oj.uz

Submission #626091

# Submission time Handle Problem Language Result Execution time Memory
626091 2022-08-11T08:14:37 Z I_love_Hoang_Yen Catfish Farm (IOI22_fish) C++17
32 / 100
 772 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;
    }
};

// RMQ {{{
//
// Sparse table
// Usage:
// RMQ<int, _min> st(v);
//
// Note:
// - doesn't work for empty range
//
// Tested:
// - https://judge.yosupo.jp/problem/staticrmq
template<class T, T (*op) (T, T)> struct RMQ {
    RMQ() = default;
    RMQ(const vector<T>& v) : t{v}, n{(int) v.size()} {
        for (int k = 1; (1<<k) <= n; ++k) {
            t.emplace_back(n - (1<<k) + 1);
            for (int i = 0; i + (1<<k) <= n; ++i) {
                t[k][i] = op(t[k-1][i], t[k-1][i + (1<<(k-1))]);
            }
        }
    }

    // get range [l, r-1]
    // doesn't work for empty range
    T get(int l, int r) const {
        if (l == r) return 0;
        assert(0 <= l && l < r && r <= n);
        int k = __lg(r - l);
        return op(t[k][l], t[k][r - (1<<k)]);
    }

private:
    vector<vector<T>> t;
    int n;
};
template<class T> T _min(T a, T b) { return b < a ? b : a; }
template<class T> T _max(T a, T b) { return a < b ? b : a; }
// }}}

// 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)),
                                  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<RMQ<int, _max>> st_g(n), st_g_with_next_col(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].get(0, 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], st_g[c-1].get(r+1, n-1));
                        upMax(g[c][r], st_g_with_next_col[c-1].get(r+1, n-1) - weights[c][r]);
                    }
                }
                // last pier at column i-2
                if (c >= 2) {
                    int cur = std::max(
                            st_g[c-2].get(0, n-1) + weights[c-1][r],
                            st_g_with_next_col[c-2].get(0, n-1));
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);
                }
                // last pier at column i-3
                if (c >= 3) {
                    int cur = st_g_with_next_col[c-3].get(0, n-1) + weights[c-1][r];
                    upMax(f[c][r], cur);
                    upMax(g[c][r], cur);
                }
            }
        }
        // }}}
        
        // aggregate {{{
        st_g[c] = RMQ<int, _max> (g[c]);

        auto MAX = [] (auto a, auto b) { return std::max(a, b); };
        if (c + 1 < n) {
            // g_with_next_col[c][r] = g[c][r] + weights[c+1][r]
            std::vector<int> g_with_next_col(n);
            for (int r = 0; r < n; ++r) {
                g_with_next_col[r] = g[c][r] + weights[c+1][r];
            }
            st_g_with_next_col[c] = RMQ<int, _max> (g_with_next_col);

            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

# Verdict Execution time Memory Grader output
1 Correct 27 ms 5824 KB Output is correct
2 Correct 31 ms 6256 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 96 ms 20472 KB Output is correct
6 Correct 101 ms 20392 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 57 ms 10856 KB Output is correct
3 Correct 83 ms 11840 KB Output is correct
4 Correct 29 ms 5708 KB Output is correct
5 Correct 31 ms 6440 KB Output is correct
6 Correct 1 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 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 27 ms 5756 KB Output is correct
13 Correct 38 ms 7100 KB Output is correct
14 Correct 28 ms 5724 KB Output is correct
15 Correct 33 ms 6416 KB Output is correct
16 Correct 27 ms 5724 KB Output is correct
17 Correct 29 ms 6352 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 2 ms 1876 KB Output is correct
3 Correct 17 ms 4840 KB Output is correct
4 Correct 13 ms 3868 KB Output is correct
5 Correct 29 ms 6716 KB Output is correct
6 Correct 31 ms 7024 KB Output is correct
7 Correct 30 ms 7076 KB Output is correct
8 Correct 31 ms 7124 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory 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 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 300 KB Output is correct
9 Correct 3 ms 3284 KB Output is correct
10 Correct 12 ms 13908 KB Output is correct
11 Correct 3 ms 3376 KB Output is correct
12 Correct 12 ms 13780 KB Output is correct
13 Correct 1 ms 980 KB Output is correct
14 Correct 14 ms 13748 KB Output is correct

