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Submission #1092544

# Submission time Handle Problem Language Result Execution time Memory
1092544 2024-09-24T10:48:53 Z onbert Mergers (JOI19_mergers) C++17
100 / 100
 938 ms 234324 KB 
#include <bits/stdc++.h>
using namespace std;
#define int long long
const int maxn = 5e5 + 5, maxk = 5e5+5, lg = 20;
int n, k;
vector<int> ADJ[maxn];
int A[maxn];

int SZ[maxn], FA[maxn], newid[maxn], lim[maxn], cnt = 0;
bool cmp(int x, int y) {
    return SZ[x] > SZ[y];
}
void DFS0(int u) {
    SZ[u] = 1;
    for (int v:ADJ[u]) {
        FA[v] = u;
        ADJ[v].erase(find(ADJ[v].begin(), ADJ[v].end(), u));
        DFS0(v);
        SZ[u] += SZ[v];
    }
    sort(ADJ[u].begin(), ADJ[u].end(), cmp);
}
void DFS1(int u) {
    cnt++;
    newid[u] = cnt;
    for (int v:ADJ[u]) DFS1(v);
    lim[newid[u]] = cnt;
}

vector<int> adj[maxn];
int fa[maxn], sz[maxn];
vector<int> mem[maxk];
int a[maxn];

int st[maxn][lg];
void dfs0(int u) {
    for (int i=1;i<lg;i++) {
        if (!st[u][i-1] || !st[st[u][i-1]][i-1]) break;
        st[u][i] = st[st[u][i-1]][i-1];
    }
    for (int v:adj[u]) {
        st[v][0] = u;
        dfs0(v);
    }
}

int psum[maxn];
int lca(int u, int c) {
    int l = mem[c][0], r = mem[c].back();
    for (int i=lg-1;i>=0;i--) if (st[u][i]) {
        int v = st[u][i];
        if (!(v<=l && r<=lim[v])) u = v;
    }
    // cout << c << " " << l << " " << r << endl;
    if (!(u<=l && r<=lim[u])) u = fa[u];
    return u;
}

bool sep[maxn];
bool sepleaf[maxn];

int sum[maxn];
int dead = 0, ans = 0;
bool frst = false;

void dfs1(int u, int minus) {
    // cout << u << " " << minus << endl;
    if (minus==0 && sep[u]) frst = true;
    if (sum[lim[u]] - sum[u-1] - minus == 1 && sep[u]) dead++;
    if (adj[u].size()==0) return;
    vector<pair<int,int>> vec;
    for (int v:adj[u]) {
        vec.push_back({sum[lim[v]] - sum[v-1], v});
    }
    sort(vec.begin(), vec.end());
    int l = 0, r = 1e18;
    while (l<r) {
        int mid = (l+r)/2, used = 0;
        for (auto [x, y]:vec) used += max(x - mid, (int)0);
        if (used <= minus) r = mid;
        else l = mid+1;
    }
    for (auto &[x, y]:vec) x = min(x, l);
    int total = sum[lim[u]] - sum[u] - minus;
    if (vec[0].first <= (total+1)/2) {
        ans += (total+1)/2;
        return;
    }
    int rest = total - vec[0].first;
    vec[0].first -= rest;
    int v = vec[0].second;
    ans += rest;
    dfs1(v, sum[lim[v]] - sum[v-1] - vec[0].first);
}


signed main() {
    ios::sync_with_stdio(0); cin.tie(0);
    cin >> n >> k;
    for (int i=1;i<=n-1;i++) {
        int u, v;
        cin >> u >> v;
        ADJ[u].push_back(v), ADJ[v].push_back(u);
    }
    for (int i=1;i<=n;i++) cin >> A[i];
    DFS0(1);
    DFS1(1);
    // for (int i=1;i<=n;i++) cout << newid[i] << " "; cout << endl;
    // for (int i=1;i<=n;i++) cout << lim[i] << " "; cout << endl;
    for (int i=1;i<=n;i++) {
        for (int j:ADJ[i]) adj[newid[i]].push_back(newid[j]);
        if (i!=1) fa[newid[i]] = newid[FA[i]];
        else fa[i] = 0;
        sz[newid[i]] = SZ[i];
    }
    for (int i=1;i<=n;i++) {
        a[newid[i]] = A[i];
        mem[A[i]].push_back(newid[i]);
    }
    dfs0(1);
    for (int i=1;i<=k;i++) {
        sort(mem[i].begin(), mem[i].end());
        psum[lca(mem[i][0], i)] += mem[i].size();
    }
    for (int i=1;i<=n;i++) psum[i] += psum[i-1];

