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답안 #626081

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
626081 2022-08-11T08:03:59 Z I_love_Hoang_Yen 메기 농장 (IOI22_fish) C++17
53 / 100
 1000 ms 2097152 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;
}
// }}}

// SegTree, copied from AtCoder library {{{
// AtCoder doc: https://atcoder.github.io/ac-library/master/document_en/segtree.html
//
// Notes:
// - Index of elements from 0 -> n-1
// - Range queries are [l, r-1]
//
// Tested:
// - (binary search) https://atcoder.jp/contests/practice2/tasks/practice2_j
// - https://oj.vnoi.info/problem/gss
// - https://oj.vnoi.info/problem/nklineup
// - (max_right & min_left for delete position queries) https://oj.vnoi.info/problem/segtree_itstr
// - https://judge.yosupo.jp/problem/point_add_range_sum
// - https://judge.yosupo.jp/problem/point_set_range_composite
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

template<
    class T,  // data type for nodes
    T (*op) (T, T),  // operator to combine 2 nodes
    T (*e)() // identity element
>
struct SegTree {
    SegTree() : SegTree(0) {}
    explicit SegTree(int n) : SegTree(vector<T> (n, e())) {}
    explicit SegTree(const vector<T>& v) : _n((int) v.size()) {
        log = ceil_pow2(_n);
        size = 1<<log;
        d = vector<T> (2*size, e());

        for (int i = 0; i < _n; i++) d[size+i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    // 0 <= p < n
    void set(int p, T x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    // 0 <= p < n
    T get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    // Get product in range [l, r-1]
    // 0 <= l <= r <= n
    // For empty segment (l == r) -> return e()
    T prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        T sml = e(), smr = e();
        l += size;
        r += size;
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    T all_prod() const {
        return d[1];
    }

    // Binary search on SegTree to find largest r:
    //    f(op(a[l] .. a[r-1])) = true   (assuming empty array is always true)
    //    f(op(a[l] .. a[r])) = false    (assuming op(..., a[n]), which is out of bound, is always false)
    template <bool (*f)(T)> int max_right(int l) const {
        return max_right(l, [](T x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        T sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    // Binary search on SegTree to find smallest l:
    //    f(op(a[l] .. a[r-1])) = true      (assuming empty array is always true)
    //    f(op(a[l-1] .. a[r-1])) = false   (assuming op(a[-1], ..), which is out of bound, is always false)
    template <bool (*f)(T)> int min_left(int r) const {
        return min_left(r, [](T x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        T sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

private:
    int _n, size, log;
    vector<T> d;

    void update(int k) {
        d[k] = op(d[2*k], d[2*k+1]);
    }
};
// }}}

struct MaxSegTreeOp {
    static int op(int x, int y) {
        return max(x, y);
    }
    static int e() {
        return 0;
    }
};

// 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_with_next_col_suffix_max(n, std::vector<int> (n, 0)),
                                  f_with_next_col_prefix_max(n, std::vector<int> (n, 0));
    std::vector<int> g_with_next_col_prefix_max(n, 0);
    std::vector<SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e>> st_g(n);

    // 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(
                            st_g[c-1].prod(0, r+1),
                            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], st_g[c-1].prod(r+1, n));
                        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(
                            st_g[c-2].all_prod() + weights[c-1][r],
                            g_with_next_col_prefix_max[c-2]);
                    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] + weights[c-1][r];
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);
                }
            }
        }
        // }}}
        
        // aggregate {{{
        st_g[c] = SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e> (g[c]);

        auto MAX = [] (auto a, auto b) { return std::max(a, b); };
        if (c + 1 < n) {
            // g_with_next_col_prefix_max[c] = max(
            //     g_with_next_col_prefix_max[c-1],
            //     g[c][0] + weights[c+1][0],
            //     ...
            //     g[c][r] + weights[c+1][r])
            g_with_next_col_prefix_max[c] = (c > 0) ? g_with_next_col_prefix_max[c-1] : 0;

            for (int r = 0; r < n; ++r) {
                g_with_next_col_suffix_max[c][r] = g[c][r] + weights[c+1][r];
            }
            g_with_next_col_prefix_max[c] = std::max(g_with_next_col_prefix_max[c], *max_element(g_with_next_col_suffix_max[c].begin(), g_with_next_col_suffix_max[c].end()));

            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;

}
// }}}

#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 sub6(n, fishes);
}

Subtask #1
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 25 ms 5572 KB Output is correct
2 Correct 31 ms 6316 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 114 ms 20744 KB Output is correct
6 Correct 107 ms 20808 KB Output is correct

