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Submission #575167

# Submission time Handle Problem Language Result Execution time Memory
575167 2022-06-09T19:54:01 Z erekle Collecting Stamps 3 (JOI20_ho_t3) C++17
100 / 100
 176 ms 65708 KB 
#include <iostream>
#include <vector>

using namespace std;

const int N = 200;
const long long INF = 1e18;

long long dp[1+N][1+N][2][1+N];
// dp[l][r][p][s] is minimum time where:
//  - [l, r] is range of stamps left
//  - p is the current position (boolean - either l-1 or r+1)
//  - s is the current number of stamps collected

int main() {
    int n, L;
    cin >> n >> L;
    vector<int> x(1+n), t(1+n);
    for (int i = 1; i <= n; ++i) cin >> x[i];
    for (int i = 1; i <= n; ++i) cin >> t[i];
    x[0] = 0, t[0] = -1; // add stamp at x=0 that cannot be collected

    auto d = [&x, &n, &L](int i, int j) {
        if (i > j) swap(i, j);
        return min(x[j]-x[i], x[i]+L-x[j]);
    };

    // fill with INF
    for (int l = 0; l <= n; ++l) {
        for (int r = max(0, l-1); r <= n; ++r) {
            for (int p = 0; p <= 1; ++p) {
                for (int s = 0; s <= n; ++s) dp[l][r][p][s] = INF;
            }
        }
    }
   
    // addition of extra stamp makes base case easier
    dp[1][n][0][0] = dp[1][n][1][0] = 0;

    /* answers will be stored at sz = 0 (r = l-1), but we do not traverse
    since they are final states - they do not need to contribute to other states */

    // dp - pushing answers to later states rather than pulling from previous
    for (int sz = n; sz >= 1; --sz) {
        for (int l = 1; l+sz-1 <= n; ++l) {
            int r = l+sz-1, before = (l-1+(n+1))%(n+1), after = (r+1)%(n+1);
            for (int s = 0; s <= n; ++s) {
                // p = 0 means at l-1, p = 1 means at r+1
                for (int p = 0; p <= 1; ++p) { // current position
                    for (int p1 = 0; p1 <= 1; ++p1) { // next position
                        int cur = (!p ? before : after); // current location
                        int nxt = (!p1 ? l : r); // next location
                        long long time = dp[l][r][p][s] + d(cur, nxt); // total time taken
                        bool delta = time <= t[nxt]; // extra stamps collected (0 or 1)
                        
                        int l1 = l + (p1 == 0), r1 = r - (p1 == 1), s1 = s+delta;
                        if (l1 > n) continue; // r1 < 0 will never happen since l >= 1
                        dp[l1][r1][p1][s1] = min(dp[l1][r1][p1][s1], time);
                    }
                }
            }
        }
    }

    int maxCollected = 0;
    for (int s = 1; s <= n; ++s) {
        for (int l = 1; l <= n; ++l) {
            if (dp[l][l-1][0][s] != INF || dp[l][l-1][1][s] != INF) {
                maxCollected = s;
            }
        }
    }
    cout << maxCollected << endl;
    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 308 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 596 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 596 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 564 KB Output is correct
17 Correct 1 ms 596 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 308 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 596 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 596 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 564 KB Output is correct
17 Correct 1 ms 596 KB Output is correct
18 Correct 1 ms 724 KB Output is correct
19 Correct 1 ms 468 KB Output is correct
20 Correct 1 ms 596 KB Output is correct
21 Correct 1 ms 724 KB Output is correct
22 Correct 0 ms 468 KB Output is correct
23 Correct 1 ms 724 KB Output is correct
24 Correct 1 ms 724 KB Output is correct
25 Correct 1 ms 724 KB Output is correct
26 Correct 1 ms 724 KB Output is correct
27 Correct 1 ms 468 KB Output is correct
28 Correct 1 ms 468 KB Output is correct
29 Correct 1 ms 724 KB Output is correct
30 Correct 1 ms 816 KB Output is correct
31 Correct 1 ms 724 KB Output is correct
32 Correct 1 ms 688 KB Output is correct
33 Correct 1 ms 724 KB Output is correct
34 Correct 1 ms 816 KB Output is correct
35 Correct 1 ms 724 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 308 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 596 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 596 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 564 KB Output is correct
17 Correct 1 ms 596 KB Output is correct
18 Correct 116 ms 52820 KB Output is correct
19 Correct 59 ms 32396 KB Output is correct
20 Correct 28 ms 17492 KB Output is correct
21 Correct 61 ms 30512 KB Output is correct
22 Correct 82 ms 39508 KB Output is correct
23 Correct 22 ms 15024 KB Output is correct
24 Correct 16 ms 11860 KB Output is correct
25 Correct 21 ms 14724 KB Output is correct
26 Correct 7 ms 5812 KB Output is correct
27 Correct 23 ms 15328 KB Output is correct
28 Correct 14 ms 10964 KB Output is correct
29 Correct 24 ms 15552 KB Output is correct
30 Correct 16 ms 12372 KB Output is correct
31 Correct 21 ms 14676 KB Output is correct
32 Correct 10 ms 7940 KB Output is correct
33 Correct 22 ms 14724 KB Output is correct
34 Correct 5 ms 5528 KB Output is correct
35 Correct 21 ms 14388 KB Output is correct
36 Correct 8 ms 6996 KB Output is correct
37 Correct 22 ms 15328 KB Output is correct
38 Correct 10 ms 8532 KB Output is correct
39 Correct 24 ms 15924 KB Output is correct
40 Correct 11 ms 9556 KB Output is correct
41 Correct 168 ms 65072 KB Output is correct
42 Correct 97 ms 43980 KB Output is correct
43 Correct 175 ms 65076 KB Output is correct
44 Correct 95 ms 43684 KB Output is correct
45 Correct 168 ms 65072 KB Output is correct
46 Correct 97 ms 44096 KB Output is correct

