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답안 #625636

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
625636 2022-08-10T16:13:15 Z I_love_Hoang_Yen 메기 농장 (IOI22_fish) C++17
53 / 100
 1000 ms 423756 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_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
                    f[c][r] = std::max(f[c][r], g_prefix_max[c-1][r]);
                    g[c][r] = std::max(g[c][r], g_prefix_max[c-1][r]);

                    // last row > r
                    if (r + 1 < n) {
                        f[c][r] = std::max(f[c][r], g_suffix_max[c-1][r + 1]);
                    }
                }
                for (int lastRow = 0; lastRow < n; ++lastRow) {
                    if (lastRow <= r) {
                        int cur = f[c-1][lastRow] + weights[c-1][r] - weights[c-1][lastRow];
                        f[c][r] = std::max(f[c][r], cur);
                        g[c][r] = std::max(g[c][r], cur);
                    } else {
                        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) {
                    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])
        std::partial_sum(g[c].begin(), g[c].end(), g_prefix_max[c].begin(),
                [] (auto a, auto b) { return std::max(a, b); });
        std::partial_sum(g[c].rbegin(), g[c].rend(), g_suffix_max[c].rbegin(),
                [] (auto a, auto b) { return std::max(a, b); });

        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])
            g_with_next_col_prefix_max[c][0] = g[c][0] + weights[c+1][0];
            for (int r = 1; r < n; ++r) {
                g_with_next_col_prefix_max[c][r] = std::max(
                        g_with_next_col_prefix_max[c][r-1],
                        g[c][r] + weights[c+1][r]);
            }
        }
        // }}}
    }

    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 23 ms 5312 KB Output is correct
2 Correct 29 ms 5816 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 93 ms 19768 KB Output is correct
6 Correct 98 ms 19788 KB Output is correct

Subtask #2
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 51 ms 10388 KB Output is correct
3 Correct 64 ms 11208 KB Output is correct
4 Correct 23 ms 5312 KB Output is correct
5 Correct 31 ms 5808 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 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 28 ms 5468 KB Output is correct
13 Correct 44 ms 6452 KB Output is correct
14 Correct 26 ms 5472 KB Output is correct
15 Correct 33 ms 6088 KB Output is correct
16 Correct 26 ms 5476 KB Output is correct
17 Correct 29 ms 6072 KB Output is correct

Subtask #3
9.0 / 9.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 2 ms 1748 KB Output is correct
3 Correct 18 ms 4168 KB Output is correct
4 Correct 15 ms 3656 KB Output is correct
5 Correct 30 ms 6456 KB Output is correct
6 Correct 25 ms 6460 KB Output is correct
7 Correct 28 ms 6460 KB Output is correct
8 Correct 31 ms 6452 KB Output is correct

Subtask #4
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 276 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 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 15 ms 1364 KB Output is correct
10 Correct 95 ms 4692 KB Output is correct
11 Correct 13 ms 1364 KB Output is correct
12 Correct 102 ms 4640 KB Output is correct
13 Correct 2 ms 468 KB Output is correct
14 Correct 100 ms 4564 KB Output is correct

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 276 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 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 15 ms 1364 KB Output is correct
10 Correct 95 ms 4692 KB Output is correct
11 Correct 13 ms 1364 KB Output is correct
12 Correct 102 ms 4640 KB Output is correct
13 Correct 2 ms 468 KB Output is correct
14 Correct 100 ms 4564 KB Output is correct
15 Correct 96 ms 4600 KB Output is correct
16 Correct 4 ms 596 KB Output is correct
17 Correct 106 ms 6728 KB Output is correct
18 Correct 114 ms 6600 KB Output is correct
19 Correct 106 ms 6600 KB Output is correct
20 Correct 103 ms 6628 KB Output is correct
21 Correct 109 ms 6708 KB Output is correct
22 Correct 120 ms 8828 KB Output is correct
23 Correct 96 ms 5012 KB Output is correct
24 Correct 104 ms 5964 KB Output is correct
25 Correct 91 ms 4644 KB Output is correct
26 Correct 95 ms 4984 KB Output is correct