    for (int i=2;i<=n;i++) {
        sep[i] = (psum[lim[i]] - psum[i-1] == lim[i] - i + 1);
        // cout << psum[lim[i]] - psum[i-1] << " " << lim[i] - i + 1 << endl;
    }
    // for (int i=1;i<=n;i++) cout << sep[i]; cout << endl;
    
    for (int i=1;i<=n;i++) sum[i] = sum[i-1] + sep[i];

    for (int i=1;i<=n;i++) sepleaf[i] = (sep[i] && sum[lim[i]] - sum[i-1] == 1);

    bool add = false;
    for (int i=2;i<=n;i++) if (sum[lim[i]] - sum[i-1] == sum[n] && sep[i] && !sepleaf[i]) add = true;

    int ans = 0;
    for (int i=1;i<=n;i++) ans += sepleaf[i];
    if (ans%2==1) cout << (ans+1)/2 << endl;
    else cout << ans/2 + add << endl;
    // if (sum[n]==0) {
    //     cout << 0 << endl;
    //     return 0;
    // }
    // dfs1(1, 0);
    // // assert(dead<=1);
    // cout << ans + (dead+1)/2 << endl;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35672 KB Output is correct
2 Correct 17 ms 35676 KB Output is correct
3 Correct 16 ms 35672 KB Output is correct
4 Correct 18 ms 35676 KB Output is correct
5 Correct 16 ms 35676 KB Output is correct
6 Correct 17 ms 35700 KB Output is correct
7 Correct 17 ms 35676 KB Output is correct
8 Correct 16 ms 35676 KB Output is correct
9 Correct 16 ms 35620 KB Output is correct
10 Correct 18 ms 35676 KB Output is correct
11 Correct 19 ms 35676 KB Output is correct
12 Correct 20 ms 35688 KB Output is correct
13 Correct 17 ms 35676 KB Output is correct
14 Correct 17 ms 35676 KB Output is correct
15 Correct 15 ms 35676 KB Output is correct
16 Correct 17 ms 35676 KB Output is correct
17 Correct 16 ms 35724 KB Output is correct
18 Correct 17 ms 35676 KB Output is correct
19 Correct 17 ms 35676 KB Output is correct
20 Correct 15 ms 35676 KB Output is correct
21 Correct 17 ms 35696 KB Output is correct
22 Correct 16 ms 35676 KB Output is correct
23 Correct 16 ms 35588 KB Output is correct
24 Correct 17 ms 35676 KB Output is correct

