Submission #964301

#	Time	Username	Problem	Language	Result	Execution time	Memory
964301		Nhoksocqt1	Sequence (APIO23_sequence)	C++17	47 / 100	1481 ms	53692 KiB

sequence

#ifndef Nhoksocqt1
    #include "sequence.h"
#endif // Nhoksocqt1
#include<bits/stdc++.h>
using namespace std;

#define inf 0x3f3f3f3f
#define sz(x) int((x).size())
#define fi first
#define se second
typedef long long ll;
typedef pair<int, int> ii;

template<class X, class Y>
	inline bool maximize(X &x, const Y &y) {return (x < y ? x = y, 1 : 0);}
template<class X, class Y>
	inline bool minimize(X &x, const Y &y) {return (x > y ? x = y, 1 : 0);}

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int Random(int l, int r) {
    return uniform_int_distribution<int>(l, r)(rng);
}

const int MAXN = 500005;

vector<int> B[MAXN];
int fen[2 * MAXN], fenp[2 * MAXN];
int val[MAXN], cnt[MAXN], nArr;

int sub2(void) {
    int res(1);
    for (int l = 1; l <= nArr; ++l) {
        set<int> Set;
        int pos(val[l]), cntPos(1);
        Set.insert(pos);
        ++cnt[pos];

        for (int r = l + 1; r <= nArr; ++r) {
            cntPos += (val[r] <= pos);
            if(++cnt[val[r]] == 1)
                Set.insert(val[r]);

            while(cntPos < (r - l + 1) / 2 + 1) {
                auto it = Set.lower_bound(pos); ++it;
                assert(it != Set.end());
                pos = *it;
                cntPos += cnt[pos];
            }

            while(cntPos - cnt[pos] >= (r - l + 1) / 2 + 1) {
                cntPos -= cnt[pos];
                auto it = Set.lower_bound(pos);
                assert(it != Set.begin()); --it;
                pos = *it;
            }

            //cout << l << ' ' << r << ' ' << pos << ' ' << cntPos << '\n';
            res = max(res, cnt[pos]);
            if((r - l + 1) % 2 == 0 && cntPos - cnt[pos] >= (r - l + 1) / 2) {
                auto it = Set.lower_bound(pos);
                assert(it != Set.begin()); --it;
                res = max(res, cnt[*it]);
            }
        }

        for (int r = l; r <= nArr; ++r)
            --cnt[val[r]];
    }

    return res;
}

int sub3(void) {
    int res(0);
    for (int i = 1; i <= nArr; ) {
        int j(i);
        while(j <= nArr && val[j] == val[i])
            ++j;

        res = max(res, j - i);
        i = j;
    }

    for (int i = 1; i <= nArr; ++i)
        ++cnt[val[i]];

    int j(nArr);
    for (int i = 1; i <= j; ++i) {
        if(i > 1 && val[i] == val[i - 1])
            continue;

        while(j > i && val[j] < val[i])
            --cnt[val[j--]];

        if(j > i && val[i] == val[j]) {
            int cntPos = cnt[val[i]];
            if(cnt[val[i]] + i - 1 + nArr - j >= (nArr + 1) / 2)
                res = max(res, cnt[val[i]]);
        }
    }

    return res;
}

void modify(int fen[], int i, int v) {
    for (i += nArr + 1; i <= 2 * nArr + 1; i += i & -i)
        fen[i] += v;
}

int get(int fen[], int i) {
    int res(0);
    for (i += nArr + 1; i > 0; i -= i & -i)
        res += fen[i];

    return res;
}

bool check4(int minCnt, int x) {
    for (int i = 1; i <= 2 * nArr; ++i)
        fen[i] = fenp[i] = 0;

    ll res(0);
    int j(1), cnt(0), sumx(0), sumpx(0), sumxj(0), sumpxj(0);
    for (int i = 1; i <= nArr; ++i) {
        cnt += (val[i] == x);
        while(j <= i && cnt >= minCnt) {
            cnt -= (val[j] == x);
            modify(fen, sumxj, +1);
            modify(fenp, sumpxj, +1);
            sumxj += 2 * (val[j] <= x) - 1;
            sumpxj += 2 * (val[j] < x) - 1;
            ++j;
        }

        sumx += 2 * (val[i] <= x) - 1;
        sumpx += 2 * (val[i] < x) - 1;
        res += get(fen, sumx) - get(fenp, sumpx);
    }

    return (res > 0);
}

int sub4(void) {
    int res(1);
    for (int i = 1; i <= 3; ++i) {
        int l(2), r(nArr);
        while(l <= r) {
            int mid = (l + r) >> 1;
            if(check4(mid, i)) {
                res = max(res, mid);
                l = mid + 1;
            } else {
                r = mid - 1;
            }
        }
    }

    return res;
}

struct SegNode {
    int minv, maxv, lz;
} seg[4 * MAXN];

inline void pushDown(int id) {
    int &lz(seg[id].lz);

    id <<= 1;
    seg[id] = {seg[id].minv + lz, seg[id].maxv + lz, seg[id].lz + lz};
    seg[id | 1] = {seg[id | 1].minv + lz, seg[id | 1].maxv + lz, seg[id | 1].lz + lz};
    lz = 0;
}

