CSES Solutions - Even Outdegree Edges

#include <bits/stdc++.h>
using namespace std;

typedef pair<int, int> pii;
const int maxN = 1e5 + 5, maxM = 2e5 + 5;

int N, M, timer, in[maxN];
bool even[maxN];
vector<pii> G[maxN];
pii ans[maxM];

// Depth-first search (DFS) function to traverse the graph
void dfs(int u, int p = -1)
{
    // Mark the current node with a visitation timestamp
    in[u] = ++timer;
    // Iterate over all adjacent nodes
    for (pii e : G[u]) {
        int v = e.first, id = e.second;
        // Skip the parent node to avoid traversing back
        if (v != p) {
            // If the adjacent node has not been visited
            if (!in[v]) {
                // Recursively perform DFS on the adjacent
                // node
                dfs(v, u);
                // If the adjacent node has an even
                // outdegree
                if (even[v]) {
                    // Direct the edge from the current
                    // node to the adjacent node
                    ans[id] = { u, v };
                    // Toggle the outdegree of the current
                    // node
                    even[u] ^= true;
                }
                else {
                    // If the adjacent node has an odd
                    // outdegree Direct the edge from the
                    // adjacent node to the current node
                    ans[id] = { v, u };
                    // Toggle the outdegree of the adjacent
                    // node
                    even[v] ^= true;
                }
            }
            else if (in[v] < in[u]) {
                // If the adjacent node was visited earlier
                // Toggle the outdegree of the current node
                even[u] ^= true;
                // Direct the edge from the current node to
                // the adjacent node
                ans[id] = { u, v };
            }
        }
    }
}

int main()
{
    // Predefined input
    N = 4;
    M = 4;
    // List of edges
    vector<pair<int, int> > edges
        = { { 1, 3 }, { 3, 2 }, { 3, 4 }, { 1, 4 } };

    // Construct the graph from the predefined edges
    for (int i = 0; i < M; i++) {
        cin >> edges[i].first >> edges[i].second;
        int a = edges[i].first, b = edges[i].second;
        // Add edge to adjacency list for node a
        G[a].push_back({ b, i });
        // Add edge to adjacency list for
        // node b (undirected graph)
        G[b].push_back({ a, i });
    }

    // Initialize all nodes to have even outdegrees
    fill(even + 1, even + N + 1, true);

    // Perform DFS traversal on all unvisited nodes
    for (int i = 1; i <= N; i++) {
        if (!in[i]) {
            dfs(i);
        }
    }

    // Check if all nodes have even outdegrees
    bool good = true;
    for (int i = 1; i <= N; i++) {
        good &= even[i];
    }

    // Print the result
    if (good) {
        for (int i = 0; i < M; i++) {
            // Print directed edges
            printf("%d %d\n", ans[i].first, ans[i].second);
        }
    }
    else {
        // Print "IMPOSSIBLE" if any node has an odd
        // outdegree
        printf("IMPOSSIBLE\n");
    }

    return 0;
}