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Submission #550393

# Submission time Handle Problem Language Result Execution time Memory
550393 2022-04-18T03:39:04 Z Duy_e Beads and wires (APIO14_beads) C++14
100 / 100
 346 ms 45916 KB 
/*
**  TASK:
**  LINK:
*/

#include <bits/stdc++.h>
#define ll long long
#define pii pair<ll, ll>
#define st first
#define nd second
#define file "test"
using namespace std;
const long long INF = 1e18;
const long long N = 2e5 + 5;

struct edge {
    ll u, v, w;
} g[N];

vector <int> d[N];

int n;
ll dp[N][2], dp2[N][2], ans;

/*
    0: là node được nối với dây đỏ
    1: là node được thêm sau 2 node trước
*/

void dfs(int p, int u) {

    ll s0 = 0;
    vector <ll> f; f.push_back(0);
    for (int i: d[u]) {
        int v = g[i].u ^ g[i].v ^ u;
        int w = g[i].w;
        if (v == p) continue;
        dfs(u, v);
        s0 += dp[v][0];
        f.push_back(f.back() + max(dp[v][0], dp[v][1] + w));
    }

    f.push_back(f.back());

    dp[u][0] = s0;
    int pos = 1;
    for (int i: d[u]) {
        int v = g[i].u ^ g[i].v ^ u;
        int w = g[i].w;

        if (v == p) continue;

        dp[u][1] = max(dp[u][1], f[pos - 1] + f[f.size() - 1] - f[pos] + dp[v][0] + w);
        dp[u][0] = max(dp[u][0] + dp[v][1] + w - dp[v][0], dp[u][0]);
        pos ++;
    }

    // cout << u << ": " << dp[u][0] << ' ' << dp[u][1] << ' ' << d[u].size() << '\n';

    dp2[u][0] = dp[u][0];
    dp2[u][1] = dp[u][1];

}

void dfs_reroot(int p, int u) {
    vector <ll> f, lef, rig;
    f.push_back(0);

    ll s0 = 0;

    //cout << u << ": " << dp2[u][0] << ' ' << dp2[u][1] <<
    //"; " << p << ": " << dp2[p][0] << ' ' << dp2[p][1] << '\n';

    for (int i: d[u]) {
        int v = g[i].v ^ g[i].u ^ u;
        int w = g[i].w;
        s0 += dp2[v][0];
        f.push_back(f.back() + max(dp2[v][0], dp2[v][1] + w));
    }

    dp2[u][0] = s0;
    dp2[u][1] = -INF;
    f.push_back(f.back());
    lef.push_back(0);
    int pos = 1;
    for (int i: d[u]) {
        int v = g[i].v ^ g[i].u ^ u;
        int w = g[i].w;
        dp2[u][0] = max(dp2[u][0], dp2[u][0] - dp2[v][0] + dp2[v][1] + w);
        dp2[u][1] = max(dp2[u][1], f[pos - 1] + f[f.size() - 1] - f[pos] + dp2[v][0] + w);
        lef.push_back(f[pos - 1] + f[f.size() - 1] - f[pos] + dp2[v][0] + w);
        pos ++;
    }

    //cout << u << ": " << dp2[u][0] << ' ' << dp2[u][1] << '\n';

    ans = max(ans, dp2[u][0]);

    lef.push_back(0);
    rig = lef;

    for (int i = 1; i < lef.size(); i ++) lef[i] = max(lef[i - 1], lef[i]);
    for (int i = rig.size() - 2; i >= 0; i --) rig[i] = max(rig[i + 1], rig[i]);

    pos = 1;

    for (int i: d[u]) {
        int v = g[i].u ^ g[i].v ^ u;
        int w = g[i].w;

        ll tmp1 = dp2[u][1], tmp0 = dp2[u][0];

        dp2[u][0] -= max(dp[v][0], dp[v][1] + w);
        dp2[u][1] = max(lef[pos - 1], rig[pos + 1]) - max(dp2[v][0], dp2[v][1] + w);
        if (p != v) dfs_reroot(u, v);

        dp2[u][1] = tmp1; dp2[u][0] = tmp0;
        pos ++;
    }

    dp2[u][0] = dp[u][0];
    dp2[u][1] = dp[u][1];

}


int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
     //#ifndef ONLINE_JUDGE
     //    freopen(file".inp", "r", stdin); freopen(file".out", "w", stdout);
     //#endif

    cin >> n;
    for (int i = 1; i < n; i ++) {
        cin >> g[i].u >> g[i].v >> g[i].w;
        d[g[i].u].push_back(i);
        d[g[i].v].push_back(i);
    }

//    for (int i = 1; i <= n; i ++) {
//        for (int j = 0; j <= n; j ++)
//            dp[j][0] = dp[j][1] = -INF;
//        dfs(0, i);
//
//        ans = max(ans, dp[i][0]);
//        // cout << i << ' ' << dp[i][0] << '\n';
//    }

    for (int i = 0; i <= n; i ++)
        for (int j = 0; j <= 1; j ++)
            dp[i][j] = dp2[i][j] = -INF;

    dfs(0, 1);
    dfs_reroot(0, 1);
    cout << ans;

    return 0;
}
/**  /\_/\
*   (= ._.)
*   / >🍵 \>🍮

1 node chỉ có thể được nối với tối đa là 2 dây xanh và chỉ có thể có đúng 2 dây xanh liên tiếp?



