oj.uz

Submission #362629

# Submission time Handle Problem Language Result Execution time Memory
362629 2021-02-03T18:19:53 Z JerryLiu06 Toll (BOI17_toll) Java 11
100 / 100
 2483 ms 368100 KB 
import java.io.*;
import java.util.*;

// Solution Notes: Split the graph into N / K "layers" with K nodes each. Notice that each edge leads from one layer to the
// next layer. Now, let DP[a][b][x][y] denote the minimum cost of a path between nodes Ka + x and Kb + y. For any triple 
// a < b < c, the following recurrence holds: DP[a][c][x][y] = MIN_{z in [0, K)} (DP[a][b][x][z] + DP[b][c][z][y]). This is
// known as the (min, +) product. Now, we have to note that there are N^2 K^2 states, so we have to reduce the number of
// states. This motivates us to, instead of storing DP[a][b][x][y], we can store only DP[a][a + 2^i][x][y] for each a, i, x,
// y. Then we can find the value of DP[A / K][B / K][A % K][B % K] in O(K^3 (N + O) log N) complexity.

public class toll {

    static int K, N, M, O; static int[][][][] DP = new int[50010][20][5][5];

    static int[][] temp = new int[5][5]; static int[][] ans = new int[5][5];

    static final int INF = Integer.MAX_VALUE / 3;
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());

        K = Integer.parseInt(st.nextToken());
        N = Integer.parseInt(st.nextToken());
        M = Integer.parseInt(st.nextToken());
        O = Integer.parseInt(st.nextToken());

        for (int i = 0; i < 50010; i++) for (int j = 0; j < 20; j++) {
            for (int k = 0; k < 5; k++) Arrays.fill(DP[i][j][k], INF);
        }
        for (int i = 0; i < M; i++) { st = new StringTokenizer(br.readLine());
            int A = Integer.parseInt(st.nextToken());
            int B = Integer.parseInt(st.nextToken());
            int W = Integer.parseInt(st.nextToken());

            DP[A / K][0][A % K][B % K] = W;
        }
        for (int j = 1; j < 20; j++) for (int i = 0; i + (1 << j) < (N + K - 1) / K; i++) {
            combine(DP[i][j], DP[i][j - 1], DP[i + (1 << (j - 1))][j - 1]);
        }
        for (int i = 0; i < O; i++) { st = new StringTokenizer(br.readLine());
            int A = Integer.parseInt(st.nextToken());
            int B = Integer.parseInt(st.nextToken());

            for (int j = 0; j < 5; j++) Arrays.fill(ans[j], INF);

            for (int j = 0; j < 5; j++) ans[j][j] = 0;

            int jump = (B / K) - (A / K); int curLev = A / K;

            for (int j = 0; j < 20; j++) if ((jump & (1 << j)) > 0) {
                for (int k = 0; k < 5; k++) Arrays.fill(temp[k], INF);

                combine(temp, ans, DP[curLev][j]); 

                for (int k = 0; k < 5; k++) for (int l = 0; l < 5; l++) ans[k][l] = temp[k][l];

                curLev += (1 << j);
            }
            System.out.println(ans[A % K][B % K] == INF ? -1 : ans[A % K][B % K]);
        }
    }
    static void combine(int[][] res, int[][] A, int[][] B) {
        for (int i = 0; i < 5; i++) for (int j = 0; j < 5; j++) for (int k = 0; k < 5; k++) {
            res[i][j] = Math.min(res[i][j], A[i][k] + B[k][j]);
        }
    }
}

Subtask #1
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2345 ms 275468 KB Output is correct
2 Correct 1269 ms 257516 KB Output is correct
3 Correct 1261 ms 257380 KB Output is correct
4 Correct 1297 ms 257152 KB Output is correct
5 Correct 1504 ms 259108 KB Output is correct
6 Correct 1512 ms 258876 KB Output is correct
7 Correct 1498 ms 258968 KB Output is correct
8 Correct 2349 ms 274768 KB Output is correct
9 Correct 2387 ms 274376 KB Output is correct
10 Correct 2220 ms 261744 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2419 ms 366088 KB Output is correct
2 Correct 1299 ms 257572 KB Output is correct
3 Correct 1303 ms 257044 KB Output is correct
4 Correct 1271 ms 257224 KB Output is correct
5 Correct 1273 ms 257296 KB Output is correct
6 Correct 1286 ms 257268 KB Output is correct
7 Correct 1936 ms 261836 KB Output is correct
8 Correct 2151 ms 262936 KB Output is correct
9 Correct 2291 ms 274776 KB Output is correct
10 Correct 2469 ms 367008 KB Output is correct
11 Correct 2420 ms 366484 KB Output is correct
12 Correct 2199 ms 281468 KB Output is correct
13 Correct 2054 ms 367392 KB Output is correct
14 Correct 1825 ms 282480 KB Output is correct
15 Correct 1793 ms 278496 KB Output is correct
16 Correct 1800 ms 278600 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1301 ms 257012 KB Output is correct
2 Correct 1270 ms 257144 KB Output is correct
3 Correct 1291 ms 257280 KB Output is correct
4 Correct 1270 ms 257408 KB Output is correct
5 Correct 1262 ms 257264 KB Output is correct
6 Correct 1423 ms 258932 KB Output is correct
7 Correct 1448 ms 258324 KB Output is correct
8 Correct 1480 ms 258984 KB Output is correct
9 Correct 1477 ms 258704 KB Output is correct
10 Correct 1874 ms 272004 KB Output is correct
11 Correct 1940 ms 364788 KB Output is correct
12 Correct 1931 ms 367184 KB Output is correct
13 Correct 1976 ms 367464 KB Output is correct
14 Correct 1906 ms 366424 KB Output is correct
15 Correct 1648 ms 278400 KB Output is correct
16 Correct 1658 ms 278396 KB Output is correct

