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Submission #198439

# Submission time Handle Problem Language Result Execution time Memory
198439 2020-01-26T03:35:45 Z model_code Travels (LMIO17_keliones) C++17
100 / 100
 230 ms 18852 KB 
#include <stdio.h>
#include <assert.h>
#include <vector>
#include <algorithm>

using namespace std;

typedef long long ll;

const ll MOD = 1000000000 + 7;

const int MAXN = 2 * 100000 + 100; 


vector<int> E[MAXN][2]; // E[i][0] saugo išimtas iš grafo briaunas, kurios prasideda viršūnėje i, 
                        // o E[i][1] saugo išimtas iš grafo briaunas, kurios baigiasi viršūnėje i.
ll W[MAXN]; // Viršūnių svoriai.

ll A[MAXN]; // A[i] - kelių, pasibaigiančių viršūnėje i, skaičius.
ll B[MAXN]; // B[i] - kelių, prasidedančių viršūnėje i, skaičius.

int N, M;

int main() {
  scanf("%d %d", &N, &M);

  for (int i = 0;i < N;++i) {
    scanf("%lld", &W[i]);
  }

  for (int i = 0;i < M;++i) {
    int a, b;
    scanf("%d %d", &a, &b);
    
    // Numeruojame nuo 0.
    a--;
    b--;

    E[a][0].push_back(b);
    E[b][1].push_back(a);
  }
  
  // Kelių, pasibaigiančių nulinėje viršūnėje, skaičius yra 0, nes kelias turi turėti bent dvi viršūnes.
  A[0] = 0;
  
  // A[i] = (A[0] + 1) + (A[1] + 1) + .. + (A[i - 1] + 1) - (A[x1] + 1) - (A[x2] + 1) - .. - (A[xk] + 1)
  // kur x1, x2, .., xk yra viršūnės, iš kurių briaunos į viršūnę i neina, t.y. buvo išimtos.
  // Kintamajame s saugome (A[0] + 1) + (A[1] + 1) + .. + (A[i - 1] + 1) reikšmę.
  ll s = 1;

  for (int i = 1;i < N;++i) {
    A[i] = s;

    for (int j = 0;j < E[i][1].size();++j) {
      int u = E[i][1][j];

      A[i] = (A[i] - A[u] - 1) % MOD;
    }
    
    s = (s + A[i] + 1) % MOD;
  }
  
  // Analogiškai, B[i] = (B[N - 1] + 1) + .. + (B[i + 1] + 1) - (B[x1] + 1) - .. - (B[xk] + 1),
  // kur x1, .., xk yra viršūnės, į kurias briaunos iš viršūnės i nėra, t.y. buvo išimtos.
  B[N - 1] = 0;
  s = 1;

  for (int i = N - 2;i >= 0;--i) {
    B[i] = s;

    for (int j = 0;j < E[i][0].size();++j) {
      int u = E[i][0][j];

      B[i] = (B[i] - B[u] - 1) % MOD;
    }

    s = (s + B[i] + 1) % MOD;
  }
  
  // Jei A[i] - visų kelių, pasibaigiančių viršūnėje i, skaičius, o B[i] - visų kelių, prasidedančių viršūnėje i, skaičius, tai
  // A[i] * B[i] + A[i] + B[i] - visų kelių einančių per viršūnę i skaičius.
  // Todėl atsakymas yra suma per visus i W[i] * (A[i] * B[i] + A[i] + B[i])
  ll answer = 0;
  
  // Išnaudojame tapatybę A[i] * B[i] + A[i] + B[i] = (A[i] + 1) * (B[i] + 1) - 1.
  for (int i = 0;i < N;++i) {
    answer = ((W[i] * ((A[i] + 1) * (B[i] + 1) % MOD) % MOD) + answer) % MOD;
  }

  for (int i = 0;i < N;++i) {
    answer = (answer - W[i]) % MOD;
  }
  answer = (answer + MOD) % MOD;
  printf("%lld\n", answer);
  return 0;
}

