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Submission #993148

# Submission time Handle Problem Language Result Execution time Memory
993148 2024-06-05T11:02:44 Z NValchanov Intergalactic ship (IZhO19_xorsum) C++17
56 / 100
 1963 ms 5836 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 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(4000, 0);
    last[0] = 1;
    ll ans = 0;

    for(int i = 0; i < n; i++)
    {
        d.assign(4000, 0);

        for(int j = 0; j < 32; j++)
        {
            for(int k = 0; j + k < 4000; k++)
            {
                d[j + k] = (d[j + k] + (last[k] * cnt[i][j]) % MOD) % MOD;
            }
        }

        for(int j = 0; j < 4000; j++)
        {
            last[j] = d[j];
            ans = (ans + d[j] * (j * j) * (n + 1) % MOD * curcnt[i + 1]) % MOD;
        }
    }

    last.assign(200000, 0);
    last[0] = 1;

    for(int i = 0; i < n; i++)
    {
        d.assign(200000, 0);
        for(int j = 0; j < 32; j++)
        {
            for(int k = 0; k + j * (n - i) < 200000; 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 < 200000; 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 448 KB Output is correct
7 Correct 52 ms 456 KB Output is correct
8 Correct 53 ms 452 KB Output is correct

Subtask #3
0 / 6.0

# Verdict Execution time Memory Grader output
1 Runtime error 14 ms 5576 KB Execution killed with signal 11
2 Halted 0 ms 0 KB -

Subtask #4
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 382 ms 488 KB Output is correct
2 Correct 322 ms 484 KB Output is correct
3 Correct 153 ms 344 KB Output is correct
4 Correct 120 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 472 KB Output is correct
3 Correct 12 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 472 KB Output is correct
3 Correct 12 ms 348 KB Output is correct
4 Correct 1911 ms 616 KB Output is correct
5 Correct 1935 ms 600 KB Output is correct
6 Correct 1953 ms 604 KB Output is correct
7 Correct 1963 ms 600 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 448 KB Output is correct
7 Correct 52 ms 456 KB Output is correct
8 Correct 53 ms 452 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 472 KB Output is correct
11 Correct 12 ms 348 KB Output is correct
12 Correct 1214 ms 348 KB Output is correct
13 Correct 1254 ms 480 KB Output is correct
14 Correct 1267 ms 480 KB Output is correct
15 Correct 1215 ms 348 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 448 KB Output is correct
7 Correct 52 ms 456 KB Output is correct
8 Correct 53 ms 452 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 472 KB Output is correct
11 Correct 12 ms 348 KB Output is correct
12 Correct 1911 ms 616 KB Output is correct
13 Correct 1935 ms 600 KB Output is correct
14 Correct 1953 ms 604 KB Output is correct
15 Correct 1963 ms 600 KB Output is correct
16 Correct 1214 ms 348 KB Output is correct
17 Correct 1254 ms 480 KB Output is correct
18 Correct 1267 ms 480 KB Output is correct
19 Correct 1215 ms 348 KB Output is correct
20 Runtime error 15 ms 5836 KB Execution killed with signal 11
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 448 KB Output is correct
7 Correct 52 ms 456 KB Output is correct
8 Correct 53 ms 452 KB Output is correct
9 Runtime error 14 ms 5576 KB Execution killed with signal 11
10 Halted 0 ms 0 KB -