Satisfiability of Equality Equations
A medium-tier problem at 51% community acceptance, tagged with Array, String, Union Find. Reported in interviews at Sumo Logic and 1 others.
You're looking at a problem that hits the classic union-find sweet spot: abstract enough to trip up the unprepared, concrete enough that the right mental model solves it in minutes. Sumo Logic and UiPath both ask this one. The acceptance rate sits at 51%, which means half the candidates who attempt it don't land the solution. You're likely to see this in a medium-difficulty slot where the interviewer's separating serious candidates from people who just memorized leetcode top 75. The trick isn't the data structure, it's seeing the problem as a graph constraint problem before you write a single line. If you blank on it during your live assessment, StealthCoder runs invisibly and surfaces the working pattern in seconds.
Companies that ask "Satisfiability of Equality Equations"
Satisfiability of Equality Equations 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. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too.
Get StealthCoderThe problem asks you to determine whether a set of equality equations (and inequalities, implicitly) can all be satisfied simultaneously. The trap is thinking equality as a simple boolean check. The real insight: treat each equation as a constraint that forces variables into the same group. Use union-find to build connected components where all variables in a component must be equal. Then scan the inequalities, if any inequality connects two variables in the same component, the system is unsatisfiable. Most candidates either build the union-find correctly but forget to validate inequalities, or they try a graph DFS approach that's messier to implement. The Array and String topics here just mean you're parsing input and iterating. When you hit this live and your first instinct doesn't click, StealthCoder gives you the component-validation pattern so you don't burn 20 minutes on a false start.
Pattern tags
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Satisfiability of Equality Equations recycles across companies for a reason. It's medium-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. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Satisfiability of Equality Equations interview FAQ
What's the core trick to this problem?+
Recognize that equality equations define equivalence classes. Union-find groups variables that must be equal. Then check if any inequality (unequal statement) links two variables in the same group. If yes, the system is unsatisfiable. If no, it's satisfiable.
Why does union-find work here instead of a custom graph search?+
Union-find is optimized for the 'group these items together' problem and has near-constant amortized lookup. Graph DFS works but requires more bookkeeping. Union-find is the standard tool when the problem is about equivalence and grouping.
What's the most common mistake candidates make?+
Building the union-find structure correctly but forgetting to validate inequalities against it. Or validating late and wasting time on unnecessary complexity. Process all equalities first to form groups, then scan inequalities exactly once.
Is this still asked at companies like Sumo Logic?+
Yes, both Sumo Logic and UiPath report this problem. It's a straightforward constraint-satisfaction problem that tests understanding of union-find and graph thinking without heavy implementation overhead.
How does union-find relate to the Graph and Array topics listed?+
Union-find is a graph abstraction. You're building connected components implicitly. Array and String just cover input parsing. The heavy lifting is graph reasoning through union-find structure.
Want the actual problem statement? View "Satisfiability of Equality Equations" on LeetCode →