Google Software Engineer Interview Questions

Apply Dijkstra's algorithm utilizing a binary min-heap-based Priority Queue to keep track of the cheapest known paths. Initialize the source node path distance to zero and all other vertices to infinity. Continually extract the node with the lowest accumulated path cost from the min-heap, iterate through its outward edges, and perform path relaxation updates on neighboring vertices if a more efficient route is discovered. The time complexity scales smoothly to O((V + E) log V). Note that this algorithm fails if negative edge weights are present, which instead requires the Bellman-Ford approach.

Dynamic Programming (DP) is an algorithmic optimization paradigm designed to solve complex computational problems by systematically breaking them down into simpler, overlapping subproblems and caching their evaluations to eliminate redundant computations. It is applicable when a problem satisfies two core characteristics: optimal substructure (the global optimal solution can be constructed from optimal subproblem solutions) and overlapping subproblems (the recursive execution path visits identical states repeatedly). Implementations utilize top-down recursive memoization or bottom-up iterative tabulation.

Optimize the Longest Increasing Subsequence (LIS) problem from a naive O(n²) dynamic programming approach down to O(n log n) by integrating dynamic programming with binary search. Maintain an active tail-tracking array where index i stores the smallest tail value discovered among all valid increasing subsequences of length i+1. Iterate through each element of the input collection, executing a binary search (such as std::lower_bound) on the tail array to locate its optimal position. If the element is larger than all elements, append it; otherwise, update the tracked value to optimize future candidate lengths.

Implement a Token Bucket or Leaky Bucket algorithm to handle burst traffic gracefully, or use a Sliding Window Log for precise boundary enforcement. To deploy at high-scale distributed production volumes, store rate metrics inside a centralized Redis cluster. To eliminate distributed data race conditions when multiple server instances execute atomic updates simultaneously, run rate checks using Redis Lua scripts or atomic increments. This approach ensures low latency while protecting downstream services from traffic spikes.

Utilize Consistent Hashing supplemented with virtual nodes to distribute keys across a cluster of server nodes, which prevents heavy data migration cascades when scaling the node count up or down. Implement local cache eviction policies via node-level LRU tracking bound by absolute TTL parameters. To prevent the 'Cache Stampede' problem on highly popular hot-keys, implement single-flight request consolidation on cache misses (blocking redundant database reads) and route hot-key data across local replica storage tiers.