void update(int id, int l, int r, int u, int v, int k) {
    if(u <= l && r <= v) {
        seg[id] = {seg[id].minv + k, seg[id].maxv + k, seg[id].lz + k};
        return;
    }

    if(seg[id].lz)
        pushDown(id);

    int mid = (l + r) >> 1;
    if(mid >= u)
        update(id << 1, l, mid, u, v, k);

    if(mid + 1 <= v)
        update(id << 1 | 1, mid + 1, r, u, v, k);

    seg[id].minv = min(seg[id << 1].minv, seg[id << 1 | 1].minv);
    seg[id].maxv = max(seg[id << 1].maxv, seg[id << 1 | 1].maxv);
}

ii query(int id, int l, int r, int u, int v) {
    if(u <= l && r <= v)
        return make_pair(seg[id].minv, seg[id].maxv);

    if(seg[id].lz)
        pushDown(id);

    ii res = {1e9, -1e9};
    int mid = (l + r) >> 1;
    if(mid >= u)
        res = query(id << 1, l, mid, u, v);

    if(mid + 1 <= v) {
        ii qr = query(id << 1 | 1, mid + 1, r, u, v);
        res = {min(res.fi, qr.fi), max(res.se, qr.se)};
    }

    return res;
}

int sub5(void) {
    for (int i = 1; i <= nArr; ++i) {
        B[val[i]].push_back(i);
        update(1, 1, nArr, i, i, -i);
    }

    int res(1);
    for (int i = 1; i <= nArr; ++i) {
        if(!sz(B[i]))
            continue;

        for (int it = 0; it < sz(B[i]); ++it) {
            int j(B[i][it]);
            update(1, 1, nArr, j, nArr, +2);
        }

        if(sz(B[i]) != 2)
            continue;

        int l = B[i][0], r = B[i][1];
        ii qrL = (l > 1) ? query(1, 1, nArr, 1, l - 1) : ii(1e9, -1e9), qrR = query(1, 1, nArr, r, nArr);
        qrL.fi = min(qrL.fi, 0), qrL.se = max(qrL.se, 0);

        //cout << i << ' ' << l << ' ' << r << ' ' << qrL.fi << ' ' << qrL.se << ' ' << qrR.fi << ' ' << qrR.se << '\n';
        if(qrR.se - qrL.fi >= 0 && qrR.fi - qrR.se <= 1) {
            res = 2;
            break;
        }
    }

    return res;
}

int sequence(int _N, vector<int> _A) {
    nArr = _N;
    bool check5(1);
    for (int i = 1; i <= nArr; ++i) {
        val[i] = _A[i - 1];
        check5 &= (++cnt[val[i]] <= 2);
    }

    bool check3(1);
    for (int i = 1; i <= nArr; ++i) {
        check3 &= (i <= 2 || val[i - 2] <= val[i - 1] || val[i - 2] >= val[i - 1] && val[i - 1] >= val[i]);
        cnt[i] = 0;
    }

    //cout << sub5() << '\n';
    if(nArr <= 2000) {
        return sub2();
    } else
        if(check3) {
            return sub3();
        } else
            if(*max_element(val + 1, val + nArr + 1) <= 3) {
                return sub4();
            } else
                if(check5) {
                    return sub5();
                }
}

#ifdef Nhoksocqt1

int main(void) {
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);

    #define TASK "sequence"
    if(fopen(TASK".inp", "r")) {
        freopen(TASK".inp", "r", stdin);
        freopen(TASK".out", "w", stdout);
    }

    vector<int> _A;
    int _N;
    cin >> _N;

    _A.resize(_N);
    //vector<int> _B; for (int i = 0; sz(_B) < _N; ++i) {int x = Random(1, 2); _B.push_back(i + 1); if(sz(_B) < _N && x > 1) _B.push_back(i + 1); } shuffle(_B.begin(), _B.end(), rng);
    for (int i = 0; i < _N; ++i) {
        cin >> _A[i];
        //_A[i] = _B[i]; cout << _A[i] << " \n"[i + 1 == _N];
    }

    int ans = sequence(_N, _A);
    cout << "ANSWER: " << ans << '\n';

    return 0;
}

#endif // Nhoksocqt1

Compilation message (stderr)

sequence.cpp: In function 'int sub3()':
sequence.cpp:96:17: warning: unused variable 'cntPos' [-Wunused-variable]
   96 |             int cntPos = cnt[val[i]];
      |                 ^~~~~~
sequence.cpp: In function 'int sequence(int, std::vector<int>)':
sequence.cpp:257:83: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
  257 |         check3 &= (i <= 2 || val[i - 2] <= val[i - 1] || val[i - 2] >= val[i - 1] && val[i - 1] >= val[i]);
      |                                                          ~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:274:1: warning: control reaches end of non-void function [-Wreturn-type]
  274 | }
      | ^

• Subtask 1: 11 / 11
• Subtask 2: 17 / 17
• Subtask 3: 7 / 7
• Subtask 4: 12 / 12
• Subtask 5: 0 / 13
• Subtask 6: 0 / 22
• Subtask 7: 0 / 18