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Submission #648706

# Submission time Handle Problem Language Result Execution time Memory
648706 2022-10-07T14:07:18 Z alvinpiter Nautilus (BOI19_nautilus) C++17
100 / 100
 287 ms 157024 KB 
/*
dp[r][c][idx] -> Is it possible to reach cell (r, c) after executing idx-th command. idx starts from 1.

Base case:
dp[r][c][0] = 1 if isWater(r, c), 0 otherwise.

Transition:
command[idx] = 'N' -> dp[r][c][idx] = dp[r + 1][c][idx - 1] && isWater(r, c)
command[idx] = 'E' -> dp[r][c][idx] = dp[r][c - 1][idx - 1] && isWater(r, c)
command[idx] = 'S' -> dp[r][c][idx] = dp[r - 1][c][idx - 1] && isWater(r, c)
command[idx] = 'W' -> dp[r][c][idx] = dp[r][c + 1][idx - 1] && isWater(r, c)
command[idx] = '?' -> dp[r][c][idx] = (d[r + 1][c][idx - 1] & isWater(r, c)) | ...

Naive implementation will get TLE/MLE, because there are R*C*M states. We need C++'s bitset.

isWater(r) -> a bitset that represents whether a certain column in row r is filled with water.
dp[r][idx] -> a bitset that represents whether a certain column in row r can be reached after executing idx-th command.

command[idx] = 'N' -> dp[r][idx] = dp[r + 1][idx - 1] && isWater(r)
command[idx] = 'E' -> dp[r][idx] = (dp[r][idx - 1]) << 1) && isWater(r)
command[idx] = 'S' -> dp[r][idx] = dp[r - 1][idx - 1] && isWater(r)
command[idx] = 'W' -> dp[r][idx] = (dp[r][idx - 1] >> 1) && isWater(r)
command[idx] = '?' -> dp[r][idx] = (dp[r + 1][idx - 1] && isWater(r)) | ...

Notice the direction of the left shift and right shift. It is reversed because the bitset is indexed starting from 0
from the right.
*/

#include<bits/stdc++.h>
using namespace std;
#define MAXR 500
#define MAXM 5000

int R, C, M;
string command;
bitset<MAXR + 3> isWater[MAXR + 3], dp[MAXR + 3][MAXM + 3];

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);

  cin >> R >> C >> M;

  for (int r = 1; r <= R; r++) {
    for (int c = 1; c <= C; c++) {
      char cell;
      cin >> cell;

      if (cell == '.') {
        isWater[r].set(c, 1);
        dp[r][0].set(c, 1);
      }
    }
  }

  cin >> command;

  for (int idx = 1; idx <= M; idx++) {
    for (int r = 1; r <= R; r++) {
      switch (command[idx - 1]) {
        case 'N':
          dp[r][idx] = dp[r + 1][idx - 1] & isWater[r];
          break;
        case 'E':
          dp[r][idx] = (dp[r][idx - 1] << 1) & isWater[r];
          break;
        case 'S':
          dp[r][idx] = dp[r - 1][idx - 1] & isWater[r];
          break;
        case 'W':
          dp[r][idx] = (dp[r][idx - 1] >> 1) & isWater[r];
          break;
        case '?':
          dp[r][idx] = (dp[r + 1][idx - 1] | (dp[r][idx - 1] << 1) | dp[r - 1][idx - 1] | (dp[r][idx - 1] >> 1)) & isWater[r];
          break;
      }
    }
  }

  int ans = 0;
  for (int r = 1; r <= R; r++) {
    for (int c = 1; c <= C; c++) {
      if (dp[r][M].test(c)) {
        ans += 1;
      }
    }
  }

  cout << ans << endl;
}

Subtask #1
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1364 KB Output is correct
2 Correct 1 ms 1364 KB Output is correct
3 Correct 1 ms 1492 KB Output is correct
4 Correct 1 ms 1364 KB Output is correct
5 Correct 1 ms 1364 KB Output is correct
6 Correct 1 ms 1364 KB Output is correct

Subtask #2
37.0 / 37.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1364 KB Output is correct
2 Correct 1 ms 1364 KB Output is correct
3 Correct 1 ms 1492 KB Output is correct
4 Correct 1 ms 1364 KB Output is correct
5 Correct 1 ms 1364 KB Output is correct
6 Correct 1 ms 1364 KB Output is correct
7 Correct 1 ms 1364 KB Output is correct
8 Correct 2 ms 1364 KB Output is correct
9 Correct 2 ms 1364 KB Output is correct
10 Correct 2 ms 1364 KB Output is correct
11 Correct 1 ms 1364 KB Output is correct
12 Correct 2 ms 1364 KB Output is correct
13 Correct 1 ms 1364 KB Output is correct
14 Correct 2 ms 1364 KB Output is correct
15 Correct 2 ms 1364 KB Output is correct
16 Correct 2 ms 1364 KB Output is correct
17 Correct 2 ms 1364 KB Output is correct
18 Correct 3 ms 1364 KB Output is correct
19 Correct 2 ms 1364 KB Output is correct
20 Correct 2 ms 1364 KB Output is correct
21 Correct 2 ms 1364 KB Output is correct

Subtask #3
34.0 / 34.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1364 KB Output is correct
2 Correct 1 ms 1364 KB Output is correct
3 Correct 1 ms 1492 KB Output is correct
4 Correct 1 ms 1364 KB Output is correct
5 Correct 1 ms 1364 KB Output is correct
6 Correct 1 ms 1364 KB Output is correct
7 Correct 1 ms 1364 KB Output is correct
8 Correct 2 ms 1364 KB Output is correct
9 Correct 2 ms 1364 KB Output is correct
10 Correct 2 ms 1364 KB Output is correct
11 Correct 1 ms 1364 KB Output is correct
12 Correct 2 ms 1364 KB Output is correct
13 Correct 1 ms 1364 KB Output is correct
14 Correct 2 ms 1364 KB Output is correct
15 Correct 2 ms 1364 KB Output is correct
16 Correct 2 ms 1364 KB Output is correct
17 Correct 2 ms 1364 KB Output is correct
18 Correct 3 ms 1364 KB Output is correct
19 Correct 2 ms 1364 KB Output is correct
20 Correct 2 ms 1364 KB Output is correct
21 Correct 2 ms 1364 KB Output is correct
22 Correct 171 ms 156948 KB Output is correct
23 Correct 150 ms 156976 KB Output is correct
24 Correct 162 ms 156976 KB Output is correct
25 Correct 193 ms 156956 KB Output is correct
26 Correct 158 ms 157024 KB Output is correct
27 Correct 215 ms 157004 KB Output is correct
28 Correct 252 ms 156900 KB Output is correct
29 Correct 229 ms 156972 KB Output is correct
30 Correct 216 ms 157004 KB Output is correct
31 Correct 244 ms 156908 KB Output is correct
32 Correct 272 ms 157004 KB Output is correct
33 Correct 287 ms 156980 KB Output is correct
34 Correct 265 ms 156980 KB Output is correct
35 Correct 263 ms 156940 KB Output is correct
36 Correct 284 ms 156892 KB Output is correct