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Submission #547578

# Submission time Handle Problem Language Result Execution time Memory
547578 2022-04-11T02:56:11 Z Jomnoi Valley (BOI19_valley) C++17
100 / 100
 337 ms 29688 KB 
#include <bits/stdc++.h>
#define DEBUG 0
using namespace std;

const int MAX_N = 1e5 + 10;
const long long INF = 1e18 + 7;

int A[MAX_N], B[MAX_N], W[MAX_N];
vector <pair <int, int>> graph[MAX_N];
long long dist[MAX_N];

// Heavy Light Decomposition
int timer;
int sz[MAX_N], depth[MAX_N], parent[MAX_N][20];
int head[MAX_N], st[MAX_N], pos[MAX_N];

// Segment Tree
long long tree[4 * MAX_N];

int get_size(const int &u, const int &p) {
    sz[u] = 1;
    for(int i = 1; i < 20; i++) {
        parent[u][i] = parent[parent[u][i - 1]][i - 1];
    }
    for(auto [v, w] : graph[u]) {
        if(v == p) {
            continue;
        }

        depth[v] = depth[u] + 1;
        parent[v][0] = u;
        dist[v] = dist[u] + w;
        sz[u] += get_size(v, u);
    }
    return sz[u];
}

void build_hld(const int &u, const int &p, const int &t) {
    timer++;
    head[u] = t;
    st[u] = timer;
    pos[timer] = u;

    int max_size = 0, biggest = -1;
    for(auto [v, w] : graph[u]) {
        if(v != p and max_size < sz[v]) {
            max_size = sz[v];
            biggest = v;
        }
    }

    if(biggest != -1) {
        build_hld(biggest, u, t);
    }
    for(auto [v, w] : graph[u]) {
        if(v != p and v != biggest) {
            build_hld(v, u, v);
        }
    }
}

int find_lca(const int &a, const int &b) {
    int u = a, v = b;
    if(depth[u] < depth[v]) {
        swap(u, v);
    }
    for(int i = 19; i >= 0; i--) {
        if(depth[parent[u][i]] >= depth[v]) {
            u = parent[u][i];
        }
    }
    for(int i = 19; i >= 0; i--) {
        if(parent[u][i] != parent[v][i]) {
            u = parent[u][i];
            v = parent[v][i];
        }
    }
    return (u == v ? u : parent[u][0]);
}

void build_seg(const int &idx, const int &l, const int &r) {
    tree[idx] = INF;
    if(l == r) {
        return;
    }

    int mid = (l + r) / 2;
    build_seg(idx * 2, l, mid);
    build_seg(idx * 2 + 1, mid + 1, r);
}

void update(const int &idx, const int &l, const int &r, const int &ql, const int &qr, const long long &v) {
    if(r < ql or qr < l) {
        return;
    }
    if(ql <= l and r <= qr) {
        tree[idx] = min(tree[idx], v);
        return;
    }

    int mid = (l + r) / 2;
    update(idx * 2, l, mid, ql, qr, v);
    update(idx * 2 + 1, mid + 1, r, ql, qr, v);
}

void construct(const int &idx, const int &l, const int &r) {
    if(l == r) {
        if(tree[idx] != INF) {
            tree[idx] -= 2 * dist[pos[l]];
        }
        return;
    }

    tree[idx * 2] = min(tree[idx * 2], tree[idx]);
    tree[idx * 2 + 1] = min(tree[idx * 2 + 1], tree[idx]);

    int mid = (l + r) / 2;
    construct(idx * 2, l, mid);
    construct(idx * 2 + 1, mid + 1, r);
    tree[idx] = min(tree[idx * 2], tree[idx * 2 + 1]);
}

long long query(int idx, int l, int r, int ql, int qr) {
    if(r < ql or qr < l) {
        return INF;
    }
    if(ql <= l and r <= qr) {
        return tree[idx];
    }

    int mid = (l + r) / 2;
    return min(query(idx * 2, l, mid, ql, qr), query(idx * 2 + 1, mid + 1, r, ql, qr));
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    int N, S, Q, E;
    cin >> N >> S >> Q >> E;
    for(int i = 1; i <= N - 1; i++) {
        cin >> A[i] >> B[i] >> W[i];
        graph[A[i]].emplace_back(B[i], W[i]);
        graph[B[i]].emplace_back(A[i], W[i]);
    }

    depth[0] = -1;
    get_size(E, -1);
    build_hld(E, -1, E);
    build_seg(1, 1, N);

