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Submission #625695

# Submission time Handle Problem Language Result Execution time Memory
625695 2022-08-10T17:13:23 Z I_love_Hoang_Yen Catfish Farm (IOI22_fish) C++17
70 / 100
 729 ms 2097152 KB 
#include "bits/stdc++.h"
using namespace std;

#define int long long
#define i_1 jakcjacjl
struct Fish {
    int col, row;
    int weight;
};
bool operator < (const Fish& a, const Fish& b) {
    if (a.col != b.col) return a.col < b.col;
    return a.row < b.row;
}

void upMax(int& f, int val) {
    if (val > f) f = val;
}

// sub1 - 3 {{{
// fishes are on even columns -> build piers on odd columns
// & catch all fishes
int sub1(const std::vector<Fish>& fishes) {
    int res = 0;
    for (const auto& fish : fishes) {
        res += fish.weight;
    }
    return res;
}

// fishes are on first 2 columns
int sub2(int n, const std::vector<Fish>& fishes) {
    std::vector<int> zeroes(n);  // prefix sum of fish weights at column == 0
    std::vector<int> ones(n);    // prefix sum of fish weights at column == 1
    for (const auto& fish : fishes) {
        if (fish.col == 0) zeroes[fish.row] += fish.weight;
        if (fish.col == 1) ones[fish.row] += fish.weight;
    }

    std::partial_sum(zeroes.begin(), zeroes.end(), zeroes.begin());
    std::partial_sum(ones.begin(), ones.end(), ones.begin());

    int res = ones.back();  // init: only catch fishes at column == 1
    for (int i = 0; i < n; ++i) {
        // build pier until at column 1, row 0-i
        if (n == 2) upMax(res, zeroes[i]);
        else upMax(res, zeroes[i] + ones.back() - ones[i]);
    }
    return res;
}

// all fishes are on row == 0
int sub3(int n, const std::vector<Fish>& fishes) {
    std::vector<int> weights(n);  // weights[i] = weight of fish at column i
    for (const auto& fish : fishes) {
        weights[fish.col] += fish.weight;
    }

    // f[i] = best strategy if we BUILD PIER AT i, only considering col 0..i
    // i-4 i-3 i-2 i-1 i
    std::vector<int> f(n);
    f[0] = 0;
    for (int i = 1; i < n; ++i) {
        f[i] = std::max(f[i-1], weights[i-1]);
        if (i >= 2) {
            upMax(f[i], f[i-2] + weights[i-1]);
        }
        if (i >= 3) {
            upMax(f[i], f[i-3] + weights[i-2] + weights[i-1]);
        }
    }

    int res = 0;
    for (int i = 0; i < n; ++i) {
        int cur = f[i];
        if (i + 1 < n) cur += weights[i+1];
        upMax(res, cur);
    }
    return res;
}
// }}}

// sub 5 N <= 300 {{{
int sub5(int n, const std::vector<Fish>& fishes) {
    // Init weights[i][j] = sum of fish on column i, from row 0 -> row j
    std::vector<std::vector<int>> weights(n, std::vector<int> (n, 0));
    for (const auto& fish : fishes) {
        weights[fish.col][fish.row] += fish.weight;
    }
    for (int col = 0; col < n; ++col) {
        std::partial_sum(weights[col].begin(), weights[col].end(), weights[col].begin());
    }

    // f[c][r] = best strategy if we last BUILD PIER AT column c, row r
    //           only considering fishes <= (c, r)
    // g[c][r] = similar to f[c][r] but consider fishes at column c, in row [r, n-1]
    std::vector<std::vector<int>> f(n, std::vector<int> (n, 0)),
                                  g(n, std::vector<int> (n, 0));
    // f <= g
    for (int c = 1; c < n; ++c) {
        for (int r = 0; r < n; ++r) {
            // this is first pier
            f[c][r] = g[c][r] = weights[c-1][r];

