oj.uz

Submission #753015

# Submission time Handle Problem Language Result Execution time Memory
753015 2023-06-04T13:10:05 Z I_love_Hoang_Yen Sequence (APIO23_sequence) C++17
40 / 100
 2000 ms 42144 KB 
#include "sequence.h"
#include <bits/stdc++.h>
#define SZ(s) ((int) ((s).size()))
using namespace std;

// 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]);
    }
};
// }}}
// SegTree examples {{{
// Examples: Commonly used SegTree ops: max / min / sum
struct MaxSegTreeOp {
    static int op(int x, int y) {
        return max(x, y);
    }
    static int e() {
        return INT_MIN;
    }
};

struct MinSegTreeOp {
    static int op(int x, int y) {
        return min(x, y);
    }
    static int e() {
        return INT_MAX;
    }
};

struct SumSegTreeOp {
    static long long op(long long x, long long y) {
        return x + y;
    }
    static long long e() {
        return 0;
    }
};

// using STMax = SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e>;
// using STMin = SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e>;
// using STSum = SegTree<int, SumSegTreeOp::op, SumSegTreeOp::e>;
// }}}

bool can(int n, int eq, const vector<int>& a, const vector<vector<int>>& ids) {
    int ln = *max_element(a.begin(), a.end());
    for (int median = 0; median <= ln; median++) {
        if (SZ(ids[median]) < eq) continue;

        vector<int> f(n+1, 0);
        for (int i = 1; i <= n; ++i) {
            f[i] = max(-1, min(a[i] - median, 1));
        }
        std::partial_sum(f.begin(), f.end(), f.begin());

        SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e> st_max(f);
        SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e> st_min(f);

        for (int ix = 0, iy = eq-1; iy < SZ(ids[median]); ++ix, ++iy) {
            int x = ids[median][ix];
            int y = ids[median][iy];

            // find [l, r]:
            // - l <= x < y <= r
            // - less + eq >= greater
            // - greater + eq >= less
            // - eq >= greater - less >= -eq
            // - eq >= (greater(r) - less(r)) - (greater(l-1) - less(l-1)) >= -eq

            int max_val = st_max.prod(y, n+1) - st_min.prod(0, x);
            int min_val = st_min.prod(y, n+1) - st_max.prod(0, x);

            // [-eq, eq] and [min_val, max_val] intersects
            if (min_val <= eq && max_val >= -eq) return true;
        }
    }
    return false;
}
int sequence(int n, std::vector<int> a) {
    // ids from 1
    a.insert(a.begin(), 0);

    vector<vector<int>> ids(n + 1);
    for (int i = 1; i <= n; ++i) {
        ids[a[i]].push_back(i);
    }

    int left = 1, right = n, res = 1;
    while (left <= right) {
        int mid = (left + right) / 2;
        if (can(n, mid, a, ids)) {
            res = mid;
            left = mid + 1;
        } else {
            right = mid - 1;
        }
    }
    return res;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 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 1 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 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct

Subtask #2
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 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 1 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 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 3 ms 340 KB Output is correct
14 Correct 4 ms 340 KB Output is correct
15 Correct 2 ms 340 KB Output is correct
16 Correct 2 ms 340 KB Output is correct
17 Correct 2 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 2 ms 380 KB Output is correct
22 Correct 2 ms 340 KB Output is correct

Subtask #3
0.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 138 ms 36016 KB Output is correct
3 Correct 194 ms 36092 KB Output is correct
4 Correct 178 ms 28772 KB Output is correct
5 Correct 147 ms 35152 KB Output is correct
6 Correct 125 ms 35108 KB Output is correct
7 Correct 838 ms 28688 KB Output is correct
8 Execution timed out 2081 ms 28940 KB Time limit exceeded
9 Halted 0 ms 0 KB -

Subtask #4
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 123 ms 28972 KB Output is correct
3 Correct 323 ms 29552 KB Output is correct
4 Correct 171 ms 29608 KB Output is correct
5 Correct 114 ms 29020 KB Output is correct
6 Correct 1202 ms 29764 KB Output is correct

Subtask #5
0.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 222 ms 41776 KB Output is correct
2 Execution timed out 2077 ms 42144 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #6
0.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 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 1 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 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 3 ms 340 KB Output is correct
14 Correct 4 ms 340 KB Output is correct
15 Correct 2 ms 340 KB Output is correct
16 Correct 2 ms 340 KB Output is correct
17 Correct 2 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 2 ms 380 KB Output is correct
22 Correct 2 ms 340 KB Output is correct
23 Correct 1708 ms 6952 KB Output is correct
24 Correct 1473 ms 6944 KB Output is correct
25 Correct 1675 ms 6900 KB Output is correct
26 Correct 766 ms 6056 KB Output is correct
27 Correct 49 ms 5884 KB Output is correct
28 Correct 1850 ms 6176 KB Output is correct
29 Correct 85 ms 5632 KB Output is correct
30 Correct 54 ms 5680 KB Output is correct
31 Correct 42 ms 5524 KB Output is correct
32 Correct 19 ms 7612 KB Output is correct
33 Correct 31 ms 6592 KB Output is correct
34 Incorrect 47 ms 6640 KB Output isn't correct
35 Halted 0 ms 0 KB -

Subtask #7
0.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 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 1 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 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 3 ms 340 KB Output is correct
14 Correct 4 ms 340 KB Output is correct
15 Correct 2 ms 340 KB Output is correct
16 Correct 2 ms 340 KB Output is correct
17 Correct 2 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 2 ms 380 KB Output is correct
22 Correct 2 ms 340 KB Output is correct
23 Correct 138 ms 36016 KB Output is correct
24 Correct 194 ms 36092 KB Output is correct
25 Correct 178 ms 28772 KB Output is correct
26 Correct 147 ms 35152 KB Output is correct
27 Correct 125 ms 35108 KB Output is correct
28 Correct 838 ms 28688 KB Output is correct
29 Execution timed out 2081 ms 28940 KB Time limit exceeded
30 Halted 0 ms 0 KB -