2 thao tác:
+ append(w, v): gắn nút w mới vào một nút v "ĐÃ TỒN TẠI"
-> nếu fix root của 1 subtree root v thì v không thể được thêm vào sau 2 nút con được

+ insert(w, u, v): gắn nút w mới vào giữa 2 nút u, v "ĐÃ TỒN TẠI"

3 sub đầu dp n ^ 2 -> solve for each root

**/

Compilation message

beads.cpp:160:9: warning: "/*" within comment [-Wcomment]
  160 | /**  /\_/\
      |          
beads.cpp: In function 'void dfs_reroot(int, int)':
beads.cpp:102:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  102 |     for (int i = 1; i < lef.size(); i ++) lef[i] = max(lef[i - 1], lef[i]);
      |                     ~~^~~~~~~~~~~~

Subtask #1
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 3 ms 4948 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 2 ms 4948 KB Output is correct
8 Correct 2 ms 4948 KB Output is correct
9 Correct 3 ms 4948 KB Output is correct
10 Correct 3 ms 5012 KB Output is correct
11 Correct 3 ms 4948 KB Output is correct
12 Correct 2 ms 4948 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 3 ms 4948 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 2 ms 4948 KB Output is correct
8 Correct 2 ms 4948 KB Output is correct
9 Correct 3 ms 4948 KB Output is correct
10 Correct 3 ms 5012 KB Output is correct
11 Correct 3 ms 4948 KB Output is correct
12 Correct 2 ms 4948 KB Output is correct
13 Correct 3 ms 4948 KB Output is correct
14 Correct 3 ms 4948 KB Output is correct
15 Correct 3 ms 4948 KB Output is correct
16 Correct 3 ms 4948 KB Output is correct
17 Correct 3 ms 4948 KB Output is correct
18 Correct 2 ms 4948 KB Output is correct
19 Correct 3 ms 5076 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 3 ms 4948 KB Output is correct
22 Correct 2 ms 5076 KB Output is correct

Subtask #3
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 3 ms 4948 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 2 ms 4948 KB Output is correct
8 Correct 2 ms 4948 KB Output is correct
9 Correct 3 ms 4948 KB Output is correct
10 Correct 3 ms 5012 KB Output is correct
11 Correct 3 ms 4948 KB Output is correct
12 Correct 2 ms 4948 KB Output is correct
13 Correct 3 ms 4948 KB Output is correct
14 Correct 3 ms 4948 KB Output is correct
15 Correct 3 ms 4948 KB Output is correct
16 Correct 3 ms 4948 KB Output is correct
17 Correct 3 ms 4948 KB Output is correct
18 Correct 2 ms 4948 KB Output is correct
19 Correct 3 ms 5076 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 3 ms 4948 KB Output is correct
22 Correct 2 ms 5076 KB Output is correct
23 Correct 7 ms 5460 KB Output is correct
24 Correct 7 ms 5560 KB Output is correct
25 Correct 7 ms 5540 KB Output is correct
26 Correct 11 ms 6076 KB Output is correct
27 Correct 11 ms 6072 KB Output is correct
28 Correct 9 ms 6388 KB Output is correct
29 Correct 9 ms 6216 KB Output is correct
30 Correct 9 ms 6228 KB Output is correct
31 Correct 13 ms 7712 KB Output is correct

Subtask #4
43.0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 3 ms 4948 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 2 ms 4948 KB Output is correct
8 Correct 2 ms 4948 KB Output is correct
9 Correct 3 ms 4948 KB Output is correct
10 Correct 3 ms 5012 KB Output is correct
11 Correct 3 ms 4948 KB Output is correct
12 Correct 2 ms 4948 KB Output is correct
13 Correct 3 ms 4948 KB Output is correct
14 Correct 3 ms 4948 KB Output is correct
15 Correct 3 ms 4948 KB Output is correct
16 Correct 3 ms 4948 KB Output is correct
17 Correct 3 ms 4948 KB Output is correct
18 Correct 2 ms 4948 KB Output is correct
19 Correct 3 ms 5076 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 3 ms 4948 KB Output is correct
22 Correct 2 ms 5076 KB Output is correct
23 Correct 7 ms 5460 KB Output is correct
24 Correct 7 ms 5560 KB Output is correct
25 Correct 7 ms 5540 KB Output is correct
26 Correct 11 ms 6076 KB Output is correct
27 Correct 11 ms 6072 KB Output is correct
28 Correct 9 ms 6388 KB Output is correct
29 Correct 9 ms 6216 KB Output is correct
30 Correct 9 ms 6228 KB Output is correct
31 Correct 13 ms 7712 KB Output is correct
32 Correct 53 ms 10160 KB Output is correct
33 Correct 52 ms 10152 KB Output is correct
34 Correct 48 ms 10060 KB Output is correct
35 Correct 335 ms 25956 KB Output is correct
36 Correct 332 ms 25864 KB Output is correct
37 Correct 336 ms 25976 KB Output is correct
38 Correct 225 ms 31464 KB Output is correct
39 Correct 219 ms 31512 KB Output is correct
40 Correct 233 ms 30988 KB Output is correct
41 Correct 346 ms 45916 KB Output is correct