            // last pier at column i-1
            for (int lastRow = 0; lastRow < n; ++lastRow) {
                if (lastRow <= r) {
                    int cur = std::max(
                            f[c-1][lastRow] + weights[c-1][r] - weights[c-1][lastRow],
                            g[c-1][lastRow]);
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);
                } else {
                    upMax(f[c][r], g[c-1][lastRow]);
                    upMax(g[c][r], g[c-1][lastRow] + weights[c][lastRow] - weights[c][r]);
                }
            }

            // last pier at column i-2
            if (c >= 2) {
                for (int lastRow = 0; lastRow < n; ++lastRow) {
                    int cur = g[c-2][lastRow] + weights[c-1][std::max(lastRow, r)];
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);
                }
            }
            
            // last pier at column i-3
            if (c >= 3) {
                for (int lastRow = 0; lastRow < n; ++lastRow) {
                    int cur = g[c-3][lastRow] + weights[c-2][lastRow] + weights[c-1][r];
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);
                }
            }
        }
    }

    int res = 0;
    for (int c = 0; c < n; ++c) {
        for (int r = 0; r < n; ++r) {
            assert(g[c][r] >= f[c][r]);
            int cur = g[c][r];
            if (c + 1 < n) {
                cur += weights[c+1][r];
            }
            upMax(res, cur);
        }
    }
    return res;
}
// }}}

// N <= 3000 {{{
int sub6(int n, const std::vector<Fish>& fishes) {
    // Init weights[i][j] = sum of fish on column i, from row 0 -> row j
    std::vector<std::vector<int>> weights(n, std::vector<int> (n, 0));
    for (const auto& fish : fishes) {
        weights[fish.col][fish.row] += fish.weight;
    }
    for (int col = 0; col < n; ++col) {
        std::partial_sum(weights[col].begin(), weights[col].end(), weights[col].begin());
    }

    // f[c][r] = best strategy if we last BUILD PIER AT column c, row r
    //           only considering fishes <= (c, r)
    // g[c][r] = similar to f[c][r] but consider fishes at column c, in row [r, n-1]
    std::vector<std::vector<int>> f(n, std::vector<int> (n, 0)),
                                  g(n, std::vector<int> (n, 0)),
                                  g_prefix_max(n, std::vector<int> (n, 0)),
                                  g_suffix_max(n, std::vector<int> (n, 0)),
                                  g_with_next_col_suffix_max(n, std::vector<int> (n, 0)),
                                  g_with_next_col_prefix_max(n, std::vector<int> (n, 0)),
                                  f_with_next_col_prefix_max(n, std::vector<int> (n, 0));

    // f <= g
    for (int c = 0; c < n; ++c) {
        // compute {{{
        if (c > 0) {
            for (int r = 0; r < n; ++r) {
                // this is first pier
                f[c][r] = g[c][r] = weights[c-1][r];

                // last pier at column i-1
                if (c >= 1) {
                    // last row <= r
                    int cur = std::max(
                            g_prefix_max[c-1][r],
                            f_with_next_col_prefix_max[c-1][r] + weights[c-1][r]);
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);

                    // last row > r
                    if (r + 1 < n) {
                        upMax(f[c][r], g_suffix_max[c-1][r + 1]);
                        upMax(g[c][r], g_with_next_col_suffix_max[c-1][r + 1] - weights[c][r]);
                    }
                }

                // last pier at column i-2
                if (c >= 2) {
                    int cur = std::max(
                            g_prefix_max[c-2].back() + weights[c-1][r],
                            g_with_next_col_prefix_max[c-2].back());
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);
                }

                // last pier at column i-3
                if (c >= 3) {
                    int cur = g_with_next_col_prefix_max[c-3].back() + weights[c-1][r];
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);
                }
            }
        }
        // }}}
        
