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Submission #1086442

# Submission time Handle Problem Language Result Execution time Memory
1086442 2024-09-10T16:20:38 Z Thalleous One-Way Streets (CEOI17_oneway) C++17
100 / 100
 133 ms 48332 KB 
#include <bits/stdc++.h>

using namespace std;
#define maxN 1000000
typedef long long ll;
const int N = 100000;
const int M = 100000;
const int P = 100000;
const int K = 18;

ll n, m, q;
vector<pair<ll, ll>> adj[N];  // Original adjacency list
ll edge[M][2];                 // Edge information
ll path[P][3];                 // Path queries

ll bridge[M];                  // Tracks bridge edges
ll comp[N];                    // Component array
char label[M + 1];              // Labels for edges ('B', 'L', 'R')
vector<pair<ll, ll>> adjc[N];  // Compressed adjacency list

ll t = 0;
ll lo[N], ind[N];              // Tarjan's algorithm data
ll v[N];                       // Visited array for component finding
ll depth[N];                   // Depth for DFS
ll parent[N][2];               // Parent and edge index
ll p[N][K];                    // LCA sparse table
ll direction[N];               // Edge direction array
bool ok = true;                 // To check if the solution is valid

void tarjan(ll x, ll par = -1) {
    ind[x] = lo[x] = t++;
    for (auto& yi : adj[x]) {
        ll y = yi.first, i = yi.second;
        if (i == par) continue;
        if (ind[y] == -1) {
            tarjan(y, i); lo[x] = min(lo[x], lo[y]);
            if (lo[y] > ind[x]) bridge[i] = 1;  // It's a bridge
        } else lo[x] = min(lo[x], ind[y]);
    }
}

void components(ll x, ll c) {
    v[x] = 1; comp[x] = c;
    for (auto& yi : adj[x]) {
        ll y = yi.first, i = yi.second;
        if (!v[y] && !bridge[i]) components(y, c);
    }
}

void dfs(ll x, ll d = 0, ll par = -1, ll pari = -1) {
    depth[x] = d; parent[x][0] = par; parent[x][1] = pari;
    for (auto& yi : adjc[x]) {
        int y = yi.first, i = yi.second;
        if (y != par) dfs(y, d + 1, x, i);
    }
}

void LCA_init(ll c) {
    fill(&p[0][0], &p[0][0]+N*K, -1);
    for (int i = 0; i < c; i++)
        p[i][0] = parent[i][0];
    for (int k = 1; k < K; k++)
        for (int i = 0; i < c; i++)
            if (p[i][k - 1] != -1)
                p[i][k] = p[p[i][k - 1]][k - 1];
}

ll LCA_query(ll a, ll b) {
    if (depth[a] < depth[b]) swap(a, b);
    for (int k = K - 1; k >= 0; k--)
        if (depth[a] - (1 << k) >= depth[b])
            a = p[a][k];
    if (a == b) return a;
    for (int k = K - 1; k >= 0; k--)
        if (p[a][k] != p[b][k]) 
            a = p[a][k], b = p[b][k];
    return parent[a][0];
}

void direct(ll x, ll z, ll dir) {
    if (x == z) return;
    if (direction[x] == 0) {
        direction[x] = dir;
        ll y = parent[x][0], i = parent[x][1];
        ll a = comp[edge[i][0]], b = comp[edge[i][1]];
        if (dir == -1)
            label[i] = (a == x && b == y) ? 'R' : 'L';
        else
            label[i] = (a == y && b == x) ? 'R' : 'L';
        direct(y, z, dir);
    } else {
        if (direction[x] != dir) ok = false;
    }
}

