oj.uz

Submission #563849

# Submission time Handle Problem Language Result Execution time Memory
563849 2022-05-18T07:28:43 Z piOOE Pipes (CEOI15_pipes) C++17
100 / 100
 2247 ms 9116 KB 
#include <bits/stdc++.h>

using namespace std;

#define all(x) begin(x), end(x)
#define sz(x) ((int)size(x))
#define trace(x) cout << #x << ": " << (x) << endl;

typedef long long ll;

const int N = 100000, M = 6000000;

int p[2][N];

int get(int a, int i) {
    return (p[i][a] != a ? p[i][a] = get(p[i][a], i) : a);
}

bool same(int a, int b, int i) {
    return get(a, i) == get(b, i);
}

bool mrg(int a, int b, int i) {
    a = get(a, i), b = get(b, i);
    if (a == b) return false;
    p[i][b] = a;
    return true;
}


vector<pair<int, int>> g[N];

//binary jumps with O(n) memory
//https://peltorator.ru/posts/linear_binups/

int jump[N], parent[N], depth[N], id_p[N];

int lca(int a, int b) {
    if (depth[a] < depth[b]) swap(a, b);
    while (depth[a] > depth[b]) {
        if (depth[jump[a]] >= depth[b]) {
            a = jump[a];
        } else {
            a = parent[a];
        }
    }
    while (a != b) {
        if (jump[a] != jump[b]) {
            a = jump[a];
            b = jump[b];
        } else {
            a = parent[a];
            b = parent[b];
        }
    }
    return a;
}

void add_leaf(int v, int par) {
    assert(par != -1 && par != v);
    parent[v] = par;
    depth[v] = depth[par] + 1;
    if (depth[par] - depth[jump[par]] == depth[jump[par]] - depth[jump[jump[par]]]) {
        jump[v] = jump[jump[par]];
    } else {
        jump[v] = par;
    }
}

int sz[N];
bool usedE[N];
//used edges
//d1 is just our tree, d2 is for merging in a path

void dfs(int v, int par, int id) {
    add_leaf(v, par);
    p[1][v] = v;
    id_p[v] = id;
    for (auto [to, i]: g[v]) {
        if (to != par) {
            dfs(to, v, i);
        }
    }
}

void union_path(int a, int b) {
    int c = lca(a, b);
    while (depth[a = get(a, 1)] > depth[c]) {
        usedE[id_p[a]] = true;
        mrg(parent[a], a, 1);
    }
    while (depth[b = get(b, 1)] > depth[c]) {
        usedE[id_p[b]] = true;
        mrg(parent[b], b, 1);
    }
}

void merge(int a, int b, int idx) {
    int pa = get(a, 0);
    int pb = get(b, 0);
    if (sz[pa] < sz[pb]) {
        swap(a, b);
        swap(pa, pb);
    }
    g[a].emplace_back(b, idx);
    g[b].emplace_back(a, idx);
    dfs(b, a, idx);
    mrg(pa, pb, 0);
    sz[pa] += sz[pb];
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    iota(jump, jump + N, 0);
    iota(parent, parent + N, 0);
    iota(p[0], p[0] + N, 0);
    iota(p[1], p[1] + N, 0);
    fill(sz, sz + N, 1);
    int n, m;
    cin >> n >> m;
    int idx = 0;
    for (int i = 0; i < m; ++i) {
        int a, b;
        cin >> a >> b;
        --a, --b;
        if (same(a, b, 0)) {
            union_path(a, b);
        } else {
            merge(a, b, idx);
            ++idx;
        }
    }
    for (int i = 0; i < n; ++i) {
        for (auto [to, j] : g[i]) {
            if (!usedE[j]) {
                cout << i + 1 << " " << to + 1 << "\n";
                usedE[j] = true;
            }
        }
    }
    return 0;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4564 KB Output is correct
2 Correct 3 ms 4564 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 4820 KB Output is correct
2 Correct 11 ms 4820 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 174 ms 4692 KB Output is correct
2 Correct 141 ms 4692 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 275 ms 4948 KB Output is correct
2 Correct 309 ms 5048 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 717 ms 5600 KB Output is correct
2 Correct 414 ms 5880 KB Output is correct

Subtask #6
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 882 ms 7856 KB Output is correct
2 Correct 715 ms 7764 KB Output is correct

Subtask #7
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1336 ms 8240 KB Output is correct
2 Correct 1131 ms 8056 KB Output is correct

Subtask #8
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1623 ms 9072 KB Output is correct
2 Correct 1488 ms 9100 KB Output is correct

Subtask #9
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1899 ms 9060 KB Output is correct
2 Correct 1843 ms 9116 KB Output is correct

Subtask #10
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2247 ms 8844 KB Output is correct
2 Correct 1975 ms 9036 KB Output is correct