        // aggregate {{{
        // g_prefix_max[c][r] = max(g[c][0], .., g[c][r])
        auto MAX = [] (auto a, auto b) { return std::max(a, b); };
        std::partial_sum(g[c].begin(), g[c].end(), g_prefix_max[c].begin(), MAX);
        std::partial_sum(g[c].rbegin(), g[c].rend(), g_suffix_max[c].rbegin(), MAX);

        if (c + 1 < n) {
            // g_with_next_col_prefix_max[c][r] = max(
            //     g[c][0] + weights[c+1][0],
            //     ...
            //     g[c][r] + weights[c+1][r])
            for (int r = 0; r < n; ++r) {
                g_with_next_col_prefix_max[c][r] = g[c][r] + weights[c+1][r];
            }
            g_with_next_col_suffix_max[c] = g_with_next_col_prefix_max[c];

            std::partial_sum(
                    g_with_next_col_prefix_max[c].begin(),
                    g_with_next_col_prefix_max[c].end(),
                    g_with_next_col_prefix_max[c].begin(),
                    MAX);
            std::partial_sum(
                    g_with_next_col_suffix_max[c].rbegin(),
                    g_with_next_col_suffix_max[c].rend(),
                    g_with_next_col_suffix_max[c].rbegin(),
                    MAX);

            for (int r = 0; r < n; ++r) {
                f_with_next_col_prefix_max[c][r] = f[c][r] - weights[c][r];
            }
            std::partial_sum(
                    f_with_next_col_prefix_max[c].begin(),
                    f_with_next_col_prefix_max[c].end(),
                    f_with_next_col_prefix_max[c].begin(),
                    MAX);
        }
        // }}}
    }

    int res = 0;
    for (int c = 0; c < n; ++c) {
        for (int r = 0; r < n; ++r) {
            assert(g[c][r] >= f[c][r]);
            int cur = g[c][r];
            if (c + 1 < n) {
                cur += weights[c+1][r];
            }
            upMax(res, cur);
        }
    }
    return res;

}
// }}}

/*
int sub7(int n, const std::vector<Fish>& fishes) {
    // fishesAt[col] = vector storing all fishes at column `col`
    std::vector<std::vector<std::pair<int, int>>> fishesAt(n);
    std::vector<std::vector<int>> weights(n);

    for (const auto& fish : fishes) {
        fishesAt[fish.col].push_back({fish.row, fish.weight});
    }

    for (int c = 0; c < n; ++c) {
        fishesAt[c].push_back({-1, 0});
        std::sort(fishesAt[c].begin(), fishesAt[c].end());
        fishesAt[c].push_back({1000111, 0});

        for (auto [row, weight] : fishesAt[c]) {
            weights[c].push_back(weight);
        }
        std::partial_sum(weights[c].begin(), weights[c].end(), weights[c].begin());
    }

    // f[c][r] = best strategy if we last BUILD PIER AT column c, row r
    //           only considering fishes <= (c, r)
    // g[c][r] = similar to f[c][r] but consider fishes at column c, in row [r, n-1]
    std::vector<std::vector<int>> f(n),
                                  g(n),
                                  g_prefix_max(n),
                                  g_suffix_max(n),
                                  g_with_next_col_suffix_max(n),
                                  g_with_next_col_prefix_max(n),
                                  f_with_next_col_prefix_max(n);

    for (int c = 0; c < n; ++c) {
        // compute {{{
        int k = (int) fishesAt[c].size();
        f[c].resize(k);
        g[c].resize(k);

        if (c > 0) {
            for (int i = 0; i < k - 1; ++i) {  // ignore last
                int r = fishesAt[c][i].first;
                int i_1 = lower_bound(
                        fishesAt[c-1].begin(), fishesAt[c-1].end(), std::make_pair(r+1, -1LL))
                    - fishesAt[c-1].begin();
                --i_1;
                assert(fishesAt[c-1][i_1].first <= r && fishesAt[c-1][i_1 + 1].first > r);

#define r ajckajcl

                // this is first pier
                f[c][i] = g[c][i] = weights[c-1][i_1];

                // last pier at column i-1
                {
                    // last row <= r
                    int cur = std::max(
                            g_prefix_max[c-1][i_1],
                            f_with_next_col_prefix_max[c-1][i_1] + weights[c-1][i_1]);
                    f[c][i] = std::max(f[c][i], cur);
                    g[c][i] = std::max(g[c][i], cur);

                    // last row > r
                    if (r + 1 < k-1) {
                        f[c][i] = std::max(f[c][i], 
                    }
                }