Subtask #2
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 53 ms 10640 KB Output is correct
3 Correct 78 ms 12064 KB Output is correct
4 Correct 27 ms 6084 KB Output is correct
5 Correct 31 ms 6556 KB Output is correct
6 Correct 1 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 27 ms 6132 KB Output is correct
13 Correct 32 ms 7228 KB Output is correct
14 Correct 28 ms 6212 KB Output is correct
15 Correct 32 ms 6772 KB Output is correct
16 Correct 32 ms 6128 KB Output is correct
17 Correct 30 ms 6816 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 1876 KB Output is correct
3 Correct 23 ms 4668 KB Output is correct
4 Correct 12 ms 4060 KB Output is correct
5 Correct 30 ms 6724 KB Output is correct
6 Correct 25 ms 6984 KB Output is correct
7 Correct 29 ms 7100 KB Output is correct
8 Correct 37 ms 7100 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 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 Correct 1 ms 212 KB Output is correct
9 Correct 3 ms 1840 KB Output is correct
10 Correct 11 ms 6356 KB Output is correct
11 Correct 3 ms 1748 KB Output is correct
12 Correct 10 ms 6340 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 11 ms 6320 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 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 Correct 1 ms 212 KB Output is correct
9 Correct 3 ms 1840 KB Output is correct
10 Correct 11 ms 6356 KB Output is correct
11 Correct 3 ms 1748 KB Output is correct
12 Correct 10 ms 6340 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 11 ms 6320 KB Output is correct
15 Correct 9 ms 6216 KB Output is correct
16 Correct 2 ms 824 KB Output is correct
17 Correct 24 ms 8884 KB Output is correct
18 Correct 25 ms 8796 KB Output is correct
19 Correct 24 ms 8848 KB Output is correct
20 Correct 29 ms 8800 KB Output is correct
21 Correct 24 ms 8796 KB Output is correct
22 Correct 39 ms 11108 KB Output is correct
23 Correct 12 ms 6864 KB Output is correct
24 Correct 18 ms 8152 KB Output is correct
25 Correct 9 ms 6328 KB Output is correct
26 Correct 12 ms 6740 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 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 Correct 1 ms 212 KB Output is correct
9 Correct 3 ms 1840 KB Output is correct
10 Correct 11 ms 6356 KB Output is correct
11 Correct 3 ms 1748 KB Output is correct
12 Correct 10 ms 6340 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 11 ms 6320 KB Output is correct
15 Correct 9 ms 6216 KB Output is correct
16 Correct 2 ms 824 KB Output is correct
17 Correct 24 ms 8884 KB Output is correct
18 Correct 25 ms 8796 KB Output is correct
19 Correct 24 ms 8848 KB Output is correct
20 Correct 29 ms 8800 KB Output is correct
21 Correct 24 ms 8796 KB Output is correct
22 Correct 39 ms 11108 KB Output is correct
23 Correct 12 ms 6864 KB Output is correct
24 Correct 18 ms 8152 KB Output is correct
25 Correct 9 ms 6328 KB Output is correct
26 Correct 12 ms 6740 KB Output is correct
27 Execution timed out 1076 ms 545856 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 1876 KB Output is correct
3 Correct 23 ms 4668 KB Output is correct
4 Correct 12 ms 4060 KB Output is correct
5 Correct 30 ms 6724 KB Output is correct
6 Correct 25 ms 6984 KB Output is correct
7 Correct 29 ms 7100 KB Output is correct
8 Correct 37 ms 7100 KB Output is correct
9 Runtime error 802 ms 2097152 KB Execution killed with signal 9
10 Halted 0 ms 0 KB -

Subtask #8
0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 25 ms 5572 KB Output is correct
2 Correct 31 ms 6316 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 114 ms 20744 KB Output is correct
6 Correct 107 ms 20808 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 53 ms 10640 KB Output is correct
9 Correct 78 ms 12064 KB Output is correct
10 Correct 27 ms 6084 KB Output is correct
11 Correct 31 ms 6556 KB Output is correct
12 Correct 1 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 27 ms 6132 KB Output is correct
19 Correct 32 ms 7228 KB Output is correct
20 Correct 28 ms 6212 KB Output is correct
21 Correct 32 ms 6772 KB Output is correct
22 Correct 32 ms 6128 KB Output is correct
23 Correct 30 ms 6816 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 2 ms 1876 KB Output is correct
26 Correct 23 ms 4668 KB Output is correct
27 Correct 12 ms 4060 KB Output is correct
28 Correct 30 ms 6724 KB Output is correct
29 Correct 25 ms 6984 KB Output is correct
30 Correct 29 ms 7100 KB Output is correct
31 Correct 37 ms 7100 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 Correct 1 ms 212 KB Output is correct
40 Correct 3 ms 1840 KB Output is correct
41 Correct 11 ms 6356 KB Output is correct
42 Correct 3 ms 1748 KB Output is correct
43 Correct 10 ms 6340 KB Output is correct
44 Correct 1 ms 596 KB Output is correct
45 Correct 11 ms 6320 KB Output is correct
46 Correct 9 ms 6216 KB Output is correct
47 Correct 2 ms 824 KB Output is correct
48 Correct 24 ms 8884 KB Output is correct
49 Correct 25 ms 8796 KB Output is correct
50 Correct 24 ms 8848 KB Output is correct
51 Correct 29 ms 8800 KB Output is correct
52 Correct 24 ms 8796 KB Output is correct
53 Correct 39 ms 11108 KB Output is correct
54 Correct 12 ms 6864 KB Output is correct
55 Correct 18 ms 8152 KB Output is correct
56 Correct 9 ms 6328 KB Output is correct
57 Correct 12 ms 6740 KB Output is correct
58 Execution timed out 1076 ms 545856 KB Time limit exceeded
59 Halted 0 ms 0 KB -