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Submission #993132

# Submission time Handle Problem Language Result Execution time Memory
993132 2024-06-05T10:52:49 Z NValchanov Intergalactic ship (IZhO19_xorsum) C++17
56 / 100
 2000 ms 4816 KB 
#include <bits/stdc++.h>

#define endl '\n'

using namespace std;

typedef long long ll;

const ll MAXN = 1e3 + 10;
const ll MOD = 1e9 + 7;
const ll MAXLOG = 7;
const ll MAXA = 128;

struct upd
{
    ll left, right;
    ll val;

    upd()
    {
        left = right = 1;
        val = 0;
    }

    upd(ll _left, ll _right, ll _val)
    {
        left = _left;
        right = _right;
        val = _val;
    }
};

ll n, q;
ll a[MAXN];
ll cur[MAXN];
ll pow2[MAXN];
ll tmp[32];
ll cnt[MAXN][32];
ll curcnt[MAXN];
ll pow2q;
vector < upd > updates;
bool lampa = true;

void read()
{
    cin >> n;
    for(int i = 1; i <= n; i++)
    {
        cin >> a[i];
    }
    cin >> q;
    for(int i = 1; i <= q; i++)
    {
        ll left, right;
        ll x;

        if(left != right)
            lampa = false;

        cin >> left >> right >> x;

        upd u = upd(left, right, x);

        updates.push_back(u);
    }
}

void solve()
{
    ll ans = 0;
    pow2[0] = 1;
    for(int i = 1; i < MAXN; i++)
    {
        pow2[i] = (pow2[i - 1] * 2) % MOD;
    }

    for(int i = 1; i <= n; i++)
    {
        for(int j = i; j <= n; j++)
        {
            ll cnt = (i * (n - j + 1)) % MOD;
            ll type;

            if(i != j)
                type = (cnt * 2) % MOD;
            else
                type = cnt;

            ll cursum = 0;

            for(int bit1 = 0; bit1 < MAXLOG; bit1++)
            {
                for(int bit2 = 0; bit2 < MAXLOG; bit2++)
                {
                    vector < vector < ll > > dp;
                    dp.resize(2);
                    dp[0].resize(4);
                    dp[1].resize(4);

                    dp[0][(bool(a[i] & (1 << bit1)) << 1) | (bool(a[j] & (1 << bit2)))] = 1;

                    for(int k = 0; k < q; k++)
                    {
                        dp[1] = dp[0];

                        int in1 = 0;
                        int in2 = 0;

                        if(updates[k].left <= i && i <= updates[k].right)
                            in1 = (bool(updates[k].val & (1 << bit1)));
                        
                        if(updates[k].left <= j && j <= updates[k].right)
                            in2 = (bool(updates[k].val & (1 << bit2)));
                        
                        int h = (in1 << 1) | in2; /// 00; 01; 10; 11

                        for(int x = 0; x < 4; x++)
                        {
                            dp[1][x ^ h] = (dp[1][x ^ h] + dp[0][x]) % MOD;
                        }

                        swap(dp[1], dp[0]);
                    }

                    cursum = (cursum + (pow2[bit1 + bit2] * dp[0][3]) % MOD) % MOD;
                }
            }
            cursum = (cursum * type) % MOD;
            ans = (ans + cursum) % MOD;
        }
    }

    cout << ans << endl;
}

void update(bitset < MAXA >&bs, ll val)
{
    if(bs[bs._Find_first() ^ val])
        return;

    vector < int > to_add;

    for(int i = bs._Find_first(); i < MAXA; i = bs._Find_next(i))
        to_add.push_back(i ^ val);

    for(int i : to_add)
        bs[i] = 1;
}

ll binpow(ll a, ll b)
{
    ll result = 1;

    while(b)
    {
        if(b & 1)
            result = (result * a) % MOD;
        
        a = (a * a) % MOD;
        b /= 2;
    }

    return result;
}

void solve_2()
{
    pow2q = 1;
    for(int i = 1; i <= q; i++)
    {
        pow2q = (pow2q * 2) % MOD;
    }

    ll ans = 0;

    for(int i = 1; i <= n; i++)
    {
        for(int j = i; j <= n; j++)
        {
            bitset < MAXA > bs1;
            bitset < MAXA > bs2;
            bitset < MAXA > bs3;

            bs1[a[i]] = bs2[a[j]] = bs3[0] = 1;

            for(int k = 0; k < q; k++)
            {
                bool in1 = false;
                bool in2 = false;

                if(updates[k].left <= i && i <= updates[k].right)
                    in1 = true;

                if(updates[k].left <= j && j <= updates[k].right)
                    in2 = true;

                if(in1 && in2)
                    update(bs3, updates[k].val);
                else if(in1)
                    update(bs1, updates[k].val);
                else if(in2)
                    update(bs2, updates[k].val);
            } 

            ll sum = 0;

            for(int idx1 = bs1._Find_first(); idx1 < MAXA; idx1 = bs1._Find_next(idx1))
            {
                for(int idx2 = bs2._Find_first(); idx2 < MAXA; idx2 = bs2._Find_next(idx2))
                {
                    for(int idx3 = bs3._Find_first(); idx3 < MAXA; idx3 = bs3._Find_next(idx3))
                    {
                        ll cur = ((idx1 ^ idx3) * (idx2 ^ idx3)) % MOD;

                        if(i != j)
                            cur = (cur * 2) % MOD;

