Hierholzer's Pseudocode

function findEulerPath(graph, start):
    stack = [start]
    path = []

    while stack is not empty:
        v = stack.top()
        if v has unused edges:
            u = any neighbor with unused edge
            mark edge (v, u) as used
            stack.push(u)
        else:
            path.append(stack.pop())

    return path.reversed()

For undirected graphs, mark both directions when using an edge.

Time: $O(E)$ since each edge is visited exactly once. Space: $O(V + E)$ for the stack and path.

Space complexity is $O(E)$ for the data structures used.