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답안 #625645

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
625645 2022-08-10T16:20:40 Z I_love_Hoang_Yen 메기 농장 (IOI22_fish) C++17
70 / 100
 693 ms 584204 KB 
#include "bits/stdc++.h"
using namespace std;

#define int long long
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;
}

// 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) res = std::max(res, zeroes[i]);
        else res = std::max(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) {
            f[i] = std::max(f[i], f[i-2] + weights[i-1]);
        }
        if (i >= 3) {
            f[i] = std::max(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];
        res = std::max(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]);
                    f[c][r] = std::max(f[c][r], cur);
                    g[c][r] = std::max(g[c][r], cur);
                } else {
                    f[c][r] = std::max(f[c][r], g[c-1][lastRow]);
                    g[c][r] = std::max(
                            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)];
                    f[c][r] = std::max(f[c][r], cur);
                    g[c][r] = std::max(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];
                    f[c][r] = std::max(f[c][r], cur);
                    g[c][r] = std::max(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];
            }
            res = std::max(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]);
                    f[c][r] = std::max(f[c][r], cur);
                    g[c][r] = std::max(g[c][r], cur);

                    // last row > r
                    if (r + 1 < n) {
                        f[c][r] = std::max(f[c][r], g_suffix_max[c-1][r + 1]);
                        g[c][r] = std::max(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());
                    f[c][r] = std::max(f[c][r], cur);
                    g[c][r] = std::max(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];
                    f[c][r] = std::max(f[c][r], cur);
                    g[c][r] = std::max(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];
            }
            res = std::max(res, cur);
        }
    }
    return res;

}

#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 <= 3000) {
        return sub6(n, fishes);
    }
    return 0;
}

Subtask #1
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 27 ms 5340 KB Output is correct
2 Correct 35 ms 5816 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 136 ms 20500 KB Output is correct
6 Correct 171 ms 20568 KB Output is correct

Subtask #2
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 56 ms 10388 KB Output is correct
3 Correct 76 ms 11204 KB Output is correct
4 Correct 36 ms 5336 KB Output is correct
5 Correct 36 ms 5820 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 27 ms 5484 KB Output is correct
13 Correct 34 ms 6584 KB Output is correct
14 Correct 38 ms 5436 KB Output is correct
15 Correct 38 ms 6076 KB Output is correct
16 Correct 28 ms 5444 KB Output is correct
17 Correct 32 ms 6076 KB Output is correct

Subtask #3
9.0 / 9.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 2 ms 1876 KB Output is correct
3 Correct 21 ms 4120 KB Output is correct
4 Correct 13 ms 3672 KB Output is correct
5 Correct 43 ms 6456 KB Output is correct
6 Correct 26 ms 6460 KB Output is correct
7 Correct 41 ms 6460 KB Output is correct
8 Correct 32 ms 6452 KB Output is correct

Subtask #4
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 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 1 ms 1748 KB Output is correct
10 Correct 5 ms 6100 KB Output is correct
11 Correct 2 ms 1748 KB Output is correct
12 Correct 7 ms 5972 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 5 ms 5972 KB Output is correct

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 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 1 ms 1748 KB Output is correct
10 Correct 5 ms 6100 KB Output is correct
11 Correct 2 ms 1748 KB Output is correct
12 Correct 7 ms 5972 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 5 ms 5972 KB Output is correct
15 Correct 5 ms 5972 KB Output is correct
16 Correct 1 ms 724 KB Output is correct
17 Correct 20 ms 8868 KB Output is correct
18 Correct 18 ms 8836 KB Output is correct
19 Correct 27 ms 8856 KB Output is correct
20 Correct 21 ms 8776 KB Output is correct
21 Correct 20 ms 8836 KB Output is correct
22 Correct 41 ms 11060 KB Output is correct
23 Correct 11 ms 6584 KB Output is correct
24 Correct 21 ms 7912 KB Output is correct
25 Correct 6 ms 6092 KB Output is correct
26 Correct 8 ms 6556 KB Output is correct