                        sum = (sum + cur) % MOD;
                    }
                }
            }
            ll cnt = (i * (n - j + 1)) % MOD;
            sum = (sum * cnt) % MOD;
            sum = (sum * pow2q) % MOD;

            sum = (sum * (binpow(bs1.count() * bs2.count() * bs3.count(), MOD - 2))) % MOD;

            ans = (ans + sum) % MOD;
        }
    }

    cout << ans << endl;
}

void solve_3()
{
    vector < int > chep;

    for(int i = 1; i <= n; i++)
    {
        chep[i - 1] = a[i];
    }

    for(int i = 0; i < n; i++)
    {
        cnt[i][chep[i]]++;
    }

    for(int i = 0; i < q; i++)
    {
        ll left = updates[i].left;
        ll right = updates[i].right;
        ll val = updates[i].val;

        left--;

        assert(left == right);

        curcnt[left]++;

        for(int i = 0; i < 32; i++)
            tmp[i] = cnt[left][i];

        for(int i = 0; i < 32; i++)
        {
            cnt[left][i ^ val] = (cnt[left][i ^ val] + tmp[i]) % MOD;
        }        
    }

    for(int i = n; i > 0; i--)
    {
        curcnt[i - 1] += curcnt[i];
    }

    for(int i = 0; i <= n; i++)
    {
        ll x = curcnt[i];
        ll p = 1;

        while(x--)
            p = (p * 2) % MOD;
        
        curcnt[i] = p;
    }
    
    vector < ll > last;
    vector < ll > d;

    last.assign(3000, 0);
    last[0] = 1;
    ll ans = 0;

    for(int i = 0; i < n; i++)
    {
        d.assign(3000, 0);

        for(int j = 0; j < 32; j++)
        {
            for(int k = 0; j + k < 3000; k++)
            {
                d[j + k] = (d[j + k] + (last[k] * cnt[i][j]) % MOD) % MOD;
            }
        }

        for(int j = 0; j < 3000; j++)
        {
            last[j] = d[j];
            ans = (ans + d[j] * (j * j) * (n + 1) % MOD * curcnt[i + 1]) % MOD;
        }
    }

    last.assign(100000, 0);
    last[0] = 1;

    for(int i = 0; i < n; i++)
    {
        d.assign(100000, 0);
        for(int j = 0; j < 32; j++)
        {
            for(int k = 0; k + j * (n - i + 1) < 100000; k++)
            {
                d[k + j * (n - i + 1)] = (d[k + j * (n - i + 1)] + last[k] * cnt[i][j] % MOD) % MOD;
            }
            last = d;
        }
    }

    for(int i = 0; i < 100000; i++)
    {
        ans = (ans + MOD - d[i] * i % MOD * i % MOD) % MOD;
    }

    cout << ans << endl;
}

int main()
{
    ios_base :: sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    read();
    if(lampa && q > 5001)
        solve_3();
    else if(n > 500)
        solve_2();
    else
        solve();

    return 0;
}

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct

Subtask #2
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 53 ms 348 KB Output is correct
7 Correct 52 ms 344 KB Output is correct
8 Correct 52 ms 344 KB Output is correct

Subtask #3
0 / 6.0

# Verdict Execution time Memory Grader output
1 Execution timed out 2052 ms 3536 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #4
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 422 ms 344 KB Output is correct
2 Correct 363 ms 596 KB Output is correct
3 Correct 173 ms 344 KB Output is correct
4 Correct 125 ms 348 KB Output is correct

Subtask #5
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 348 KB Output is correct
2 Correct 9 ms 480 KB Output is correct
3 Correct 9 ms 476 KB Output is correct

Subtask #6
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 348 KB Output is correct
2 Correct 9 ms 480 KB Output is correct
3 Correct 9 ms 476 KB Output is correct
4 Correct 1945 ms 1052 KB Output is correct
5 Correct 1909 ms 600 KB Output is correct
6 Correct 1899 ms 664 KB Output is correct
7 Correct 1912 ms 616 KB Output is correct

Subtask #7
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 53 ms 348 KB Output is correct
7 Correct 52 ms 344 KB Output is correct
8 Correct 52 ms 344 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 480 KB Output is correct
11 Correct 9 ms 476 KB Output is correct
12 Correct 1214 ms 480 KB Output is correct
13 Correct 1219 ms 480 KB Output is correct
14 Correct 1243 ms 480 KB Output is correct
15 Correct 1205 ms 344 KB Output is correct

Subtask #8
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 53 ms 348 KB Output is correct
7 Correct 52 ms 344 KB Output is correct
8 Correct 52 ms 344 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 480 KB Output is correct
11 Correct 9 ms 476 KB Output is correct
12 Correct 1945 ms 1052 KB Output is correct
13 Correct 1909 ms 600 KB Output is correct
14 Correct 1899 ms 664 KB Output is correct
15 Correct 1912 ms 616 KB Output is correct
16 Correct 1214 ms 480 KB Output is correct
17 Correct 1219 ms 480 KB Output is correct
18 Correct 1243 ms 480 KB Output is correct
19 Correct 1205 ms 344 KB Output is correct
20 Execution timed out 2050 ms 4816 KB Time limit exceeded
21 Halted 0 ms 0 KB -

Subtask #9
0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 53 ms 348 KB Output is correct
7 Correct 52 ms 344 KB Output is correct
8 Correct 52 ms 344 KB Output is correct
9 Execution timed out 2052 ms 3536 KB Time limit exceeded
10 Halted 0 ms 0 KB -