Subtask #5
0 / 21.0

# Verdict Execution time Memory 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 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 300 KB Output is correct
9 Correct 3 ms 3284 KB Output is correct
10 Correct 12 ms 13908 KB Output is correct
11 Correct 3 ms 3376 KB Output is correct
12 Correct 12 ms 13780 KB Output is correct
13 Correct 1 ms 980 KB Output is correct
14 Correct 14 ms 13748 KB Output is correct
15 Correct 11 ms 13768 KB Output is correct
16 Incorrect 2 ms 1108 KB 1st lines differ - on the 1st token, expected: '741526820812', found: '732681666244'
17 Halted 0 ms 0 KB -

Subtask #6
0 / 17.0

# Verdict Execution time Memory 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 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 300 KB Output is correct
9 Correct 3 ms 3284 KB Output is correct
10 Correct 12 ms 13908 KB Output is correct
11 Correct 3 ms 3376 KB Output is correct
12 Correct 12 ms 13780 KB Output is correct
13 Correct 1 ms 980 KB Output is correct
14 Correct 14 ms 13748 KB Output is correct
15 Correct 11 ms 13768 KB Output is correct
16 Incorrect 2 ms 1108 KB 1st lines differ - on the 1st token, expected: '741526820812', found: '732681666244'
17 Halted 0 ms 0 KB -

Subtask #7
0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 2 ms 1876 KB Output is correct
3 Correct 17 ms 4840 KB Output is correct
4 Correct 13 ms 3868 KB Output is correct
5 Correct 29 ms 6716 KB Output is correct
6 Correct 31 ms 7024 KB Output is correct
7 Correct 30 ms 7076 KB Output is correct
8 Correct 31 ms 7124 KB Output is correct
9 Runtime error 772 ms 2097152 KB Execution killed with signal 9
10 Halted 0 ms 0 KB -

Subtask #8
0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 27 ms 5824 KB Output is correct
2 Correct 31 ms 6256 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 96 ms 20472 KB Output is correct
6 Correct 101 ms 20392 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 57 ms 10856 KB Output is correct
9 Correct 83 ms 11840 KB Output is correct
10 Correct 29 ms 5708 KB Output is correct
11 Correct 31 ms 6440 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 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 1 ms 212 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 27 ms 5756 KB Output is correct
19 Correct 38 ms 7100 KB Output is correct
20 Correct 28 ms 5724 KB Output is correct
21 Correct 33 ms 6416 KB Output is correct
22 Correct 27 ms 5724 KB Output is correct
23 Correct 29 ms 6352 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 2 ms 1876 KB Output is correct
26 Correct 17 ms 4840 KB Output is correct
27 Correct 13 ms 3868 KB Output is correct
28 Correct 29 ms 6716 KB Output is correct
29 Correct 31 ms 7024 KB Output is correct
30 Correct 30 ms 7076 KB Output is correct
31 Correct 31 ms 7124 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 0 ms 212 KB Output is correct
38 Correct 0 ms 212 KB Output is correct
39 Correct 1 ms 300 KB Output is correct
40 Correct 3 ms 3284 KB Output is correct
41 Correct 12 ms 13908 KB Output is correct
42 Correct 3 ms 3376 KB Output is correct
43 Correct 12 ms 13780 KB Output is correct
44 Correct 1 ms 980 KB Output is correct
45 Correct 14 ms 13748 KB Output is correct
46 Correct 11 ms 13768 KB Output is correct
47 Incorrect 2 ms 1108 KB 1st lines differ - on the 1st token, expected: '741526820812', found: '732681666244'
48 Halted 0 ms 0 KB -