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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#114835#6194. Knapsack Problemstd_abs#WA 362ms3484kbC++205.0kb2023-06-23 17:58:122023-06-23 17:58:14

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-06-23 17:58:14]
  • 评测
  • 测评结果:WA
  • 用时:362ms
  • 内存:3484kb
  • [2023-06-23 17:58:12]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
#define pii pair<int, int>
#define all(a) a.begin(), a.end()
#define sz(a) ((int)a.size())
const int mod = 998244353, N = 100005;

struct Simplex {
    using T = long double;
    static const int N = 16, M = 8;
    const T eps = 1e-7;
    int n, m;
    int Left[M], Down[N];
    T a[M][N], b[M], c[N], v, sol[N];
    bool eq(T a, T b) {return fabs(a - b) < eps;}
    bool ls(T a, T b) {return a < b && !eq(a, b);}
    void init(int _n, int _m) {
        n = _n, m = _m, v = 0;
        for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) {
            a[i][j] = 0;
        }
        for (int i = 0; i < m; ++i) {
            b[i] = 0;
        }
        for (int i = 0; i < n; ++i) {
            c[i] = sol[i] = 0;
        }
    }
    void pivot(int x, int y) {
        swap(Left[x], Down[y]);
        T k = a[x][y]; a[x][y] = 1;
        vector <int> nz;
        for (int i = 0; i < n; ++i) {
            a[x][i] /= k;
            if (!eq(a[x][i], 0)) {
                nz.pb(i);
            }
        }
        b[x] /= k;
        for (int i = 0; i < m; ++i) {
            if (i == x || eq(a[i][y], 0)) {
                continue;
            }
            k = a[i][y], a[i][y] = 0;
            b[i] -= k * b[x];
            for (int j : nz) {
                a[i][j] -= k * a[x][j];
            }
        }
        if (eq(c[y], 0)) {
            return;
        }
        k = c[y], c[y] = 0, v += k * b[x];
        for (int i : nz) {
            c[i] -= k * a[x][i];
        }
    }
    int solve() {
        for (int i = 0; i < n; ++i) {
            Down[i] = i; 
        }
        for (int i = 0; i < m; ++i) {
            Left[i] = n + i;
        }
        while (1) {
            int x = -1, y = -1;
            for (int i = 0; i < m; ++i) if (ls(b[i], 0) && (x == -1 || b[i] < b[x])) {
                x = i;
            }
            if (x == -1) {
                break;
            }
            for (int i = 0; i < n; ++i) if (ls(a[x][i], 0) && (y == -1 || a[x][i] < a[x][y])) {
                y = i;
            }
            if (y == -1) return 1;
            pivot(x, y);
        }
        while (1) {
            int x = -1, y = -1;
            for (int i = 0; i < n; ++i) if (ls(0, c[i]) && (y == -1 || c[i] > c[y])) {
                y = i;
            }
            if (y == -1) {
                break;
            }
            for (int i = 0; i < m; ++i) if (ls(0, a[i][y]) && (x == -1 || b[i] / a[i][y] < b[x] / a[x][y])) {
                x = i;
            }
            if (x == -1) {
                return 2;
            }
            pivot(x, y);
        }
        for (int i = 0; i < m; ++i) {
            if (Left[i] < n) {
                sol[Left[i]] = b[i];
            }
        }
        return 0;
    }
} solver;

