Add Edges to Make Degrees of All Nodes Even
A hard-tier problem at 34% community acceptance, tagged with Hash Table, Graph. Reported in interviews at Hudson River Trading and 0 others.
This problem sits at the intersection of graph theory and parity constraints, and it's a steep climb. You need to add minimum edges to a graph so every node has even degree. It's asked at Hudson River Trading and similar quantitative firms that lean hard on discrete math. The acceptance rate hovers around 33 percent, which reflects the real difficulty: the insight isn't obvious, and the implementation has sharp edges. If you hit this live and haven't internalized the Eulerian graph connection, you'll stall fast. StealthCoder covers this exact gap during the assessment if the pattern doesn't click.
Companies that ask "Add Edges to Make Degrees of All Nodes Even"
Add Edges to Make Degrees of All Nodes Even is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Built by an engineer who got tired of watching his cohort grind for six months and still get filtered at the OA stage.
Get StealthCoderThe core trick is recognizing this is an Eulerian path problem in disguise. A connected graph has an Eulerian circuit only if every node has even degree. So you're asked to add the minimum number of edges to force that property. The naive greedy approach fails because isolated odd-degree nodes can't always pair up directly; you need to find the minimum-weight perfect matching on the subgraph of odd-degree nodes, then add edges along shortest paths between them. Hash tables track node degrees and adjacency, and Graph traversal finds connected components and odd-degree nodes. The pitfall is treating this as a simple pairing problem without considering shortest paths. Most candidates either add redundant edges or miss that the answer isn't always linear in the number of odd nodes. This is where the problem punishes half-learned intuitions. StealthCoder solves it in real time if you blank on the matching reduction.
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Add Edges to Make Degrees of All Nodes Even recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Built by an engineer who got tired of watching his cohort grind for six months and still get filtered at the OA stage. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Add Edges to Make Degrees of All Nodes Even interview FAQ
Is this really a graph problem, or is there a math trick I'm missing?+
Both. It's graph theory rooted in Eulerian circuits. You need to recognize that even-degree nodes form the structure of an Eulerian graph, then solve a minimum-weight perfect matching subproblem on odd-degree nodes using shortest paths. No shortcut; you have to know the theory.
Why is the acceptance rate so low?+
The insight chain is long. Candidates must connect even-degree constraints to Eulerian graphs, recognize the matching reduction, implement graph traversal and shortest-path queries, and handle edge cases around disconnected components. Miss one link and you'll TLE or return wrong counts.
How much prep time does this usually need?+
If you already know Eulerian graphs and matching algorithms, maybe an hour to code cleanly. If you don't, you're looking at a week of study on graph theory, matching, and shortest paths. Most candidates underestimate the scope and run out of time in the live assessment.
Will Hash Table and Graph prep alone be enough?+
Not quite. You need to understand how hash tables and adjacency structures serve Eulerian graph algorithms and matching computations. Standard graph traversal isn't the bottleneck; the algorithmic pattern is. That requires specific knowledge of this problem class.
Is Hudson River Trading still asking this?+
It's been reported from them. Given the problem's difficulty and the firm's focus on quantitative and algorithmic rigor, it's reasonable to expect variants. If you're interviewing there, treat this as a likely surface area and drill the Eulerian logic hard.
Want the actual problem statement? View "Add Edges to Make Degrees of All Nodes Even" on LeetCode →