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답안 #625616

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
625616 2022-08-10T16:02:41 Z I_love_Hoang_Yen 메기 농장 (IOI22_fish) C++17
53 / 100
 1000 ms 353228 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;
}
// }}}

// 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_agg(n, std::vector<int> (n, 0)),
                                  g_agg_with_next_col(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
                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) {
                    int cur = std::max(
                            g_agg[c-2].back() + weights[c-1][r],
                            g_agg_with_next_col[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_agg_with_next_col[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_agg[c][r] = max(g[c][0], .., g[c][r])
        std::partial_sum(g[c].begin(), g[c].end(), g_agg[c].begin(),
                [] (auto a, auto b) { return std::max(a, b); });

        if (c + 1 < n) {
            // g_agg_with_next_col[c][r] = max(
            //     g[c][0] + weights[c+1][0],
            //     ...
            //     g[c][r] + weights[c+1][r])
            g_agg_with_next_col[c][0] = g[c][0] + weights[c+1][0];
            for (int r = 1; r < n; ++r) {
                g_agg_with_next_col[c][r] = std::max(
                        g_agg_with_next_col[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 35 ms 5328 KB Output is correct
2 Correct 48 ms 5816 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 256 KB Output is correct
5 Correct 123 ms 19768 KB Output is correct
6 Correct 135 ms 19792 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 62 ms 10392 KB Output is correct
3 Correct 92 ms 11220 KB Output is correct
4 Correct 34 ms 5320 KB Output is correct
5 Correct 35 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 268 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 37 ms 5456 KB Output is correct
13 Correct 43 ms 6496 KB Output is correct
14 Correct 31 ms 5448 KB Output is correct
15 Correct 38 ms 6084 KB Output is correct
16 Correct 31 ms 5468 KB Output is correct
17 Correct 34 ms 6080 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 3 ms 1876 KB Output is correct
3 Correct 24 ms 4156 KB Output is correct
4 Correct 19 ms 3656 KB Output is correct
5 Correct 72 ms 6444 KB Output is correct
6 Correct 28 ms 6508 KB Output is correct
7 Correct 42 ms 6460 KB Output is correct
8 Correct 33 ms 6448 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 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 256 KB Output is correct
5 Correct 1 ms 256 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 14 ms 1236 KB Output is correct
10 Correct 104 ms 3980 KB Output is correct
11 Correct 14 ms 1236 KB Output is correct
12 Correct 110 ms 3924 KB Output is correct
13 Correct 3 ms 468 KB Output is correct
14 Correct 104 ms 3912 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 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 256 KB Output is correct
5 Correct 1 ms 256 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 14 ms 1236 KB Output is correct
10 Correct 104 ms 3980 KB Output is correct
11 Correct 14 ms 1236 KB Output is correct
12 Correct 110 ms 3924 KB Output is correct
13 Correct 3 ms 468 KB Output is correct
14 Correct 104 ms 3912 KB Output is correct
15 Correct 105 ms 3796 KB Output is correct
16 Correct 3 ms 596 KB Output is correct
17 Correct 126 ms 5952 KB Output is correct
18 Correct 118 ms 5996 KB Output is correct
19 Correct 128 ms 5996 KB Output is correct
20 Correct 113 ms 5996 KB Output is correct
21 Correct 116 ms 5944 KB Output is correct
22 Correct 136 ms 8120 KB Output is correct
23 Correct 114 ms 4304 KB Output is correct
24 Correct 116 ms 5276 KB Output is correct
25 Correct 97 ms 3924 KB Output is correct
26 Correct 102 ms 4180 KB Output is correct

Subtask #6
0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 256 KB Output is correct
5 Correct 1 ms 256 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 14 ms 1236 KB Output is correct
10 Correct 104 ms 3980 KB Output is correct
11 Correct 14 ms 1236 KB Output is correct
12 Correct 110 ms 3924 KB Output is correct
13 Correct 3 ms 468 KB Output is correct
14 Correct 104 ms 3912 KB Output is correct
15 Correct 105 ms 3796 KB Output is correct
16 Correct 3 ms 596 KB Output is correct
17 Correct 126 ms 5952 KB Output is correct
18 Correct 118 ms 5996 KB Output is correct
19 Correct 128 ms 5996 KB Output is correct
20 Correct 113 ms 5996 KB Output is correct
21 Correct 116 ms 5944 KB Output is correct
22 Correct 136 ms 8120 KB Output is correct
23 Correct 114 ms 4304 KB Output is correct
24 Correct 116 ms 5276 KB Output is correct
25 Correct 97 ms 3924 KB Output is correct
26 Correct 102 ms 4180 KB Output is correct
27 Execution timed out 1105 ms 353228 KB Time limit exceeded
28 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 3 ms 1876 KB Output is correct
3 Correct 24 ms 4156 KB Output is correct
4 Correct 19 ms 3656 KB Output is correct
5 Correct 72 ms 6444 KB Output is correct
6 Correct 28 ms 6508 KB Output is correct
7 Correct 42 ms 6460 KB Output is correct
8 Correct 33 ms 6448 KB Output is correct
9 Incorrect 29 ms 5832 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 35 ms 5328 KB Output is correct
2 Correct 48 ms 5816 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 256 KB Output is correct
5 Correct 123 ms 19768 KB Output is correct
6 Correct 135 ms 19792 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 62 ms 10392 KB Output is correct
9 Correct 92 ms 11220 KB Output is correct
10 Correct 34 ms 5320 KB Output is correct
11 Correct 35 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 268 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 37 ms 5456 KB Output is correct
19 Correct 43 ms 6496 KB Output is correct
20 Correct 31 ms 5448 KB Output is correct
21 Correct 38 ms 6084 KB Output is correct
22 Correct 31 ms 5468 KB Output is correct
23 Correct 34 ms 6080 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 3 ms 1876 KB Output is correct
26 Correct 24 ms 4156 KB Output is correct
27 Correct 19 ms 3656 KB Output is correct
28 Correct 72 ms 6444 KB Output is correct
29 Correct 28 ms 6508 KB Output is correct
30 Correct 42 ms 6460 KB Output is correct
31 Correct 33 ms 6448 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 1 ms 212 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 1 ms 256 KB Output is correct
36 Correct 1 ms 256 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 14 ms 1236 KB Output is correct
41 Correct 104 ms 3980 KB Output is correct
42 Correct 14 ms 1236 KB Output is correct
43 Correct 110 ms 3924 KB Output is correct
44 Correct 3 ms 468 KB Output is correct
45 Correct 104 ms 3912 KB Output is correct
46 Correct 105 ms 3796 KB Output is correct
47 Correct 3 ms 596 KB Output is correct
48 Correct 126 ms 5952 KB Output is correct
49 Correct 118 ms 5996 KB Output is correct
50 Correct 128 ms 5996 KB Output is correct
51 Correct 113 ms 5996 KB Output is correct
52 Correct 116 ms 5944 KB Output is correct
53 Correct 136 ms 8120 KB Output is correct
54 Correct 114 ms 4304 KB Output is correct
55 Correct 116 ms 5276 KB Output is correct
56 Correct 97 ms 3924 KB Output is correct
57 Correct 102 ms 4180 KB Output is correct
58 Execution timed out 1105 ms 353228 KB Time limit exceeded
59 Halted 0 ms 0 KB -