Subtask #2
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35672 KB Output is correct
2 Correct 17 ms 35676 KB Output is correct
3 Correct 16 ms 35672 KB Output is correct
4 Correct 18 ms 35676 KB Output is correct
5 Correct 16 ms 35676 KB Output is correct
6 Correct 17 ms 35700 KB Output is correct
7 Correct 17 ms 35676 KB Output is correct
8 Correct 16 ms 35676 KB Output is correct
9 Correct 16 ms 35620 KB Output is correct
10 Correct 18 ms 35676 KB Output is correct
11 Correct 19 ms 35676 KB Output is correct
12 Correct 20 ms 35688 KB Output is correct
13 Correct 17 ms 35676 KB Output is correct
14 Correct 17 ms 35676 KB Output is correct
15 Correct 15 ms 35676 KB Output is correct
16 Correct 17 ms 35676 KB Output is correct
17 Correct 16 ms 35724 KB Output is correct
18 Correct 17 ms 35676 KB Output is correct
19 Correct 17 ms 35676 KB Output is correct
20 Correct 15 ms 35676 KB Output is correct
21 Correct 17 ms 35696 KB Output is correct
22 Correct 16 ms 35676 KB Output is correct
23 Correct 16 ms 35588 KB Output is correct
24 Correct 17 ms 35676 KB Output is correct
25 Correct 17 ms 35676 KB Output is correct
26 Correct 19 ms 36560 KB Output is correct
27 Correct 18 ms 36700 KB Output is correct
28 Correct 20 ms 36700 KB Output is correct
29 Correct 18 ms 36784 KB Output is correct
30 Correct 18 ms 36700 KB Output is correct
31 Correct 16 ms 35676 KB Output is correct
32 Correct 19 ms 36956 KB Output is correct
33 Correct 16 ms 35676 KB Output is correct
34 Correct 18 ms 36700 KB Output is correct
35 Correct 19 ms 36688 KB Output is correct
36 Correct 19 ms 36696 KB Output is correct
37 Correct 19 ms 36696 KB Output is correct
38 Correct 17 ms 35676 KB Output is correct
39 Correct 19 ms 36700 KB Output is correct
40 Correct 18 ms 36696 KB Output is correct
41 Correct 17 ms 36696 KB Output is correct
42 Correct 19 ms 36696 KB Output is correct
43 Correct 24 ms 36956 KB Output is correct
44 Correct 18 ms 35928 KB Output is correct
45 Correct 18 ms 36688 KB Output is correct
46 Correct 18 ms 36696 KB Output is correct
47 Correct 17 ms 35672 KB Output is correct
48 Correct 19 ms 36696 KB Output is correct
49 Correct 21 ms 36688 KB Output is correct
50 Correct 18 ms 36696 KB Output is correct
51 Correct 18 ms 36700 KB Output is correct
52 Correct 18 ms 36696 KB Output is correct
53 Correct 19 ms 36700 KB Output is correct
54 Correct 18 ms 36700 KB Output is correct

Subtask #3
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35672 KB Output is correct
2 Correct 17 ms 35676 KB Output is correct
3 Correct 16 ms 35672 KB Output is correct
4 Correct 18 ms 35676 KB Output is correct
5 Correct 16 ms 35676 KB Output is correct
6 Correct 17 ms 35700 KB Output is correct
7 Correct 17 ms 35676 KB Output is correct
8 Correct 16 ms 35676 KB Output is correct
9 Correct 16 ms 35620 KB Output is correct
10 Correct 18 ms 35676 KB Output is correct
11 Correct 19 ms 35676 KB Output is correct
