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Submission #993125

# Submission time Handle Problem Language Result Execution time Memory
993125 2024-06-05T10:39:54 Z NValchanov Intergalactic ship (IZhO19_xorsum) C++17
56 / 100
 1978 ms 7112 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(3e3 + 10, 0);
    last[0] = 1;
    ll ans = 0;

    for(int i = 1; i <= n; i++)
    {
        d.resize(3e3 + 10, 0);

        for(int j = 0; j < 32; j++)
        {
            for(int k = 0; j + k < 3e3 + 10; j++)
            {
                d[j + k] = (d[j + k] + (last[k] * cnt[i][j]) % MOD) % MOD;
            }
        }

        for(int j = 0; j < 3e3 + 10; j++)
        {
            last[j] = d[j];
            ans = (ans + d[j] * (j * j) * (n + 1) % MOD * curcnt[i + 1]) % MOD;
        }
    }

    last.resize(1e5 + 5e4 + 10, 0);
    last[0] = 1;

    for(int i = 1; i <= n; i++)
    {
        d.resize(1e5 + 5e4 + 10, 0);
        for(int j = 0; j < 32; j++)
        {
            for(int k = 0; k + j * (n - i + 1) < 1e5 + 5e4 + 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 < 1e5 + 5e4 + 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 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 344 KB Output is correct

Subtask #2
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 344 KB Output is correct
6 Correct 53 ms 348 KB Output is correct
7 Correct 53 ms 344 KB Output is correct
8 Correct 57 ms 348 KB Output is correct

Subtask #3
0 / 6.0

# Verdict Execution time Memory Grader output
1 Runtime error 40 ms 5568 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 383 ms 348 KB Output is correct
2 Correct 330 ms 348 KB Output is correct
3 Correct 174 ms 344 KB Output is correct
4 Correct 126 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 476 KB Output is correct
3 Correct 11 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 476 KB Output is correct
3 Correct 11 ms 348 KB Output is correct
4 Correct 1927 ms 600 KB Output is correct
5 Correct 1921 ms 612 KB Output is correct
6 Correct 1978 ms 616 KB Output is correct
7 Correct 1959 ms 600 KB Output is correct

Subtask #7
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 344 KB Output is correct
6 Correct 53 ms 348 KB Output is correct
7 Correct 53 ms 344 KB Output is correct
8 Correct 57 ms 348 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 476 KB Output is correct
11 Correct 11 ms 348 KB Output is correct
12 Correct 1255 ms 476 KB Output is correct
13 Correct 1237 ms 596 KB Output is correct
14 Correct 1262 ms 344 KB Output is correct
15 Correct 1227 ms 348 KB Output is correct

Subtask #8
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 344 KB Output is correct
6 Correct 53 ms 348 KB Output is correct
7 Correct 53 ms 344 KB Output is correct
8 Correct 57 ms 348 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 476 KB Output is correct
11 Correct 11 ms 348 KB Output is correct
12 Correct 1927 ms 600 KB Output is correct
13 Correct 1921 ms 612 KB Output is correct
14 Correct 1978 ms 616 KB Output is correct
15 Correct 1959 ms 600 KB Output is correct
16 Correct 1255 ms 476 KB Output is correct
17 Correct 1237 ms 596 KB Output is correct
18 Correct 1262 ms 344 KB Output is correct
19 Correct 1227 ms 348 KB Output is correct
20 Runtime error 16 ms 7112 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 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 344 KB Output is correct
6 Correct 53 ms 348 KB Output is correct
7 Correct 53 ms 344 KB Output is correct
8 Correct 57 ms 348 KB Output is correct
9 Runtime error 40 ms 5568 KB Execution killed with signal 11
10 Halted 0 ms 0 KB -