oj.uz

Submission #993135

# Submission time Handle Problem Language Result Execution time Memory
993135 2024-06-05T10:55:17 Z NValchanov Intergalactic ship (IZhO19_xorsum) C++17
45 / 100
 2000 ms 3532 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) < 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(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 0 ms 344 KB Output is correct
2 Correct 1 ms 344 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 344 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 55 ms 344 KB Output is correct
7 Correct 63 ms 348 KB Output is correct
8 Correct 53 ms 348 KB Output is correct

Subtask #3
0 / 6.0

# Verdict Execution time Memory Grader output
1 Execution timed out 2028 ms 3532 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #4
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 381 ms 348 KB Output is correct
2 Correct 343 ms 348 KB Output is correct
3 Correct 187 ms 344 KB Output is correct
4 Correct 126 ms 456 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 348 KB Output is correct
3 Correct 9 ms 480 KB Output is correct

Subtask #6
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 348 KB Output is correct
2 Correct 9 ms 348 KB Output is correct
3 Correct 9 ms 480 KB Output is correct
4 Correct 1941 ms 604 KB Output is correct
5 Execution timed out 2041 ms 604 KB Time limit exceeded
6 Halted 0 ms 0 KB -

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 344 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 55 ms 344 KB Output is correct
7 Correct 63 ms 348 KB Output is correct
8 Correct 53 ms 348 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 348 KB Output is correct
11 Correct 9 ms 480 KB Output is correct
12 Correct 1260 ms 480 KB Output is correct
13 Correct 1261 ms 344 KB Output is correct
14 Correct 1252 ms 480 KB Output is correct
15 Correct 1272 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 1 ms 344 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 55 ms 344 KB Output is correct
7 Correct 63 ms 348 KB Output is correct
8 Correct 53 ms 348 KB Output is correct
9 Correct 9 ms 348 KB Output is correct
10 Correct 9 ms 348 KB Output is correct
11 Correct 9 ms 480 KB Output is correct
12 Correct 1941 ms 604 KB Output is correct
13 Execution timed out 2041 ms 604 KB Time limit exceeded
14 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 344 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 55 ms 344 KB Output is correct
7 Correct 63 ms 348 KB Output is correct
8 Correct 53 ms 348 KB Output is correct
9 Execution timed out 2028 ms 3532 KB Time limit exceeded
10 Halted 0 ms 0 KB -