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Submission #993143

# Submission time Handle Problem Language Result Execution time Memory
993143 2024-06-05T11:00:59 Z NValchanov Intergalactic ship (IZhO19_xorsum) C++17
56 / 100
 1869 ms 5580 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()
{

    assert(false);

    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 j = 0; j < 32; j++)
            tmp[j] = cnt[left][j];

        for(int j = 0; j < 32; j++)
        {
            cnt[left][j ^ val] = (cnt[left][j ^ val] + tmp[j]) % 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) < 100000; k++)
            {
                d[k + j * (n - i)] = (d[k + j * (n - i)] + 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(q > 5000)
        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 0 ms 344 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 0 ms 344 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 53 ms 448 KB Output is correct
8 Correct 53 ms 344 KB Output is correct

Subtask #3
0 / 6.0

# Verdict Execution time Memory Grader output
1 Runtime error 17 ms 5520 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #4
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 422 ms 472 KB Output is correct
2 Correct 373 ms 348 KB Output is correct
3 Correct 170 ms 348 KB Output is correct
4 Correct 129 ms 344 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 412 KB Output is correct
3 Correct 9 ms 348 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 412 KB Output is correct
3 Correct 9 ms 348 KB Output is correct
4 Correct 1849 ms 604 KB Output is correct
5 Correct 1840 ms 600 KB Output is correct
6 Correct 1843 ms 612 KB Output is correct
7 Correct 1869 ms 604 KB Output is correct

Subtask #7
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 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 53 ms 448 KB Output is correct
8 Correct 53 ms 344 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 412 KB Output is correct
11 Correct 9 ms 348 KB Output is correct
12 Correct 1226 ms 480 KB Output is correct
13 Correct 1198 ms 344 KB Output is correct
14 Correct 1199 ms 600 KB Output is correct
15 Correct 1208 ms 480 KB Output is correct

Subtask #8
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 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 53 ms 448 KB Output is correct
8 Correct 53 ms 344 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 412 KB Output is correct
11 Correct 9 ms 348 KB Output is correct
12 Correct 1849 ms 604 KB Output is correct
13 Correct 1840 ms 600 KB Output is correct
14 Correct 1843 ms 612 KB Output is correct
15 Correct 1869 ms 604 KB Output is correct
16 Correct 1226 ms 480 KB Output is correct
17 Correct 1198 ms 344 KB Output is correct
18 Correct 1199 ms 600 KB Output is correct
19 Correct 1208 ms 480 KB Output is correct
20 Runtime error 15 ms 5580 KB Execution killed with signal 6
21 Halted 0 ms 0 KB -

Subtask #9
0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 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 53 ms 448 KB Output is correct
8 Correct 53 ms 344 KB Output is correct
9 Runtime error 17 ms 5520 KB Execution killed with signal 6
10 Halted 0 ms 0 KB -