oj.uz

Submission #993123

# Submission time Handle Problem Language Result Execution time Memory
993123 2024-06-05T10:37:08 Z NValchanov Intergalactic ship (IZhO19_xorsum) C++17
56 / 100
 1974 ms 6604 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;

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;

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

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

        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 + 1; i >= 1; i--)
    {
        curcnt[i - 1] += curcnt[i];
    }

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

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

    last.resize(5e3 + 10, 0);
    last[0] = 1;
    ll ans = 0;

    for(int i = 1; i <= n; i++)
    {
        d.resize(5e3 + 10, 0);

        for(int j = 0; j < 32; j++)
        {
            for(int k = 0; j + k < 5e3 + 10; j++)
            {
                d[j + k] = (d[j + k] + (last[k] * cnt[i][j]) % MOD) % MOD;
            }
        }

        for(int j = 0; j < 5e3 + 10; j++)
        {
            last[j] = d[j];
            ans = (ans + d[j] * (j * j) * (n + 1) % MOD * curcnt[i + 1]) % MOD;
        }
    }

    last.resize(2e5 + 10, 0);
    last[0] = 1;

    for(int i = 1; i <= n; i++)
    {
        d.resize(2e5 + 10, 0);
        for(int j = 0; j < 32; j++)
        {
            for(int k = 0; k + j * (n - i + 1) < 2e5 + 10; 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 < 2e5 + 10; 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 1 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 1 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 452 KB Output is correct
7 Correct 56 ms 348 KB Output is correct
8 Correct 54 ms 348 KB Output is correct

Subtask #3
0 / 6.0

# Verdict Execution time Memory Grader output
1 Runtime error 40 ms 5552 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 407 ms 472 KB Output is correct
2 Correct 324 ms 348 KB Output is correct
3 Correct 164 ms 452 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 10 ms 476 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 10 ms 476 KB Output is correct
3 Correct 9 ms 348 KB Output is correct
4 Correct 1944 ms 600 KB Output is correct
5 Correct 1936 ms 604 KB Output is correct
6 Correct 1974 ms 600 KB Output is correct
7 Correct 1937 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 1 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 452 KB Output is correct
7 Correct 56 ms 348 KB Output is correct
8 Correct 54 ms 348 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 10 ms 476 KB Output is correct
11 Correct 9 ms 348 KB Output is correct
12 Correct 1236 ms 476 KB Output is correct
13 Correct 1252 ms 476 KB Output is correct
14 Correct 1233 ms 480 KB Output is correct
15 Correct 1221 ms 344 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 1 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 452 KB Output is correct
7 Correct 56 ms 348 KB Output is correct
8 Correct 54 ms 348 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 10 ms 476 KB Output is correct
11 Correct 9 ms 348 KB Output is correct
12 Correct 1944 ms 600 KB Output is correct
13 Correct 1936 ms 604 KB Output is correct
14 Correct 1974 ms 600 KB Output is correct
15 Correct 1937 ms 604 KB Output is correct
16 Correct 1236 ms 476 KB Output is correct
17 Correct 1252 ms 476 KB Output is correct
18 Correct 1233 ms 480 KB Output is correct
19 Correct 1221 ms 344 KB Output is correct
20 Runtime error 22 ms 6604 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 1 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 452 KB Output is correct
7 Correct 56 ms 348 KB Output is correct
8 Correct 54 ms 348 KB Output is correct
9 Runtime error 40 ms 5552 KB Execution killed with signal 11
10 Halted 0 ms 0 KB -