oj.uz

Submission #753016

# Submission time Handle Problem Language Result Execution time Memory
753016 2023-06-04T13:11:20 Z I_love_Hoang_Yen Sequence (APIO23_sequence) C++17
40 / 100
 2000 ms 45868 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), greater(n+1, 0), less(n+1, 0);
        for (int i = 1; i <= n; ++i) {
            greater[i] = a[i] > median;
            less[i] = a[i] < median;
            f[i] = max(-1, min(a[i] - median, 1));
            assert(greater[i] - less[i] == f[i]);
        }
        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 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 1 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 Correct 0 ms 212 KB Output is correct
9 Correct 1 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 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 1 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 Correct 0 ms 212 KB Output is correct
9 Correct 1 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 4 ms 340 KB Output is correct
14 Correct 5 ms 340 KB Output is correct
15 Correct 3 ms 340 KB Output is correct
16 Correct 3 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 2 ms 468 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 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 1 ms 212 KB Output is correct
2 Correct 135 ms 39972 KB Output is correct
3 Correct 197 ms 39964 KB Output is correct
4 Correct 194 ms 32584 KB Output is correct
5 Correct 143 ms 39088 KB Output is correct
6 Correct 121 ms 38928 KB Output is correct
7 Correct 943 ms 32712 KB Output is correct
8 Execution timed out 2063 ms 32856 KB Time limit exceeded
9 Halted 0 ms 0 KB -

Subtask #4
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 130 ms 32912 KB Output is correct
3 Correct 351 ms 33544 KB Output is correct
4 Correct 175 ms 33440 KB Output is correct
5 Correct 116 ms 32924 KB Output is correct
6 Correct 1199 ms 33496 KB Output is correct

Subtask #5
0.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 219 ms 45692 KB Output is correct
2 Execution timed out 2079 ms 45868 KB Time limit exceeded
3 Halted 0 ms 0 KB -

Subtask #6
0.0 / 22.0

# 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 1 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 Correct 0 ms 212 KB Output is correct
9 Correct 1 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 4 ms 340 KB Output is correct
14 Correct 5 ms 340 KB Output is correct
15 Correct 3 ms 340 KB Output is correct
16 Correct 3 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 2 ms 468 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 2 ms 340 KB Output is correct
23 Correct 1832 ms 7796 KB Output is correct
24 Correct 1621 ms 7668 KB Output is correct
25 Correct 1858 ms 7540 KB Output is correct
26 Correct 886 ms 6552 KB Output is correct
27 Correct 54 ms 6532 KB Output is correct
28 Execution timed out 2011 ms 6900 KB Time limit exceeded
29 Halted 0 ms 0 KB -

Subtask #7
0.0 / 18.0

# 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 1 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 Correct 0 ms 212 KB Output is correct
9 Correct 1 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 4 ms 340 KB Output is correct
14 Correct 5 ms 340 KB Output is correct
15 Correct 3 ms 340 KB Output is correct
16 Correct 3 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 2 ms 468 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 2 ms 340 KB Output is correct
23 Correct 135 ms 39972 KB Output is correct
24 Correct 197 ms 39964 KB Output is correct
25 Correct 194 ms 32584 KB Output is correct
26 Correct 143 ms 39088 KB Output is correct
27 Correct 121 ms 38928 KB Output is correct
28 Correct 943 ms 32712 KB Output is correct
29 Execution timed out 2063 ms 32856 KB Time limit exceeded
30 Halted 0 ms 0 KB -