Subtask #6
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 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 1 ms 1748 KB Output is correct
10 Correct 5 ms 6100 KB Output is correct
11 Correct 2 ms 1748 KB Output is correct
12 Correct 7 ms 5972 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 5 ms 5972 KB Output is correct
15 Correct 5 ms 5972 KB Output is correct
16 Correct 1 ms 724 KB Output is correct
17 Correct 20 ms 8868 KB Output is correct
18 Correct 18 ms 8836 KB Output is correct
19 Correct 27 ms 8856 KB Output is correct
20 Correct 21 ms 8776 KB Output is correct
21 Correct 20 ms 8836 KB Output is correct
22 Correct 41 ms 11060 KB Output is correct
23 Correct 11 ms 6584 KB Output is correct
24 Correct 21 ms 7912 KB Output is correct
25 Correct 6 ms 6092 KB Output is correct
26 Correct 8 ms 6556 KB Output is correct
27 Correct 448 ms 564976 KB Output is correct
28 Correct 100 ms 49636 KB Output is correct
29 Correct 522 ms 584204 KB Output is correct
30 Correct 559 ms 584120 KB Output is correct
31 Correct 665 ms 584096 KB Output is correct
32 Correct 109 ms 38440 KB Output is correct
33 Correct 624 ms 584116 KB Output is correct
34 Correct 693 ms 583920 KB Output is correct
35 Correct 488 ms 571892 KB Output is correct
36 Correct 566 ms 580956 KB Output is correct

Subtask #7
0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 2 ms 1876 KB Output is correct
3 Correct 21 ms 4120 KB Output is correct
4 Correct 13 ms 3672 KB Output is correct
5 Correct 43 ms 6456 KB Output is correct
6 Correct 26 ms 6460 KB Output is correct
7 Correct 41 ms 6460 KB Output is correct
8 Correct 32 ms 6452 KB Output is correct
9 Incorrect 27 ms 5952 KB 1st lines differ - on the 1st token, expected: '99999', found: '0'
10 Halted 0 ms 0 KB -

Subtask #8
0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 27 ms 5340 KB Output is correct
2 Correct 35 ms 5816 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 136 ms 20500 KB Output is correct
6 Correct 171 ms 20568 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 56 ms 10388 KB Output is correct
9 Correct 76 ms 11204 KB Output is correct
10 Correct 36 ms 5336 KB Output is correct
11 Correct 36 ms 5820 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 27 ms 5484 KB Output is correct
19 Correct 34 ms 6584 KB Output is correct
20 Correct 38 ms 5436 KB Output is correct
21 Correct 38 ms 6076 KB Output is correct
22 Correct 28 ms 5444 KB Output is correct
23 Correct 32 ms 6076 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 2 ms 1876 KB Output is correct
26 Correct 21 ms 4120 KB Output is correct
27 Correct 13 ms 3672 KB Output is correct
28 Correct 43 ms 6456 KB Output is correct
29 Correct 26 ms 6460 KB Output is correct
30 Correct 41 ms 6460 KB Output is correct
31 Correct 32 ms 6452 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 0 ms 212 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 0 ms 212 KB Output is correct
37 Correct 0 ms 212 KB Output is correct
38 Correct 0 ms 212 KB Output is correct
39 Correct 0 ms 212 KB Output is correct
40 Correct 1 ms 1748 KB Output is correct
41 Correct 5 ms 6100 KB Output is correct
42 Correct 2 ms 1748 KB Output is correct
43 Correct 7 ms 5972 KB Output is correct
44 Correct 1 ms 596 KB Output is correct
45 Correct 5 ms 5972 KB Output is correct
46 Correct 5 ms 5972 KB Output is correct
47 Correct 1 ms 724 KB Output is correct
48 Correct 20 ms 8868 KB Output is correct
49 Correct 18 ms 8836 KB Output is correct
50 Correct 27 ms 8856 KB Output is correct
51 Correct 21 ms 8776 KB Output is correct
52 Correct 20 ms 8836 KB Output is correct
53 Correct 41 ms 11060 KB Output is correct
54 Correct 11 ms 6584 KB Output is correct
55 Correct 21 ms 7912 KB Output is correct
56 Correct 6 ms 6092 KB Output is correct
57 Correct 8 ms 6556 KB Output is correct
58 Correct 448 ms 564976 KB Output is correct
59 Correct 100 ms 49636 KB Output is correct
60 Correct 522 ms 584204 KB Output is correct
61 Correct 559 ms 584120 KB Output is correct
62 Correct 665 ms 584096 KB Output is correct
63 Correct 109 ms 38440 KB Output is correct
64 Correct 624 ms 584116 KB Output is correct
65 Correct 693 ms 583920 KB Output is correct
66 Correct 488 ms 571892 KB Output is correct
67 Correct 566 ms 580956 KB Output is correct
68 Incorrect 27 ms 5952 KB 1st lines differ - on the 1st token, expected: '99999', found: '0'
69 Halted 0 ms 0 KB -