Subtask #4
31.0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 1301 ms 257012 KB Output is correct
2 Correct 1270 ms 257144 KB Output is correct
3 Correct 1291 ms 257280 KB Output is correct
4 Correct 1270 ms 257408 KB Output is correct
5 Correct 1262 ms 257264 KB Output is correct
6 Correct 1423 ms 258932 KB Output is correct
7 Correct 1448 ms 258324 KB Output is correct
8 Correct 1480 ms 258984 KB Output is correct
9 Correct 1477 ms 258704 KB Output is correct
10 Correct 1874 ms 272004 KB Output is correct
11 Correct 1940 ms 364788 KB Output is correct
12 Correct 1931 ms 367184 KB Output is correct
13 Correct 1976 ms 367464 KB Output is correct
14 Correct 1906 ms 366424 KB Output is correct
15 Correct 1648 ms 278400 KB Output is correct
16 Correct 1658 ms 278396 KB Output is correct
17 Correct 2080 ms 365236 KB Output is correct
18 Correct 1287 ms 257388 KB Output is correct
19 Correct 1297 ms 257296 KB Output is correct
20 Correct 1280 ms 257544 KB Output is correct
21 Correct 1306 ms 257332 KB Output is correct
22 Correct 1277 ms 257156 KB Output is correct
23 Correct 1675 ms 259276 KB Output is correct
24 Correct 2081 ms 262344 KB Output is correct
25 Correct 1803 ms 260340 KB Output is correct
26 Correct 1813 ms 262168 KB Output is correct
27 Correct 1981 ms 271860 KB Output is correct
28 Correct 2137 ms 367088 KB Output is correct
29 Correct 2118 ms 367204 KB Output is correct
30 Correct 2040 ms 366996 KB Output is correct

Subtask #5
44.0 / 44.0

# Verdict Execution time Memory Grader output
1 Correct 2345 ms 275468 KB Output is correct
2 Correct 1269 ms 257516 KB Output is correct
3 Correct 1261 ms 257380 KB Output is correct
4 Correct 1297 ms 257152 KB Output is correct
5 Correct 1504 ms 259108 KB Output is correct
6 Correct 1512 ms 258876 KB Output is correct
7 Correct 1498 ms 258968 KB Output is correct
8 Correct 2349 ms 274768 KB Output is correct
9 Correct 2387 ms 274376 KB Output is correct
10 Correct 2220 ms 261744 KB Output is correct
11 Correct 2419 ms 366088 KB Output is correct
12 Correct 1299 ms 257572 KB Output is correct
13 Correct 1303 ms 257044 KB Output is correct
14 Correct 1271 ms 257224 KB Output is correct
15 Correct 1273 ms 257296 KB Output is correct
16 Correct 1286 ms 257268 KB Output is correct
17 Correct 1936 ms 261836 KB Output is correct
18 Correct 2151 ms 262936 KB Output is correct
19 Correct 2291 ms 274776 KB Output is correct
20 Correct 2469 ms 367008 KB Output is correct
21 Correct 2420 ms 366484 KB Output is correct
22 Correct 2199 ms 281468 KB Output is correct
23 Correct 2054 ms 367392 KB Output is correct
24 Correct 1825 ms 282480 KB Output is correct
25 Correct 1793 ms 278496 KB Output is correct
26 Correct 1800 ms 278600 KB Output is correct
27 Correct 1301 ms 257012 KB Output is correct
28 Correct 1270 ms 257144 KB Output is correct
29 Correct 1291 ms 257280 KB Output is correct
30 Correct 1270 ms 257408 KB Output is correct
31 Correct 1262 ms 257264 KB Output is correct
32 Correct 1423 ms 258932 KB Output is correct
33 Correct 1448 ms 258324 KB Output is correct
34 Correct 1480 ms 258984 KB Output is correct
35 Correct 1477 ms 258704 KB Output is correct
36 Correct 1874 ms 272004 KB Output is correct
37 Correct 1940 ms 364788 KB Output is correct
38 Correct 1931 ms 367184 KB Output is correct
39 Correct 1976 ms 367464 KB Output is correct
40 Correct 1906 ms 366424 KB Output is correct
41 Correct 1648 ms 278400 KB Output is correct
42 Correct 1658 ms 278396 KB Output is correct
43 Correct 2080 ms 365236 KB Output is correct
44 Correct 1287 ms 257388 KB Output is correct
45 Correct 1297 ms 257296 KB Output is correct
46 Correct 1280 ms 257544 KB Output is correct
47 Correct 1306 ms 257332 KB Output is correct
48 Correct 1277 ms 257156 KB Output is correct
49 Correct 1675 ms 259276 KB Output is correct
50 Correct 2081 ms 262344 KB Output is correct
51 Correct 1803 ms 260340 KB Output is correct
52 Correct 1813 ms 262168 KB Output is correct
53 Correct 1981 ms 271860 KB Output is correct
54 Correct 2137 ms 367088 KB Output is correct
55 Correct 2118 ms 367204 KB Output is correct
56 Correct 2040 ms 366996 KB Output is correct
57 Correct 2440 ms 368100 KB Output is correct
58 Correct 2332 ms 274960 KB Output is correct
59 Correct 2483 ms 366520 KB Output is correct