void ReadData() {
    cin>>n>>m;
    for (int i = 0; i < m; i++) {
        ll a, b; cin>>a>>b; a--; b--;
        edge[i][0] = a; edge[i][1] = b;
        adj[a].push_back({b, i});
        adj[b].push_back({a, i});
    }
    fill(ind, ind + n, -1);
    for (int i = 0; i < n; i++)
        if (ind[i] == -1) tarjan(i);
    ll c = 0; fill(comp, comp + n, -1); fill(v, v + n, 0);
    for (int i = 0; i < n; i++)
        if (!v[i]) components(i, c++);
    for (int i = 0; i < m; i++) {
        if (bridge[i]) {
            ll ca = comp[edge[i][0]], cb = comp[edge[i][1]];
            adjc[ca].push_back({cb, i});
            adjc[cb].push_back({ca, i});
        }
    }
    fill(depth, depth + n, -1);
    for (int i = 0; i < n; i++)
        if (depth[i] == -1) dfs(i);
    LCA_init(c); fill(label, label + m, 'B');
    label[m] = '\0'; cin>>q;
    vector<pair<int, int>> ord;
    for (int i = 0; i < q; i++) {
        ll a, b; cin>>a>>b; a--; b--;
        path[i][0] = comp[a]; path[i][1] = comp[b];
        path[i][2] = LCA_query(comp[a], comp[b]);
        ord.push_back({depth[path[i][2]], i});
    }
    sort(ord.begin(), ord.end()); fill(direction, direction + n, 0);
    for (auto& di : ord) {
        ll i = di.second, a = path[i][0];
        ll b = path[i][1], l = path[i][2];
        direct(a, l, -1); direct(b, l, 1);
    }
    cout<<label<<endl;
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    ReadData(); return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 19288 KB Output is correct
2 Correct 8 ms 19248 KB Output is correct
3 Correct 8 ms 19292 KB Output is correct
4 Correct 8 ms 19300 KB Output is correct
5 Correct 9 ms 19548 KB Output is correct
6 Correct 8 ms 19376 KB Output is correct
7 Correct 8 ms 19292 KB Output is correct
8 Correct 8 ms 19292 KB Output is correct
9 Correct 8 ms 19288 KB Output is correct
10 Correct 9 ms 19292 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 19288 KB Output is correct
2 Correct 8 ms 19248 KB Output is correct
3 Correct 8 ms 19292 KB Output is correct
4 Correct 8 ms 19300 KB Output is correct
5 Correct 9 ms 19548 KB Output is correct
6 Correct 8 ms 19376 KB Output is correct
7 Correct 8 ms 19292 KB Output is correct
8 Correct 8 ms 19292 KB Output is correct
9 Correct 8 ms 19288 KB Output is correct
10 Correct 9 ms 19292 KB Output is correct
11 Correct 36 ms 29268 KB Output is correct
12 Correct 37 ms 31488 KB Output is correct
13 Correct 42 ms 33676 KB Output is correct
14 Correct 53 ms 36048 KB Output is correct
15 Correct 52 ms 37064 KB Output is correct
16 Correct 73 ms 39452 KB Output is correct
17 Correct 61 ms 40784 KB Output is correct
18 Correct 79 ms 39244 KB Output is correct
19 Correct 66 ms 41932 KB Output is correct
20 Correct 34 ms 31316 KB Output is correct
21 Correct 34 ms 31604 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 19288 KB Output is correct
2 Correct 8 ms 19248 KB Output is correct
3 Correct 8 ms 19292 KB Output is correct
4 Correct 8 ms 19300 KB Output is correct
5 Correct 9 ms 19548 KB Output is correct
6 Correct 8 ms 19376 KB Output is correct
7 Correct 8 ms 19292 KB Output is correct
8 Correct 8 ms 19292 KB Output is correct
9 Correct 8 ms 19288 KB Output is correct
10 Correct 9 ms 19292 KB Output is correct
11 Correct 36 ms 29268 KB Output is correct
12 Correct 37 ms 31488 KB Output is correct
13 Correct 42 ms 33676 KB Output is correct
14 Correct 53 ms 36048 KB Output is correct
15 Correct 52 ms 37064 KB Output is correct
16 Correct 73 ms 39452 KB Output is correct
17 Correct 61 ms 40784 KB Output is correct
18 Correct 79 ms 39244 KB Output is correct
19 Correct 66 ms 41932 KB Output is correct
20 Correct 34 ms 31316 KB Output is correct
21 Correct 34 ms 31604 KB Output is correct
22 Correct 133 ms 45252 KB Output is correct
23 Correct 126 ms 43716 KB Output is correct
24 Correct 104 ms 43720 KB Output is correct
25 Correct 124 ms 48332 KB Output is correct
26 Correct 126 ms 44860 KB Output is correct
27 Correct 123 ms 43716 KB Output is correct
28 Correct 32 ms 29388 KB Output is correct
29 Correct 59 ms 35272 KB Output is correct
30 Correct 61 ms 35724 KB Output is correct
31 Correct 54 ms 35524 KB Output is correct
32 Correct 90 ms 40144 KB Output is correct