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답안 #625715

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
625715 2022-08-10T17:24:38 Z I_love_Hoang_Yen 메기 농장 (IOI22_fish) C++17
18 / 100
 185 ms 72620 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({n, 0});
        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]);
                    upMax(f[c][i], cur);
                    upMax(g[c][i], cur);

                    // last row > r
                    if (i + 1 < k-1) {
                        upMax(f[c][i], g_suffix_max[c-1][i_1 + 1]);
                        upMax(g[c][i], g_with_next_col_prefix_max[c-1][i_1 + 1] - weights[c][i]);
                    }
                }

                // last pier at column i-2
                if (c >= 2) {
                    int cur = std::max(
                            g_prefix_max[c-2].back() + weights[c-1][i_1],
                            g_with_next_col_prefix_max[c-2].back());
                    upMax(f[c][i], cur);
                    upMax(g[c][i], cur);
                }

                // last pier at column i-3
                if (c >= 3) {
                    int cur = g_with_next_col_prefix_max[c-3].back() + weights[c-1][i_1];
                    upMax(f[c][i], cur);
                    upMax(g[c][i], cur);
                }

#undef r
            }
        }
        // }}}

        // aggregate {{{
        // g_prefix_max[c][r] = max(g[c][0], .., g[c][r])
        auto MAX = [] (auto a, auto b) { return std::max(a, b); };
        g_prefix_max[c] = g[c];
        g_suffix_max[c] = g[c];
        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])
            g_with_next_col_prefix_max[c] = g[c];
            for (int i = 0; i < (int) g[c].size(); ++i) {
                g_with_next_col_prefix_max[c][i] = g[c][i] + weights[c+1][i];
            }
            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);

            f_with_next_col_prefix_max[c] = f[c];
            for (int i = 0; i < (int) f[c].size(); ++i) {
                f_with_next_col_prefix_max[c][i] = f[c][i] - weights[c][i];
            }
            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) {
        int k = fishesAt[c].size();
        for (int i = 0; i < k; ++i) {
            int r = fishesAt[c][i].first;
            int cur = g[c][i];
            if (c + 1 < n) {
                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;
                cur += weights[c+1][i_1];
            }
            upMax(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);
    }
    return sub7(n, fishes);
}

Subtask #1
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 37 ms 5312 KB Output is correct
2 Correct 30 ms 6448 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 108 ms 20988 KB Output is correct
6 Correct 99 ms 20920 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 49 ms 10380 KB Output is correct
3 Correct 66 ms 12264 KB Output is correct
4 Correct 25 ms 6368 KB Output is correct
5 Correct 31 ms 6880 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 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 32 ms 6632 KB Output is correct
13 Correct 35 ms 7532 KB Output is correct
14 Correct 27 ms 6460 KB Output is correct
15 Correct 31 ms 7080 KB Output is correct
16 Correct 27 ms 6460 KB Output is correct
17 Correct 30 ms 7104 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 1 ms 1748 KB Output is correct
3 Correct 16 ms 4168 KB Output is correct
4 Correct 13 ms 3672 KB Output is correct
5 Correct 30 ms 6452 KB Output is correct
6 Correct 23 ms 6460 KB Output is correct
7 Correct 28 ms 6456 KB Output is correct
8 Correct 32 ms 6456 KB Output is correct

Subtask #4
0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Incorrect 1 ms 232 KB 1st lines differ - on the 1st token, expected: '3', found: '2'
2 Halted 0 ms 0 KB -

Subtask #5
0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Incorrect 1 ms 232 KB 1st lines differ - on the 1st token, expected: '3', found: '2'
2 Halted 0 ms 0 KB -

Subtask #6
0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Incorrect 1 ms 232 KB 1st lines differ - on the 1st token, expected: '3', found: '2'
2 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 1 ms 1748 KB Output is correct
3 Correct 16 ms 4168 KB Output is correct
4 Correct 13 ms 3672 KB Output is correct
5 Correct 30 ms 6452 KB Output is correct
6 Correct 23 ms 6460 KB Output is correct
7 Correct 28 ms 6456 KB Output is correct
8 Correct 32 ms 6456 KB Output is correct
9 Incorrect 185 ms 72620 KB 1st lines differ - on the 1st token, expected: '99999', found: '66666'
10 Halted 0 ms 0 KB -

Subtask #8
0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 37 ms 5312 KB Output is correct
2 Correct 30 ms 6448 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 108 ms 20988 KB Output is correct
6 Correct 99 ms 20920 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 49 ms 10380 KB Output is correct
9 Correct 66 ms 12264 KB Output is correct
10 Correct 25 ms 6368 KB Output is correct
11 Correct 31 ms 6880 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 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 32 ms 6632 KB Output is correct
19 Correct 35 ms 7532 KB Output is correct
20 Correct 27 ms 6460 KB Output is correct
21 Correct 31 ms 7080 KB Output is correct
22 Correct 27 ms 6460 KB Output is correct
23 Correct 30 ms 7104 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 1 ms 1748 KB Output is correct
26 Correct 16 ms 4168 KB Output is correct
27 Correct 13 ms 3672 KB Output is correct
28 Correct 30 ms 6452 KB Output is correct
29 Correct 23 ms 6460 KB Output is correct
30 Correct 28 ms 6456 KB Output is correct
31 Correct 32 ms 6456 KB Output is correct
32 Incorrect 1 ms 232 KB 1st lines differ - on the 1st token, expected: '3', found: '2'
33 Halted 0 ms 0 KB -