12 Correct 20 ms 35688 KB Output is correct
13 Correct 17 ms 35676 KB Output is correct
14 Correct 17 ms 35676 KB Output is correct
15 Correct 15 ms 35676 KB Output is correct
16 Correct 17 ms 35676 KB Output is correct
17 Correct 16 ms 35724 KB Output is correct
18 Correct 17 ms 35676 KB Output is correct
19 Correct 17 ms 35676 KB Output is correct
20 Correct 15 ms 35676 KB Output is correct
21 Correct 17 ms 35696 KB Output is correct
22 Correct 16 ms 35676 KB Output is correct
23 Correct 16 ms 35588 KB Output is correct
24 Correct 17 ms 35676 KB Output is correct
25 Correct 17 ms 35672 KB Output is correct
26 Correct 61 ms 66632 KB Output is correct
27 Correct 82 ms 67292 KB Output is correct
28 Correct 18 ms 36696 KB Output is correct
29 Correct 19 ms 35568 KB Output is correct
30 Correct 17 ms 35676 KB Output is correct
31 Correct 79 ms 67244 KB Output is correct
32 Correct 18 ms 36700 KB Output is correct
33 Correct 96 ms 75244 KB Output is correct
34 Correct 81 ms 67492 KB Output is correct
35 Correct 19 ms 36696 KB Output is correct
36 Correct 91 ms 68692 KB Output is correct
37 Correct 19 ms 36700 KB Output is correct
38 Correct 19 ms 36700 KB Output is correct
39 Correct 69 ms 66368 KB Output is correct
40 Correct 19 ms 36956 KB Output is correct
41 Correct 80 ms 67272 KB Output is correct
42 Correct 94 ms 70484 KB Output is correct
43 Correct 20 ms 35572 KB Output is correct
44 Correct 95 ms 75464 KB Output is correct
45 Correct 85 ms 71068 KB Output is correct
46 Correct 16 ms 36696 KB Output is correct
47 Correct 19 ms 36480 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 63 ms 66640 KB Output is correct
2 Correct 94 ms 68928 KB Output is correct
3 Correct 19 ms 36700 KB Output is correct
4 Correct 19 ms 36700 KB Output is correct
5 Correct 16 ms 35676 KB Output is correct
6 Correct 16 ms 35660 KB Output is correct
7 Correct 18 ms 36692 KB Output is correct
8 Correct 97 ms 68436 KB Output is correct
9 Correct 19 ms 36700 KB Output is correct
10 Correct 71 ms 67552 KB Output is correct
11 Correct 16 ms 35924 KB Output is correct
12 Correct 90 ms 68180 KB Output is correct
13 Correct 86 ms 68404 KB Output is correct
14 Correct 83 ms 69652 KB Output is correct
15 Correct 58 ms 66576 KB Output is correct
16 Correct 16 ms 36696 KB Output is correct
17 Correct 14 ms 35676 KB Output is correct
18 Correct 66 ms 68676 KB Output is correct
19 Correct 106 ms 74576 KB Output is correct
20 Correct 16 ms 36700 KB Output is correct
21 Correct 14 ms 35656 KB Output is correct
22 Correct 62 ms 67368 KB Output is correct
23 Correct 15 ms 36700 KB Output is correct
24 Correct 79 ms 68652 KB Output is correct
25 Correct 107 ms 72252 KB Output is correct
26 Correct 15 ms 36696 KB Output is correct
27 Correct 16 ms 36596 KB Output is correct
28 Correct 16 ms 36700 KB Output is correct
29 Correct 16 ms 36616 KB Output is correct
30 Correct 16 ms 36700 KB Output is correct