int main() {
    ios::sync_with_stdio(false), cin.tie(0);
    int t;
    cin >> t;
    while (t--) {
        int k;
        cin >> k;
        int n = (1 << k) - 1;
        solver.init(n, k * 2);
        vector <int> c(n);
        for (int i = 0; i < n; ++i) {
            cin >> c[i];
            solver.c[i] = c[i]; 
        }
        vector <int> a(k);
        for (int i = 0; i < k; ++i) {
            cin >> a[i];
            for (int j = 0; j < n; ++j) {
                solver.a[i * 2][j] = ((j + 1) >> i & 1 ? 1 : 0);
                solver.a[i * 2 + 1][j] = ((j + 1) >> i & 1 ? -1 : 0);
                solver.b[i * 2] = a[i];
                solver.b[i * 2 + 1] = a[i];
            }
        }
        int x = solver.solve();
        assert(x == 0);
        vector <ll> res(n);
        for (int i = 0; i < n; ++i) {
            res[i] = solver.sol[i];
        }
        ll best = 0;
        for (int msk = 0; msk < 1 << n; ++msk) {
            ll ans = 0;
            vector <ll> sum(k);
            for (int i = 0; i < n; ++i) for (int j = 0; j < k; ++j) if ((i + 1) >> j & 1) {
                sum[j] += res[i] + (msk >> i & 1);
            }
            for (int i = 0; i < n; ++i) {
                ans += (res[i] + (msk >> i & 1)) * c[i];
            }
            bool ok = true;
            for (int i = 0; i < k; ++i) {
                ok &= sum[i] == a[i];
            }
            if (ok) {
                best = max(best, ans);
            }
        }
        for (int msk = 0; msk < 1 << n; ++msk) {
            ll ans = 0;
            vector <ll> sum(k);
            for (int i = 0; i < n; ++i) for (int j = 0; j < k; ++j) if ((i + 1) >> j & 1) {
                sum[j] += res[i] - (msk >> i & 1);
            }
            for (int i = 0; i < n; ++i) {
                ans += (res[i] - (msk >> i & 1)) * c[i];
            }
            bool ok = true;
            for (int i = 0; i < k; ++i) {
                ok &= sum[i] == a[i];
            }
            if (ok) {
                best = max(best, ans);
            }
        }
        cout << best << '\n';
    }
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 5ms
memory: 3456kb

input:

3
2
1 2 4
4 5
3
3226252 19270256 2430652 1187613 12496062 10286165 17494834
24 85 34
4
901133 6693218 13245489 14740234 16186210 11382783 19277321 3855635 16523184 10168517 16195031 971041 10303441 8395899 11618555
529321239 218214127 92942310 207467810

output:

18
1949753378
7832404777567179

result:

ok 3 number(s): "18 1949753378 7832404777567179"

Test #2:

score: 0
Accepted
time: 358ms
memory: 3480kb

input:

100
4
4488409 9842893 14331290 11289097 15777479 21131954 25620334 6146092 10634508 15988956 20477387 17435190 21923584 27278027 31766493
200477197 258791439 590664017 982949628
4
5484152 19851747 25335961 6555937 12039831 26407861 31891996 10897184 16381166 30749333 36233145 17453055 22937114 37304...

output:

16156444320083421
24565535429631234
29418802996321901
30685727712782520
21026118053726857
27272339796311010
28831028447377015
34577176834491128
9058894962996375
21525085254465501
6657186892229297
16750628911275484
11217846865301187
12674726744043780
33873234230125448
3890237279573366
319038768614465...

result:

ok 100 numbers

Test #3:

score: 0
Accepted
time: 359ms
memory: 3464kb

input:

100
4
11618334 18295966 29914477 5116382 16734869 23412289 35030567 15002473 26620994 33298395 44916782 20118655 31737127 38414456 50032872
52573649 733715025 105771527 204824011
4
2142433 13679527 15822005 7304783 9447231 20984363 23126840 6271380 8413827 19950941 22093291 13576168 15718643 2725577...

output:

17648887427676796
21625331519839488
5123483163674640
20332898488476516
10882410276737710
25799406290369942
9021794681785918
14079661025657823
19651479225495798
19108340996997031
7502197529195960
14859286025000990
26534486448012504
21196964793845212
17222108748663918
19112873745810973
150116234459639...

result:

ok 100 numbers

Test #4:

score: -100
Wrong Answer
time: 362ms
memory: 3484kb

input:

100
4
19912840 5584811 25497404 10173442 30086113 15758284 35670730 10055784 29968204 15640365 35553036 20228929 40141706 25813818 45726645
199637398 648830099 620879036 721665690
4
7571016 7507237 15078004 19283701 26854580 26790914 34361725 2809630 10380467 10316661 17887650 22093187 29664080 2960...

output:

21172351446279597
12216316207781859
31685774482329793
36066732654517313
19340822375673782
17094361082328640
19075803268324489
23946411427126244
15750520513128720
10839993372177143
28038252774564427
12098359408203383
16661717061725678
16141878677697603
10422881545500853
23195259150880456
161145733965...

result:

wrong answer 98th numbers differ - expected: '24656983842107825', found: '24656983842107818'