#undef r
            }
        }
        // }}}
    }
    return 0;
}
*/

#undef int
long long max_weights(
        int n, int nFish,
        std::vector<int> xs,
        std::vector<int> ys,
        std::vector<int> ws) {
    std::vector<Fish> fishes;
    for (int i = 0; i < nFish; ++i) {
        fishes.push_back({xs[i], ys[i], ws[i]});
    }

    if (std::all_of(xs.begin(), xs.end(), [] (int x) { return x % 2 == 0; })) {
        return sub1(fishes);
    }
    if (*std::max_element(xs.begin(), xs.end()) <= 1) {
        return sub2(n, fishes);
    }
    if (*std::max_element(ys.begin(), ys.end()) == 0) {
        return sub3(n, fishes);
    }
    if (n <= 300) return sub5(n, fishes);
    return sub6(n, fishes);
}

Subtask #1
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 23 ms 5344 KB Output is correct
2 Correct 41 ms 5812 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 95 ms 19788 KB Output is correct
6 Correct 107 ms 19788 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 51 ms 10380 KB Output is correct
3 Correct 61 ms 11236 KB Output is correct
4 Correct 24 ms 5336 KB Output is correct
5 Correct 30 ms 5808 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 25 ms 5596 KB Output is correct
13 Correct 31 ms 6460 KB Output is correct
14 Correct 32 ms 5460 KB Output is correct
15 Correct 32 ms 6088 KB Output is correct
16 Correct 26 ms 5472 KB Output is correct
17 Correct 35 ms 6064 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 2 ms 1748 KB Output is correct
3 Correct 25 ms 4128 KB Output is correct
4 Correct 14 ms 3676 KB Output is correct
5 Correct 34 ms 6508 KB Output is correct
6 Correct 25 ms 6588 KB Output is correct
7 Correct 31 ms 6452 KB Output is correct
8 Correct 34 ms 6456 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 12 ms 852 KB Output is correct
10 Correct 95 ms 2540 KB Output is correct
11 Correct 13 ms 852 KB Output is correct
12 Correct 101 ms 2488 KB Output is correct
13 Correct 2 ms 340 KB Output is correct
14 Correct 93 ms 2472 KB Output is correct

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 12 ms 852 KB Output is correct
10 Correct 95 ms 2540 KB Output is correct
11 Correct 13 ms 852 KB Output is correct
12 Correct 101 ms 2488 KB Output is correct
13 Correct 2 ms 340 KB Output is correct
14 Correct 93 ms 2472 KB Output is correct
15 Correct 98 ms 2452 KB Output is correct
16 Correct 3 ms 468 KB Output is correct
17 Correct 115 ms 4604 KB Output is correct
18 Correct 111 ms 4552 KB Output is correct
19 Correct 109 ms 4560 KB Output is correct
20 Correct 138 ms 4564 KB Output is correct
21 Correct 111 ms 4552 KB Output is correct
22 Correct 120 ms 6596 KB Output is correct
23 Correct 101 ms 2860 KB Output is correct
24 Correct 107 ms 3840 KB Output is correct
25 Correct 95 ms 2492 KB Output is correct
26 Correct 99 ms 2772 KB Output is correct

Subtask #6
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 12 ms 852 KB Output is correct
10 Correct 95 ms 2540 KB Output is correct
11 Correct 13 ms 852 KB Output is correct
12 Correct 101 ms 2488 KB Output is correct
13 Correct 2 ms 340 KB Output is correct
14 Correct 93 ms 2472 KB Output is correct
15 Correct 98 ms 2452 KB Output is correct
16 Correct 3 ms 468 KB Output is correct
17 Correct 115 ms 4604 KB Output is correct
18 Correct 111 ms 4552 KB Output is correct
19 Correct 109 ms 4560 KB Output is correct
20 Correct 138 ms 4564 KB Output is correct
21 Correct 111 ms 4552 KB Output is correct
22 Correct 120 ms 6596 KB Output is correct
23 Correct 101 ms 2860 KB Output is correct
24 Correct 107 ms 3840 KB Output is correct
25 Correct 95 ms 2492 KB Output is correct
26 Correct 99 ms 2772 KB Output is correct
27 Correct 439 ms 564984 KB Output is correct
28 Correct 89 ms 45884 KB Output is correct
29 Correct 516 ms 578948 KB Output is correct
30 Correct 526 ms 578940 KB Output is correct
31 Correct 521 ms 579056 KB Output is correct
32 Correct 105 ms 33224 KB Output is correct
33 Correct 531 ms 578916 KB Output is correct
34 Correct 514 ms 578956 KB Output is correct
35 Correct 461 ms 570328 KB Output is correct
36 Correct 515 ms 579016 KB Output is correct