    for(int i = 1; i <= S; i++) {
        int C;
        cin >> C;

        int u = C;
        while(true) {
            if(head[E] == head[u]) {
                update(1, 1, N, st[E], st[u], dist[C]);
                break;
            }

            update(1, 1, N, st[head[u]], st[u], dist[C]);
            u = parent[head[u]][0];
        }
    }

    construct(1, 1, N);

    for(int i = 1; i <= N - 1; i++) {
        if(depth[A[i]] > depth[B[i]]) {
            swap(A[i], B[i]);
        }
    }

    for(int i = 1; i <= Q; i++) {
        int I, R;
        cin >> I >> R;

        int lca = find_lca(B[I], R);
        if(lca != B[I]) {
            cout << "escaped\n";
            continue;
        }

        int u = R;
        long long res = INF;
        while(true) {
            if(head[lca] == head[u]) {
                res = min(res, query(1, 1, N, st[lca], st[u]));
                break;
            }

            res = min(res, query(1, 1, N, st[head[u]], st[u]));
            u = parent[head[u]][0];
        }

        if(res != INF) {
            cout << res + dist[R] << '\n';
        }
        else {
            cout << "oo\n";
        }
    }
    return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 2820 KB Output is correct
2 Correct 6 ms 2824 KB Output is correct
3 Correct 6 ms 2828 KB Output is correct
4 Correct 6 ms 2772 KB Output is correct

Subtask #2
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 2820 KB Output is correct
2 Correct 6 ms 2824 KB Output is correct
3 Correct 6 ms 2828 KB Output is correct
4 Correct 6 ms 2772 KB Output is correct
5 Correct 3 ms 2824 KB Output is correct
6 Correct 3 ms 2900 KB Output is correct
7 Correct 3 ms 2952 KB Output is correct
8 Correct 3 ms 2900 KB Output is correct
9 Correct 3 ms 2900 KB Output is correct
10 Correct 3 ms 2900 KB Output is correct
11 Correct 3 ms 2832 KB Output is correct
12 Correct 4 ms 2900 KB Output is correct
13 Correct 3 ms 2900 KB Output is correct
14 Correct 4 ms 2852 KB Output is correct

Subtask #3
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 277 ms 20932 KB Output is correct
2 Correct 337 ms 24532 KB Output is correct
3 Correct 333 ms 24580 KB Output is correct
4 Correct 320 ms 26596 KB Output is correct
5 Correct 309 ms 26660 KB Output is correct
6 Correct 301 ms 28964 KB Output is correct

Subtask #4
41.0 / 41.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 2820 KB Output is correct
2 Correct 6 ms 2824 KB Output is correct
3 Correct 6 ms 2828 KB Output is correct
4 Correct 6 ms 2772 KB Output is correct
5 Correct 3 ms 2824 KB Output is correct
6 Correct 3 ms 2900 KB Output is correct
7 Correct 3 ms 2952 KB Output is correct
8 Correct 3 ms 2900 KB Output is correct
9 Correct 3 ms 2900 KB Output is correct
10 Correct 3 ms 2900 KB Output is correct
11 Correct 3 ms 2832 KB Output is correct
12 Correct 4 ms 2900 KB Output is correct
13 Correct 3 ms 2900 KB Output is correct
14 Correct 4 ms 2852 KB Output is correct
15 Correct 277 ms 20932 KB Output is correct
16 Correct 337 ms 24532 KB Output is correct
17 Correct 333 ms 24580 KB Output is correct
18 Correct 320 ms 26596 KB Output is correct
19 Correct 309 ms 26660 KB Output is correct
20 Correct 301 ms 28964 KB Output is correct
21 Correct 159 ms 24376 KB Output is correct
22 Correct 172 ms 24012 KB Output is correct
23 Correct 192 ms 24012 KB Output is correct
24 Correct 225 ms 26572 KB Output is correct
25 Correct 224 ms 29688 KB Output is correct
26 Correct 161 ms 24244 KB Output is correct
27 Correct 172 ms 23936 KB Output is correct
28 Correct 195 ms 24016 KB Output is correct
29 Correct 234 ms 25508 KB Output is correct
30 Correct 247 ms 27192 KB Output is correct
31 Correct 181 ms 24352 KB Output is correct
32 Correct 214 ms 24112 KB Output is correct
33 Correct 207 ms 24044 KB Output is correct
34 Correct 254 ms 26304 KB Output is correct
35 Correct 230 ms 29644 KB Output is correct
36 Correct 281 ms 26348 KB Output is correct