Submission #799376

#	Time	Username	Problem	Language	Result	Execution time	Memory
799376		Johann	Diversity (CEOI21_diversity)	C++14	64 / 100	7084 ms	7644 KiB

diversity

#include "bits/stdc++.h"
using namespace std;

typedef long long ll;
typedef vector<ll> vi;
typedef pair<ll, ll> pii;
typedef vector<pii> vpii;
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()

const ll INF = 1e18;
int N, Q;
vi A;
vi ans;
vi freq;
vi cnts;
set<int> incnt;

struct query
{
    int l, r, idx;
};

ll numberOfSubsequences(ll n)
{
    return n * (n + 1) / 2;
}
ll totalLengthOfSubsequences(ll n)
{
    return n * (n + 1) * (n + 1) / 2 - (2 * n + 1) * (n + 1) * n / 6;
}
void add(int x)
{
    if (freq[x] > 0)
    {
        --cnts[freq[x]];
        if (cnts[freq[x]] == 0)
            incnt.erase(freq[x]);
    }
    ++freq[x];
    ++cnts[freq[x]];
    if (cnts[freq[x]] == 1)
        incnt.insert(freq[x]);
}
void sub(int x)
{
    --cnts[freq[x]];
    if (cnts[freq[x]] == 0)
        incnt.erase(freq[x]);
    --freq[x];
    if (freq[x])
    {
        ++cnts[freq[x]];
        if (cnts[freq[x]] == 1)
            incnt.insert(freq[x]);
    }
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);

    cin >> N >> Q;
    A.resize(N);
    for (int i = 0; i < N; ++i)
        cin >> A[i];

    vector<query> Qu(Q);
    ans.resize(Q);
    for (int i = 0; i < Q; ++i)
        cin >> Qu[i].l >> Qu[i].r, Qu[i].idx = i, --Qu[i].l;

    int sq = 1;
    while (sq * sq < N)
        ++sq;
    auto cmp = [&](const query &a, const query &b)
    { if (a.l / sq == b.l / sq) 
        return a.r < b.r;
    else
        return a.l < b.l; };
    sort(all(Qu), cmp);

    int lx = 0, rx = 0;
    freq.assign(*max_element(all(A)) + 1, 0);
    cnts.assign(N + 1, 0);
    for (query q : Qu)
    {
        while (rx < q.r)
            add(A[rx++]);
        while (lx > q.l)
            add(A[--lx]);
        while (rx > q.r)
            sub(A[--rx]);
        while (lx < q.l)
            sub(A[lx++]);

        ll n = q.r - q.l;
        ll left = 0, right = 0;
        ll tmp = totalLengthOfSubsequences(n);

        vpii S;
        for (int f : incnt)
        {
            if (cnts[f] & 1)
                S.push_back({f, 1});
            if (cnts[f] > 1)
            {
                S.push_back({f, cnts[f] / 2});
                S.push_back({f, cnts[f] / 2});
            }
        }

        for (auto it = S.begin(); it != S.end(); ++it)
        {
            ll x = it->first;  // how much
            ll y = it->second; // how often
            ll len = x * y;

            // if both are in set
            tmp -= totalLengthOfSubsequences(len) - x * x * (totalLengthOfSubsequences(y) - y) - y * numberOfSubsequences(x);
            // if one is inside the other isn't
            tmp -= (n - len) * (len * (len + 1) / 2 - x * y * (y + 1) / 2);
            // if both are outside
            tmp -= (len - y) * left * (n - left - len);

            left += len;
            swap(left, right);
        }

        ans[q.idx] = tmp;
    }
    for (ll x : ans)
        cout << x << "\n";

    return 0;
}

• Subtask 1: 4 / 4
• Subtask 2: 10 / 10
• Subtask 3: 8 / 8
• Subtask 4: 16 / 16
• Subtask 5: 26 / 26
• Subtask 6: 0 / 36