Subtask #7
0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 2 ms 1748 KB Output is correct
3 Correct 25 ms 4128 KB Output is correct
4 Correct 14 ms 3676 KB Output is correct
5 Correct 34 ms 6508 KB Output is correct
6 Correct 25 ms 6588 KB Output is correct
7 Correct 31 ms 6452 KB Output is correct
8 Correct 34 ms 6456 KB Output is correct
9 Runtime error 729 ms 2097152 KB Execution killed with signal 9
10 Halted 0 ms 0 KB -

Subtask #8
0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 23 ms 5344 KB Output is correct
2 Correct 41 ms 5812 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 95 ms 19788 KB Output is correct
6 Correct 107 ms 19788 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 51 ms 10380 KB Output is correct
9 Correct 61 ms 11236 KB Output is correct
10 Correct 24 ms 5336 KB Output is correct
11 Correct 30 ms 5808 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 25 ms 5596 KB Output is correct
19 Correct 31 ms 6460 KB Output is correct
20 Correct 32 ms 5460 KB Output is correct
21 Correct 32 ms 6088 KB Output is correct
22 Correct 26 ms 5472 KB Output is correct
23 Correct 35 ms 6064 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 2 ms 1748 KB Output is correct
26 Correct 25 ms 4128 KB Output is correct
27 Correct 14 ms 3676 KB Output is correct
28 Correct 34 ms 6508 KB Output is correct
29 Correct 25 ms 6588 KB Output is correct
30 Correct 31 ms 6452 KB Output is correct
31 Correct 34 ms 6456 KB Output is correct
32 Correct 0 ms 212 KB Output is correct
33 Correct 0 ms 212 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 0 ms 212 KB Output is correct
36 Correct 0 ms 212 KB Output is correct
37 Correct 1 ms 212 KB Output is correct
38 Correct 0 ms 212 KB Output is correct
39 Correct 1 ms 212 KB Output is correct
40 Correct 12 ms 852 KB Output is correct
41 Correct 95 ms 2540 KB Output is correct
42 Correct 13 ms 852 KB Output is correct
43 Correct 101 ms 2488 KB Output is correct
44 Correct 2 ms 340 KB Output is correct
45 Correct 93 ms 2472 KB Output is correct
46 Correct 98 ms 2452 KB Output is correct
47 Correct 3 ms 468 KB Output is correct
48 Correct 115 ms 4604 KB Output is correct
49 Correct 111 ms 4552 KB Output is correct
50 Correct 109 ms 4560 KB Output is correct
51 Correct 138 ms 4564 KB Output is correct
52 Correct 111 ms 4552 KB Output is correct
53 Correct 120 ms 6596 KB Output is correct
54 Correct 101 ms 2860 KB Output is correct
55 Correct 107 ms 3840 KB Output is correct
56 Correct 95 ms 2492 KB Output is correct
57 Correct 99 ms 2772 KB Output is correct
58 Correct 439 ms 564984 KB Output is correct
59 Correct 89 ms 45884 KB Output is correct
60 Correct 516 ms 578948 KB Output is correct
61 Correct 526 ms 578940 KB Output is correct
62 Correct 521 ms 579056 KB Output is correct
63 Correct 105 ms 33224 KB Output is correct
64 Correct 531 ms 578916 KB Output is correct
65 Correct 514 ms 578956 KB Output is correct
66 Correct 461 ms 570328 KB Output is correct
67 Correct 515 ms 579016 KB Output is correct
68 Runtime error 729 ms 2097152 KB Execution killed with signal 9
69 Halted 0 ms 0 KB -