); ++i) negs[i] = {-values[i].first, i};
      |                     ~~^~~~~~~~~~~~~~~
Graph.cpp:84:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   84 |     for (int i = 0; i < pos.size(); ++i) pp[i + 1] = pp[i] - pos[i];
      |                     ~~^~~~~~~~~~~~
Graph.cpp:85:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   85 |     for (int i = 0; i < neg.size(); ++i) pn[i + 1] = pn[i] - neg[i];
      |                     ~~^~~~~~~~~~~~
Graph.cpp:89:17: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   89 |       while (pi < pos.size() && pos[pi] < num) ++pi;
      |              ~~~^~~~~~~~~~~~
Graph.cpp:96:17: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   96 |       while (ni < neg.size() && neg[ni] < num) ++ni;
      |              ~~~^~~~~~~~~~~~
Graph.cpp:110:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  110 |     for (int i = 0; i < values.size(); ++i) {
      |                     ~~^~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 1 ms 212 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 300 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 1 ms 300 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 256 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 1 ms 212 KB answer = YES
2 Correct 1 ms 212 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 300 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 1 ms 300 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 256 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 212 KB answer = YES
25 Correct 1 ms 212 KB answer = YES
26 Correct 1 ms 296 KB answer = YES
27 Correct 1 ms 212 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 212 KB answer = YES
30 Correct 1 ms 212 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 212 KB answer = YES

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 1 ms 212 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 300 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 1 ms 300 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 256 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 212 KB answer = YES
25 Correct 1 ms 212 KB answer = YES
26 Correct 1 ms 296 KB answer = YES
27 Correct 1 ms 212 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 212 KB answer = YES
30 Correct 1 ms 212 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 212 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 3 ms 340 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 3 ms 468 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 2 ms 340 KB answer = YES

Subtask #4
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 1 ms 212 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 300 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 1 ms 300 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 256 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 212 KB answer = YES
25 Correct 1 ms 212 KB answer = YES
26 Correct 1 ms 296 KB answer = YES
27 Correct 1 ms 212 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 212 KB answer = YES
30 Correct 1 ms 212 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 212 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 3 ms 340 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 3 ms 468 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 2 ms 340 KB answer = YES
49 Correct 15 ms 1604 KB answer = YES
50 Correct 13 ms 1232 KB answer = YES
51 Correct 14 ms 1620 KB answer = YES
52 Correct 9 ms 1080 KB answer = NO
53 Correct 2 ms 340 KB answer = YES
54 Correct 4 ms 596 KB answer = YES
55 Correct 8 ms 980 KB answer = YES
56 Correct 15 ms 1588 KB answer = YES
57 Correct 15 ms 1364 KB answer = YES
58 Correct 12 ms 1340 KB answer = YES
59 Correct 14 ms 1108 KB answer = YES
60 Correct 15 ms 1488 KB answer = YES
61 Correct 7 ms 724 KB answer = YES
62 Correct 137 ms 5584 KB answer = NO
63 Correct 136 ms 5684 KB answer = YES
64 Correct 132 ms 5700 KB answer = NO
65 Correct 152 ms 5608 KB answer = YES
66 Correct 3 ms 468 KB answer = YES

Subtask #5
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB answer = YES
2 Correct 1 ms 212 KB answer = YES
3 Correct 1 ms 212 KB answer = YES
4 Correct 1 ms 300 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 1 ms 300 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 256 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 212 KB answer = YES
25 Correct 1 ms 212 KB answer = YES
26 Correct 1 ms 296 KB answer = YES
27 Correct 1 ms 212 KB answer = YES
28 Correct 1 ms 212 KB answer = YES
29 Correct 1 ms 212 KB answer = YES
30 Correct 1 ms 212 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 212 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 3 ms 340 KB answer = YES
41 Correct 1 ms 340 KB answer = NO
42 Correct 3 ms 468 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 2 ms 340 KB answer = YES
49 Correct 15 ms 1604 KB answer = YES
50 Correct 13 ms 1232 KB answer = YES
51 Correct 14 ms 1620 KB answer = YES
52 Correct 9 ms 1080 KB answer = NO
53 Correct 2 ms 340 KB answer = YES
54 Correct 4 ms 596 KB answer = YES
55 Correct 8 ms 980 KB answer = YES
56 Correct 15 ms 1588 KB answer = YES
57 Correct 15 ms 1364 KB answer = YES
58 Correct 12 ms 1340 KB answer = YES
59 Correct 14 ms 1108 KB answer = YES
60 Correct 15 ms 1488 KB answer = YES
61 Correct 7 ms 724 KB answer = YES
62 Correct 137 ms 5584 KB answer = NO
63 Correct 136 ms 5684 KB answer = YES
64 Correct 132 ms 5700 KB answer = NO
65 Correct 152 ms 5608 KB answer = YES
66 Correct 3 ms 468 KB answer = YES
67 Correct 139 ms 12228 KB answer = YES
68 Correct 137 ms 12184 KB answer = YES
69 Correct 124 ms 8008 KB answer = YES
70 Correct 191 ms 11144 KB answer = YES
71 Correct 127 ms 8140 KB answer = YES
72 Correct 199 ms 12596 KB answer = YES
73 Correct 184 ms 8724 KB answer = YES
74 Correct 94 ms 5404 KB answer = YES
75 Correct 68 ms 5452 KB answer = NO
76 Correct 23 ms 1876 KB answer = YES
77 Correct 40 ms 3412 KB answer = YES
78 Correct 79 ms 5624 KB answer = YES
79 Correct 144 ms 10912 KB answer = YES
80 Correct 110 ms 7972 KB answer = YES
81 Correct 102 ms 7684 KB answer = NO
82 Correct 163 ms 8136 KB answer = YES
83 Correct 179 ms 8100 KB answer = YES
84 Correct 191 ms 12200 KB answer = YES
85 Correct 141 ms 12136 KB answer = YES
86 Correct 140 ms 8048 KB answer = YES
87 Correct 114 ms 7712 KB answer = NO
88 Correct 193 ms 8200 KB answer = YES
89 Correct 163 ms 7828 KB answer = YES
90 Correct 227 ms 7840 KB answer = YES
91 Correct 181 ms 7956 KB answer = YES
92 Correct 69 ms 4664 KB answer = YES
93 Correct 63 ms 4684 KB answer = YES
94 Correct 117 ms 8164 KB answer = NO
95 Correct 107 ms 7372 KB answer = NO
96 Correct 292 ms 13944 KB answer = YES
97 Correct 90 ms 9112 KB answer = NO