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Submission #993154

# Submission time Handle Problem Language Result Execution time Memory
993154 2024-06-05T11:07:46 Z NValchanov Intergalactic ship (IZhO19_xorsum) C++17
37 / 100
 2000 ms 5072 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(n + 1);

    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--;

        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(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;
}

Compilation message

xorsum.cpp: In function 'void solve_3()':
xorsum.cpp:253:12: warning: unused variable 'right' [-Wunused-variable]
  253 |         ll right = updates[i].right;
      |            ^~~~~

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 348 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 348 KB Output is correct
6 Correct 57 ms 592 KB Output is correct
7 Correct 53 ms 452 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 Incorrect 1043 ms 5072 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #4
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 383 ms 472 KB Output is correct
2 Correct 333 ms 348 KB Output is correct
3 Correct 161 ms 456 KB Output is correct
4 Correct 121 ms 456 KB Output is correct

Subtask #5
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 480 KB Output is correct
2 Correct 9 ms 476 KB Output is correct
3 Correct 9 ms 476 KB Output is correct

Subtask #6
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 480 KB Output is correct
2 Correct 9 ms 476 KB Output is correct
3 Correct 9 ms 476 KB Output is correct
4 Correct 1908 ms 604 KB Output is correct
5 Correct 1987 ms 600 KB Output is correct
6 Correct 1904 ms 616 KB Output is correct
7 Correct 1905 ms 600 KB Output is correct

Subtask #7
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 348 KB Output is correct
6 Correct 57 ms 592 KB Output is correct
7 Correct 53 ms 452 KB Output is correct
8 Correct 53 ms 344 KB Output is correct
9 Correct 9 ms 480 KB Output is correct
10 Correct 9 ms 476 KB Output is correct
11 Correct 9 ms 476 KB Output is correct
12 Correct 1207 ms 480 KB Output is correct
13 Execution timed out 2070 ms 348 KB Time limit exceeded
14 Halted 0 ms 0 KB -

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 348 KB Output is correct
6 Correct 57 ms 592 KB Output is correct
7 Correct 53 ms 452 KB Output is correct
8 Correct 53 ms 344 KB Output is correct
9 Correct 9 ms 480 KB Output is correct
10 Correct 9 ms 476 KB Output is correct
11 Correct 9 ms 476 KB Output is correct
12 Correct 1908 ms 604 KB Output is correct
13 Correct 1987 ms 600 KB Output is correct
14 Correct 1904 ms 616 KB Output is correct
15 Correct 1905 ms 600 KB Output is correct
16 Correct 1207 ms 480 KB Output is correct
17 Execution timed out 2070 ms 348 KB Time limit exceeded
18 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 348 KB Output is correct
6 Correct 57 ms 592 KB Output is correct
7 Correct 53 ms 452 KB Output is correct
8 Correct 53 ms 344 KB Output is correct
9 Incorrect 1043 ms 5072 KB Output isn't correct
10 Halted 0 ms 0 KB -