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Submission #1089389

# Submission time Handle Problem Language Result Execution time Memory
1089389 2024-09-16T11:20:49 Z Andrei_ierdnA Homecoming (BOI18_homecoming) C++17
100 / 100
 164 ms 196440 KB 
#include "homecoming.h"
#include <iostream>

using namespace std;

using ll = long long;

const int MAXN = 2000000;
ll INF = 10000000000000000LL;

struct DpVector
{
    ll a, b;
    static const DpVector id;
};
const DpVector DpVector::id = {0, -INF};

struct DpMatrix
{
    ll a, b, c, d;
    /// f({x, y}) = {max(x+a, y+b), max(x+c, y+d)}
    /// ( a b )
    /// ( c d )
    static const DpMatrix id;
    static void mult(const DpMatrix &a, const DpMatrix &b, DpMatrix &c)
    {
        c.a = max(a.a + b.a, a.b + b.c);
        c.b = max(a.a + b.b, a.b + b.d);
        c.c = max(a.c + b.a, a.d + b.c);
        c.d = max(a.c + b.b, a.d + b.d);
    }
    static void mult(const DpMatrix &a, const DpVector &b, DpVector &c)
    {
        c.a = max(a.a + b.a, a.b + b.b);
        c.b = max(a.c + b.a, a.d + b.b);
    }
};
const DpMatrix DpMatrix::id = {0, -INF, -INF, 0};

int n, k;
int *a, *b;
ll sb[MAXN+2];
DpMatrix pref[MAXN+2], suf[MAXN+2], auxmat;
DpVector auxvec[2];

void calcSb()
{
    sb[0] = 0;
    for (int i = 0; i < k; i++) {
        sb[0] += b[i];
    }
    for (int i = 1; i < n; i++) {
        sb[i] = sb[i-1] - b[i-1] + b[(i+k-1)%n];
    }
}

void calcPrefMats()
{
    pref[0] = {0, 0, a[0]-sb[0], a[0]-b[k-1]};
    for (int i = 1; i < n; i++) {
        auxmat.c = a[i] - sb[i];
        auxmat.d = a[i] - b[(i+k-1)%n];
        DpMatrix::mult(auxmat, pref[i-1], pref[i]);
    }
}

void calcSufMats()
{
    suf[n-1] = {0, 0, a[n-1]-sb[n-1], a[n-1]-b[(n+k-2)%n]};
    for (int i = n-2; i >= 0; i--) {
        auxmat.c = a[i] - sb[i];
        auxmat.d = a[i] - b[(i+k-1)%n];
        DpMatrix::mult(suf[i+1], auxmat, suf[i]);
    }
}

long long getSimpleAns()
{
    long long ans = 0;
    for (int i = 0; i < n; i++) {
        ans = ans + a[i] - b[i];
    }
    return max(ans, 0LL);
}

long long solve(int nn, int kk, int *aa, int *bb)
{
    n = nn;
    k = kk;
    a = aa;
    b = bb;
    calcSb();
    calcPrefMats();
    calcSufMats();
    long long ans = getSimpleAns();
    DpMatrix::mult(pref[n-1], DpVector::id, auxvec[0]);
    ans = max(ans, max(auxvec[0].a, auxvec[0].b));
    for (int i = 1; i < n; i++) {
        DpMatrix::mult(suf[i], DpVector::id, auxvec[0]);
        DpMatrix::mult(pref[i-1], auxvec[0], auxvec[1]);
        ans = max(ans, max(auxvec[1].a, auxvec[1].b));
    }
    return ans;
}

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 ms 600 KB Output is correct
5 Correct 0 ms 344 KB Output is correct

Subtask #2
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 ms 600 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 1 ms 860 KB Output is correct
7 Correct 1 ms 860 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 860 KB Output is correct
10 Correct 1 ms 348 KB Output is correct

Subtask #3
31.0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 43 ms 49020 KB Output is correct
2 Correct 2 ms 860 KB Output is correct
3 Correct 164 ms 196440 KB Output is correct
4 Correct 2 ms 2136 KB Output is correct
5 Correct 7 ms 4148 KB Output is correct

Subtask #4
38.0 / 38.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 ms 600 KB Output is correct
5 Correct 0 ms 344 KB Output is correct
6 Correct 1 ms 860 KB Output is correct
7 Correct 1 ms 860 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 860 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 43 ms 49020 KB Output is correct
12 Correct 2 ms 860 KB Output is correct
13 Correct 164 ms 196440 KB Output is correct
14 Correct 2 ms 2136 KB Output is correct
15 Correct 7 ms 4148 KB Output is correct
16 Correct 163 ms 196432 KB Output is correct
17 Correct 62 ms 37948 KB Output is correct
18 Correct 103 ms 46052 KB Output is correct
19 Correct 106 ms 106016 KB Output is correct
20 Correct 139 ms 179664 KB Output is correct
21 Correct 99 ms 103436 KB Output is correct