Compilation message

keliones.cpp: In function 'int main()':
keliones.cpp:54:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int j = 0;j < E[i][1].size();++j) {
                    ~~^~~~~~~~~~~~~~~~
keliones.cpp:71:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
     for (int j = 0;j < E[i][0].size();++j) {
                    ~~^~~~~~~~~~~~~~~~
keliones.cpp:25:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d %d", &N, &M);
   ~~~~~^~~~~~~~~~~~~~~~~
keliones.cpp:28:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%lld", &W[i]);
     ~~~~~^~~~~~~~~~~~~~~
keliones.cpp:33:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d", &a, &b);
     ~~~~~^~~~~~~~~~~~~~~~~

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 9720 KB Output is correct
2 Correct 11 ms 9720 KB Output is correct
3 Correct 11 ms 9720 KB Output is correct
4 Correct 11 ms 9720 KB Output is correct
5 Correct 11 ms 9720 KB Output is correct
6 Correct 11 ms 9720 KB Output is correct
7 Correct 11 ms 9720 KB Output is correct
8 Correct 11 ms 9720 KB Output is correct
9 Correct 12 ms 9720 KB Output is correct
10 Correct 13 ms 9720 KB Output is correct
11 Correct 12 ms 9720 KB Output is correct
12 Correct 11 ms 9720 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 98 ms 10744 KB Output is correct
2 Correct 37 ms 10872 KB Output is correct
3 Correct 32 ms 10744 KB Output is correct
4 Correct 19 ms 9976 KB Output is correct
5 Correct 31 ms 10616 KB Output is correct
6 Correct 24 ms 10232 KB Output is correct
7 Correct 13 ms 9720 KB Output is correct
8 Correct 11 ms 9780 KB Output is correct
9 Correct 12 ms 9720 KB Output is correct
10 Correct 12 ms 9720 KB Output is correct
11 Correct 12 ms 9720 KB Output is correct
12 Correct 12 ms 9720 KB Output is correct
13 Correct 12 ms 9720 KB Output is correct
14 Correct 12 ms 9720 KB Output is correct
15 Correct 15 ms 9848 KB Output is correct
16 Correct 11 ms 9720 KB Output is correct
17 Correct 11 ms 9720 KB Output is correct
18 Correct 11 ms 9720 KB Output is correct
19 Correct 11 ms 9720 KB Output is correct
20 Correct 11 ms 9720 KB Output is correct
21 Correct 11 ms 9720 KB Output is correct
22 Correct 11 ms 9720 KB Output is correct
23 Correct 11 ms 9720 KB Output is correct
24 Correct 12 ms 9720 KB Output is correct
25 Correct 13 ms 9720 KB Output is correct
26 Correct 12 ms 9720 KB Output is correct
27 Correct 11 ms 9720 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 98 ms 10744 KB Output is correct
2 Correct 37 ms 10872 KB Output is correct
3 Correct 32 ms 10744 KB Output is correct
4 Correct 19 ms 9976 KB Output is correct
5 Correct 31 ms 10616 KB Output is correct
6 Correct 24 ms 10232 KB Output is correct
7 Correct 13 ms 9720 KB Output is correct
8 Correct 11 ms 9780 KB Output is correct
9 Correct 12 ms 9720 KB Output is correct
10 Correct 12 ms 9720 KB Output is correct
11 Correct 12 ms 9720 KB Output is correct
12 Correct 12 ms 9720 KB Output is correct
13 Correct 12 ms 9720 KB Output is correct
14 Correct 12 ms 9720 KB Output is correct
15 Correct 15 ms 9848 KB Output is correct
16 Correct 47 ms 11256 KB Output is correct
17 Correct 19 ms 10232 KB Output is correct
18 Correct 31 ms 10612 KB Output is correct
19 Correct 20 ms 10104 KB Output is correct
20 Correct 13 ms 9848 KB Output is correct
21 Correct 14 ms 9976 KB Output is correct
22 Correct 32 ms 10616 KB Output is correct
23 Correct 42 ms 11128 KB Output is correct
24 Correct 46 ms 11256 KB Output is correct
25 Correct 11 ms 9720 KB Output is correct
26 Correct 11 ms 9720 KB Output is correct
27 Correct 11 ms 9720 KB Output is correct
28 Correct 11 ms 9720 KB Output is correct
29 Correct 11 ms 9720 KB Output is correct
30 Correct 11 ms 9720 KB Output is correct
31 Correct 11 ms 9720 KB Output is correct
32 Correct 11 ms 9720 KB Output is correct
33 Correct 12 ms 9720 KB Output is correct
34 Correct 13 ms 9720 KB Output is correct
35 Correct 12 ms 9720 KB Output is correct
36 Correct 11 ms 9720 KB Output is correct

Subtask #4
55.0 / 55.0

# Verdict Execution time Memory Grader output
1 Correct 98 ms 10744 KB Output is correct
2 Correct 37 ms 10872 KB Output is correct
3 Correct 32 ms 10744 KB Output is correct
4 Correct 19 ms 9976 KB Output is correct
5 Correct 31 ms 10616 KB Output is correct
6 Correct 24 ms 10232 KB Output is correct
7 Correct 13 ms 9720 KB Output is correct
8 Correct 11 ms 9780 KB Output is correct
9 Correct 12 ms 9720 KB Output is correct
10 Correct 12 ms 9720 KB Output is correct
11 Correct 12 ms 9720 KB Output is correct
12 Correct 12 ms 9720 KB Output is correct
13 Correct 12 ms 9720 KB Output is correct
14 Correct 12 ms 9720 KB Output is correct
15 Correct 15 ms 9848 KB Output is correct
16 Correct 47 ms 11256 KB Output is correct
17 Correct 19 ms 10232 KB Output is correct
18 Correct 31 ms 10612 KB Output is correct
19 Correct 20 ms 10104 KB Output is correct
20 Correct 13 ms 9848 KB Output is correct
21 Correct 14 ms 9976 KB Output is correct
22 Correct 32 ms 10616 KB Output is correct
23 Correct 42 ms 11128 KB Output is correct
24 Correct 46 ms 11256 KB Output is correct
25 Correct 11 ms 9720 KB Output is correct
26 Correct 11 ms 9720 KB Output is correct
27 Correct 11 ms 9720 KB Output is correct
28 Correct 11 ms 9720 KB Output is correct
29 Correct 11 ms 9720 KB Output is correct
30 Correct 11 ms 9720 KB Output is correct
31 Correct 11 ms 9720 KB Output is correct
32 Correct 11 ms 9720 KB Output is correct
33 Correct 12 ms 9720 KB Output is correct
34 Correct 13 ms 9720 KB Output is correct
35 Correct 12 ms 9720 KB Output is correct
36 Correct 11 ms 9720 KB Output is correct
37 Correct 100 ms 16504 KB Output is correct
38 Correct 51 ms 14584 KB Output is correct
39 Correct 95 ms 16504 KB Output is correct
40 Correct 230 ms 18852 KB Output is correct
41 Correct 57 ms 14892 KB Output is correct
42 Correct 154 ms 18424 KB Output is correct
43 Correct 47 ms 14456 KB Output is correct
44 Correct 80 ms 15736 KB Output is correct
45 Correct 118 ms 16120 KB Output is correct