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답안 #625628

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
625628 2022-08-10T16:10:59 Z I_love_Hoang_Yen 메기 농장 (IOI22_fish) C++17
18 / 100
 96 ms 19672 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
                    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 31 ms 5312 KB Output is correct
2 Correct 34 ms 5800 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 94 ms 19672 KB Output is correct
6 Correct 96 ms 19668 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 10384 KB Output is correct
3 Correct 68 ms 11220 KB Output is correct
4 Correct 25 ms 5344 KB Output is correct
5 Correct 34 ms 5816 KB Output is correct
6 Correct 0 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 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 30 ms 5444 KB Output is correct
13 Correct 34 ms 6464 KB Output is correct
14 Correct 26 ms 5532 KB Output is correct
15 Correct 31 ms 6048 KB Output is correct
16 Correct 34 ms 5472 KB Output is correct
17 Correct 30 ms 6092 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 17 ms 4128 KB Output is correct
4 Correct 13 ms 3672 KB Output is correct
5 Correct 33 ms 6568 KB Output is correct
6 Correct 26 ms 6460 KB Output is correct
7 Correct 30 ms 6452 KB Output is correct
8 Correct 31 ms 6468 KB Output is correct

Subtask #4
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 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 Runtime error 1 ms 340 KB Execution killed with signal 6
9 Halted 0 ms 0 KB -

Subtask #5
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 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 Runtime error 1 ms 340 KB Execution killed with signal 6
9 Halted 0 ms 0 KB -

Subtask #6
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 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 Runtime error 1 ms 340 KB Execution killed with signal 6
9 Halted 0 ms 0 KB -

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 17 ms 4128 KB Output is correct
4 Correct 13 ms 3672 KB Output is correct
5 Correct 33 ms 6568 KB Output is correct
6 Correct 26 ms 6460 KB Output is correct
7 Correct 30 ms 6452 KB Output is correct
8 Correct 31 ms 6468 KB Output is correct
9 Incorrect 35 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 31 ms 5312 KB Output is correct
2 Correct 34 ms 5800 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 94 ms 19672 KB Output is correct
6 Correct 96 ms 19668 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 51 ms 10384 KB Output is correct
9 Correct 68 ms 11220 KB Output is correct
10 Correct 25 ms 5344 KB Output is correct
11 Correct 34 ms 5816 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 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 30 ms 5444 KB Output is correct
19 Correct 34 ms 6464 KB Output is correct
20 Correct 26 ms 5532 KB Output is correct
21 Correct 31 ms 6048 KB Output is correct
22 Correct 34 ms 5472 KB Output is correct
23 Correct 30 ms 6092 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 2 ms 1876 KB Output is correct
26 Correct 17 ms 4128 KB Output is correct
27 Correct 13 ms 3672 KB Output is correct
28 Correct 33 ms 6568 KB Output is correct
29 Correct 26 ms 6460 KB Output is correct
30 Correct 30 ms 6452 KB Output is correct
31 Correct 31 ms 6468 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 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 Runtime error 1 ms 340 KB Execution killed with signal 6
40 Halted 0 ms 0 KB -