Subtask #5
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35672 KB Output is correct
2 Correct 17 ms 35676 KB Output is correct
3 Correct 16 ms 35672 KB Output is correct
4 Correct 18 ms 35676 KB Output is correct
5 Correct 16 ms 35676 KB Output is correct
6 Correct 17 ms 35700 KB Output is correct
7 Correct 17 ms 35676 KB Output is correct
8 Correct 16 ms 35676 KB Output is correct
9 Correct 16 ms 35620 KB Output is correct
10 Correct 18 ms 35676 KB Output is correct
11 Correct 19 ms 35676 KB Output is correct
12 Correct 20 ms 35688 KB Output is correct
13 Correct 17 ms 35676 KB Output is correct
14 Correct 17 ms 35676 KB Output is correct
15 Correct 15 ms 35676 KB Output is correct
16 Correct 17 ms 35676 KB Output is correct
17 Correct 16 ms 35724 KB Output is correct
18 Correct 17 ms 35676 KB Output is correct
19 Correct 17 ms 35676 KB Output is correct
20 Correct 15 ms 35676 KB Output is correct
21 Correct 17 ms 35696 KB Output is correct
22 Correct 16 ms 35676 KB Output is correct
23 Correct 16 ms 35588 KB Output is correct
24 Correct 17 ms 35676 KB Output is correct
25 Correct 17 ms 35676 KB Output is correct
26 Correct 19 ms 36560 KB Output is correct
27 Correct 18 ms 36700 KB Output is correct
28 Correct 20 ms 36700 KB Output is correct
29 Correct 18 ms 36784 KB Output is correct
30 Correct 18 ms 36700 KB Output is correct
31 Correct 16 ms 35676 KB Output is correct
32 Correct 19 ms 36956 KB Output is correct
33 Correct 16 ms 35676 KB Output is correct
34 Correct 18 ms 36700 KB Output is correct
35 Correct 19 ms 36688 KB Output is correct
36 Correct 19 ms 36696 KB Output is correct
37 Correct 19 ms 36696 KB Output is correct
38 Correct 17 ms 35676 KB Output is correct
39 Correct 19 ms 36700 KB Output is correct
40 Correct 18 ms 36696 KB Output is correct
41 Correct 17 ms 36696 KB Output is correct
42 Correct 19 ms 36696 KB Output is correct
43 Correct 24 ms 36956 KB Output is correct
44 Correct 18 ms 35928 KB Output is correct
45 Correct 18 ms 36688 KB Output is correct
46 Correct 18 ms 36696 KB Output is correct
47 Correct 17 ms 35672 KB Output is correct
48 Correct 19 ms 36696 KB Output is correct
49 Correct 21 ms 36688 KB Output is correct
50 Correct 18 ms 36696 KB Output is correct
51 Correct 18 ms 36700 KB Output is correct
52 Correct 18 ms 36696 KB Output is correct
53 Correct 19 ms 36700 KB Output is correct
54 Correct 18 ms 36700 KB Output is correct
55 Correct 17 ms 35672 KB Output is correct
56 Correct 61 ms 66632 KB Output is correct
57 Correct 82 ms 67292 KB Output is correct
58 Correct 18 ms 36696 KB Output is correct
59 Correct 19 ms 35568 KB Output is correct
60 Correct 17 ms 35676 KB Output is correct
61 Correct 79 ms 67244 KB Output is correct
62 Correct 18 ms 36700 KB Output is correct
63 Correct 96 ms 75244 KB Output is correct
64 Correct 81 ms 67492 KB Output is correct
65 Correct 19 ms 36696 KB Output is correct
66 Correct 91 ms 68692 KB Output is correct
67 Correct 19 ms 36700 KB Output is correct
68 Correct 19 ms 36700 KB Output is correct
69 Correct 69 ms 66368 KB Output is correct
70 Correct 19 ms 36956 KB Output is correct
71 Correct 80 ms 67272 KB Output is correct
72 Correct 94 ms 70484 KB Output is correct
73 Correct 20 ms 35572 KB Output is correct
74 Correct 95 ms 75464 KB Output is correct
75 Correct 85 ms 71068 KB Output is correct
76 Correct 16 ms 36696 KB Output is correct
77 Correct 19 ms 36480 KB Output is correct
78 Correct 63 ms 66640 KB Output is correct
79 Correct 94 ms 68928 KB Output is correct
80 Correct 19 ms 36700 KB Output is correct
81 Correct 19 ms 36700 KB Output is correct
82 Correct 16 ms 35676 KB Output is correct
83 Correct 16 ms 35660 KB Output is correct
84 Correct 18 ms 36692 KB Output is correct
85 Correct 97 ms 68436 KB Output is correct
86 Correct 19 ms 36700 KB Output is correct
87 Correct 71 ms 67552 KB Output is correct
88 Correct 16 ms 35924 KB Output is correct
89 Correct 90 ms 68180 KB Output is correct
90 Correct 86 ms 68404 KB Output is correct
91 Correct 83 ms 69652 KB Output is correct
92 Correct 58 ms 66576 KB Output is correct
93 Correct 16 ms 36696 KB Output is correct
94 Correct 14 ms 35676 KB Output is correct
95 Correct 66 ms 68676 KB Output is correct
96 Correct 106 ms 74576 KB Output is correct
97 Correct 16 ms 36700 KB Output is correct
98 Correct 14 ms 35656 KB Output is correct
99 Correct 62 ms 67368 KB Output is correct
100 Correct 15 ms 36700 KB Output is correct
101 Correct 79 ms 68652 KB Output is correct
102 Correct 107 ms 72252 KB Output is correct
103 Correct 15 ms 36696 KB Output is correct
104 Correct 16 ms 36596 KB Output is correct
105 Correct 16 ms 36700 KB Output is correct
106 Correct 16 ms 36616 KB Output is correct
107 Correct 16 ms 36700 KB Output is correct
108 Correct 329 ms 196092 KB Output is correct
109 Correct 611 ms 215384 KB Output is correct
110 Correct 656 ms 226788 KB Output is correct
111 Correct 938 ms 234324 KB Output is correct
112 Correct 779 ms 221012 KB Output is correct
113 Correct 404 ms 201508 KB Output is correct
114 Correct 411 ms 193644 KB Output is correct
115 Correct 452 ms 193732 KB Output is correct
116 Correct 475 ms 199104 KB Output is correct
117 Correct 596 ms 207700 KB Output is correct
118 Correct 451 ms 193784 KB Output is correct
119 Correct 591 ms 207600 KB Output is correct
120 Correct 822 ms 221520 KB Output is correct
121 Correct 616 ms 207700 KB Output is correct
122 Correct 522 ms 202064 KB Output is correct
123 Correct 379 ms 203056 KB Output is correct
124 Correct 679 ms 207800 KB Output is correct