Subtask #6
0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 276 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 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 15 ms 1364 KB Output is correct
10 Correct 95 ms 4692 KB Output is correct
11 Correct 13 ms 1364 KB Output is correct
12 Correct 102 ms 4640 KB Output is correct
13 Correct 2 ms 468 KB Output is correct
14 Correct 100 ms 4564 KB Output is correct
15 Correct 96 ms 4600 KB Output is correct
16 Correct 4 ms 596 KB Output is correct
17 Correct 106 ms 6728 KB Output is correct
18 Correct 114 ms 6600 KB Output is correct
19 Correct 106 ms 6600 KB Output is correct
20 Correct 103 ms 6628 KB Output is correct
21 Correct 109 ms 6708 KB Output is correct
22 Correct 120 ms 8828 KB Output is correct
23 Correct 96 ms 5012 KB Output is correct
24 Correct 104 ms 5964 KB Output is correct
25 Correct 91 ms 4644 KB Output is correct
26 Correct 95 ms 4984 KB Output is correct
27 Execution timed out 1123 ms 423756 KB Time limit exceeded
28 Halted 0 ms 0 KB -

Subtask #7
0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 2 ms 1748 KB Output is correct
3 Correct 18 ms 4168 KB Output is correct
4 Correct 15 ms 3656 KB Output is correct
5 Correct 30 ms 6456 KB Output is correct
6 Correct 25 ms 6460 KB Output is correct
7 Correct 28 ms 6460 KB Output is correct
8 Correct 31 ms 6452 KB Output is correct
9 Incorrect 29 ms 5824 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 23 ms 5312 KB Output is correct
2 Correct 29 ms 5816 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 93 ms 19768 KB Output is correct
6 Correct 98 ms 19788 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 51 ms 10388 KB Output is correct
9 Correct 64 ms 11208 KB Output is correct
10 Correct 23 ms 5312 KB Output is correct
11 Correct 31 ms 5808 KB Output is correct
12 Correct 0 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 0 ms 212 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 28 ms 5468 KB Output is correct
19 Correct 44 ms 6452 KB Output is correct
20 Correct 26 ms 5472 KB Output is correct
21 Correct 33 ms 6088 KB Output is correct
22 Correct 26 ms 5476 KB Output is correct
23 Correct 29 ms 6072 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 2 ms 1748 KB Output is correct
26 Correct 18 ms 4168 KB Output is correct
27 Correct 15 ms 3656 KB Output is correct
28 Correct 30 ms 6456 KB Output is correct
29 Correct 25 ms 6460 KB Output is correct
30 Correct 28 ms 6460 KB Output is correct
31 Correct 31 ms 6452 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 276 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 1 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 15 ms 1364 KB Output is correct
41 Correct 95 ms 4692 KB Output is correct
42 Correct 13 ms 1364 KB Output is correct
43 Correct 102 ms 4640 KB Output is correct
44 Correct 2 ms 468 KB Output is correct
45 Correct 100 ms 4564 KB Output is correct
46 Correct 96 ms 4600 KB Output is correct
47 Correct 4 ms 596 KB Output is correct
48 Correct 106 ms 6728 KB Output is correct
49 Correct 114 ms 6600 KB Output is correct
50 Correct 106 ms 6600 KB Output is correct
51 Correct 103 ms 6628 KB Output is correct
52 Correct 109 ms 6708 KB Output is correct
53 Correct 120 ms 8828 KB Output is correct
54 Correct 96 ms 5012 KB Output is correct
55 Correct 104 ms 5964 KB Output is correct
56 Correct 91 ms 4644 KB Output is correct
57 Correct 95 ms 4984 KB Output is correct
58 Execution timed out 1123 ms 423756 KB Time limit exceeded
59 Halted 0 ms 0 KB -