Subtask #4
75.0 / 75.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 308 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 596 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 596 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 564 KB Output is correct
17 Correct 1 ms 596 KB Output is correct
18 Correct 1 ms 724 KB Output is correct
19 Correct 1 ms 468 KB Output is correct
20 Correct 1 ms 596 KB Output is correct
21 Correct 1 ms 724 KB Output is correct
22 Correct 0 ms 468 KB Output is correct
23 Correct 1 ms 724 KB Output is correct
24 Correct 1 ms 724 KB Output is correct
25 Correct 1 ms 724 KB Output is correct
26 Correct 1 ms 724 KB Output is correct
27 Correct 1 ms 468 KB Output is correct
28 Correct 1 ms 468 KB Output is correct
29 Correct 1 ms 724 KB Output is correct
30 Correct 1 ms 816 KB Output is correct
31 Correct 1 ms 724 KB Output is correct
32 Correct 1 ms 688 KB Output is correct
33 Correct 1 ms 724 KB Output is correct
34 Correct 1 ms 816 KB Output is correct
35 Correct 1 ms 724 KB Output is correct
36 Correct 116 ms 52820 KB Output is correct
37 Correct 59 ms 32396 KB Output is correct
38 Correct 28 ms 17492 KB Output is correct
39 Correct 61 ms 30512 KB Output is correct
40 Correct 82 ms 39508 KB Output is correct
41 Correct 22 ms 15024 KB Output is correct
42 Correct 16 ms 11860 KB Output is correct
43 Correct 21 ms 14724 KB Output is correct
44 Correct 7 ms 5812 KB Output is correct
45 Correct 23 ms 15328 KB Output is correct
46 Correct 14 ms 10964 KB Output is correct
47 Correct 24 ms 15552 KB Output is correct
48 Correct 16 ms 12372 KB Output is correct
49 Correct 21 ms 14676 KB Output is correct
50 Correct 10 ms 7940 KB Output is correct
51 Correct 22 ms 14724 KB Output is correct
52 Correct 5 ms 5528 KB Output is correct
53 Correct 21 ms 14388 KB Output is correct
54 Correct 8 ms 6996 KB Output is correct
55 Correct 22 ms 15328 KB Output is correct
56 Correct 10 ms 8532 KB Output is correct
57 Correct 24 ms 15924 KB Output is correct
58 Correct 11 ms 9556 KB Output is correct
59 Correct 168 ms 65072 KB Output is correct
60 Correct 97 ms 43980 KB Output is correct
61 Correct 175 ms 65076 KB Output is correct
62 Correct 95 ms 43684 KB Output is correct
63 Correct 168 ms 65072 KB Output is correct
64 Correct 97 ms 44096 KB Output is correct
65 Correct 149 ms 58820 KB Output is correct
66 Correct 131 ms 54076 KB Output is correct
67 Correct 123 ms 51744 KB Output is correct
68 Correct 109 ms 47852 KB Output is correct
69 Correct 140 ms 58224 KB Output is correct
70 Correct 138 ms 55832 KB Output is correct
71 Correct 144 ms 56432 KB Output is correct
72 Correct 145 ms 57020 KB Output is correct
73 Correct 128 ms 52912 KB Output is correct
74 Correct 117 ms 49612 KB Output is correct
75 Correct 135 ms 54652 KB Output is correct
76 Correct 161 ms 62536 KB Output is correct
77 Correct 163 ms 62488 KB Output is correct
78 Correct 112 ms 48404 KB Output is correct
79 Correct 118 ms 50068 KB Output is correct
80 Correct 156 ms 61232 KB Output is correct
81 Correct 120 ms 50644 KB Output is correct
82 Correct 128 ms 53456 KB Output is correct
83 Correct 169 ms 65072 KB Output is correct
84 Correct 138 ms 55764 KB Output is correct
85 Correct 155 ms 60700 KB Output is correct
86 Correct 150 ms 59444 KB Output is correct
87 Correct 131 ms 54660 KB Output is correct
88 Correct 172 ms 65700 KB Output is correct
89 Correct 176 ms 65600 KB Output is correct
90 Correct 135 ms 55248 KB Output is correct
91 Correct 165 ms 65708 KB Output is correct
92 Correct 173 ms 65704 KB Output is correct
93 Correct 167 ms 64340 KB Output is correct