Mail Delivery - Implementation

function mailDelivery(n, edges):
    adj = build adjacency list with edge indices
    used = array of false, size = number of edges

    // Check degrees
    for v from 1 to n:
        if adj[v].size is odd:
            return "IMPOSSIBLE"

    // Hierholzer
    stack = [1]
    path = []
    while stack not empty:
        v = stack.top()
        while adj[v] not empty and used[adj[v].back().edgeIndex]:
            adj[v].pop_back()
            if adj[v] not empty:
                edge = adj[v].pop_back()
                used[edge.index] = true
                stack.push(edge.to)
            else:
                path.append(stack.pop())

                return path.reversed()

This runs in $O(E)$ time and uses $O(E)$ space.