답안 #625725

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
625725	2022-08-10T17:37:25 Z	I_love_Hoang_Yen	메기 농장 (IOI22_fish)	C++17	18 / 100	355 ms	132588 KB

fish

#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::map<int, int>> fishesMap(n);
    std::vector<std::vector< std::pair<int,int> >> fishesAt(n);
    std::vector<std::vector<int>> weights(n);

    for (const auto& fish : fishes) {
        int c = fish.col;
        fishesMap[c][fish.row] += fish.weight;
        if (c + 1 < n) fishesMap[c + 1][fish.row] += 0;
        if (c + 2 < n) fishesMap[c + 2][fish.row] += 0;
        if (c + 3 < n) fishesMap[c + 3][fish.row] += 0;
    }
    
    for (int c = 0; c < n; ++c) {
        fishesAt[c].push_back({-2, 0});
        fishesAt[c].push_back({-1, 0});
        for (auto [r, w] : fishesMap[c]) {
            fishesAt[c].push_back({r, w});
        }
        fishesAt[c].push_back({n, 0});
        fishesAt[c].push_back({1000111, 0});
    }

    for (int c = 0; c < n; ++c) {
        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	25 ms	5320 KB	Output is correct
2	Correct	30 ms	5816 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	89 ms	19676 KB	Output is correct
6	Correct	95 ms	19756 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	53 ms	10380 KB	Output is correct
3	Correct	64 ms	11200 KB	Output is correct
4	Correct	24 ms	5340 KB	Output is correct
5	Correct	39 ms	5820 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	1 ms	212 KB	Output is correct
12	Correct	24 ms	5460 KB	Output is correct
13	Correct	31 ms	6456 KB	Output is correct
14	Correct	27 ms	5472 KB	Output is correct
15	Correct	33 ms	6072 KB	Output is correct
16	Correct	27 ms	5472 KB	Output is correct
17	Correct	31 ms	6076 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	1860 KB	Output is correct
3	Correct	25 ms	4120 KB	Output is correct
4	Correct	21 ms	3656 KB	Output is correct
5	Correct	43 ms	6456 KB	Output is correct
6	Correct	28 ms	6464 KB	Output is correct
7	Correct	31 ms	6456 KB	Output is correct
8	Correct	54 ms	6456 KB	Output is correct

Subtask #4

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	0 ms	212 KB	Output is correct
4	Correct	0 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	1 ms	212 KB	Output is correct
8	Incorrect	0 ms	212 KB	1st lines differ - on the 1st token, expected: '2', found: '1'
9	Halted	0 ms	0 KB	-

Subtask #5

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	0 ms	212 KB	Output is correct
4	Correct	0 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	1 ms	212 KB	Output is correct
8	Incorrect	0 ms	212 KB	1st lines differ - on the 1st token, expected: '2', found: '1'
9	Halted	0 ms	0 KB	-

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	0 ms	212 KB	Output is correct
4	Correct	0 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	1 ms	212 KB	Output is correct
8	Incorrect	0 ms	212 KB	1st lines differ - on the 1st token, expected: '2', found: '1'
9	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	1860 KB	Output is correct
3	Correct	25 ms	4120 KB	Output is correct
4	Correct	21 ms	3656 KB	Output is correct
5	Correct	43 ms	6456 KB	Output is correct
6	Correct	28 ms	6464 KB	Output is correct
7	Correct	31 ms	6456 KB	Output is correct
8	Correct	54 ms	6456 KB	Output is correct
9	Correct	355 ms	132588 KB	Output is correct
10	Correct	140 ms	57288 KB	Output is correct
11	Correct	300 ms	114116 KB	Output is correct
12	Correct	1 ms	212 KB	Output is correct
13	Correct	0 ms	212 KB	Output is correct
14	Correct	1 ms	256 KB	Output is correct
15	Correct	0 ms	212 KB	Output is correct
16	Correct	0 ms	212 KB	Output is correct
17	Incorrect	0 ms	212 KB	1st lines differ - on the 1st token, expected: '2', found: '1'
18	Halted	0 ms	0 KB	-

Subtask #8

0 / 16.0

#	결과	실행 시간	메모리	Grader output
1	Correct	25 ms	5320 KB	Output is correct
2	Correct	30 ms	5816 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	89 ms	19676 KB	Output is correct
6	Correct	95 ms	19756 KB	Output is correct
7	Correct	0 ms	212 KB	Output is correct
8	Correct	53 ms	10380 KB	Output is correct
9	Correct	64 ms	11200 KB	Output is correct
10	Correct	24 ms	5340 KB	Output is correct
11	Correct	39 ms	5820 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	1 ms	212 KB	Output is correct
18	Correct	24 ms	5460 KB	Output is correct
19	Correct	31 ms	6456 KB	Output is correct
20	Correct	27 ms	5472 KB	Output is correct
21	Correct	33 ms	6072 KB	Output is correct
22	Correct	27 ms	5472 KB	Output is correct
23	Correct	31 ms	6076 KB	Output is correct
24	Correct	0 ms	212 KB	Output is correct
25	Correct	2 ms	1860 KB	Output is correct
26	Correct	25 ms	4120 KB	Output is correct
27	Correct	21 ms	3656 KB	Output is correct
28	Correct	43 ms	6456 KB	Output is correct
29	Correct	28 ms	6464 KB	Output is correct
30	Correct	31 ms	6456 KB	Output is correct
31	Correct	54 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	0 ms	212 KB	Output is correct
35	Correct	0 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	1 ms	212 KB	Output is correct
39	Incorrect	0 ms	212 KB	1st lines differ - on the 1st token, expected: '2', found: '1'
40	Halted	0 ms	0 KB	-