Board Coloring and Query Processing
Reported by candidates from PayPay's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
PayPay reported this in June 2025, and it's a graph coloring problem wrapped in query processing. You're coloring nodes on a board and answering queries about the coloring state. The trick is realizing you don't need to recompute the entire coloring for each query. You'll likely build the coloring once, store the state efficiently, then answer queries in O(1) or O(log n) time. This is the kind of problem that looks harder than it is if you're still thinking about it live. StealthCoder can pull the pattern and walk you through the state management if you blank.
Pattern and pitfall
Board coloring is a graph problem disguised as a state-query problem. The pattern is: precompute a valid coloring (usually greedy, sometimes BFS-based), store it in a lookup structure (array, hash table, or segment tree depending on the query type), then answer queries by reading from that structure. The pitfall is trying to answer queries by re-running the coloring algorithm each time. Also watch for adjacency constraints: you may need to build the board graph explicitly to check which cells conflict. The query processing layer is often where the problem tests your ability to think about time complexity trade-offs. If queries are point updates or range checks, a segment tree or prefix sum might be needed. Otherwise, a simple array lookup is enough. Use StealthCoder as a safety net if the query format is unclear during the live OA.
The honest play: practice the pattern, and have StealthCoder ready for the one you didn't see coming.
You can drill Board Coloring and Query Processing cold, or you can hedge it. StealthCoder runs invisibly during screen share and surfaces a working solution in under 2 seconds. The proctor sees the IDE. They don't see what's behind it. Built for the candidate who saw this exact problem leak two days before his OA and wondered if anyone had a play.
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Board Coloring and Query Processing FAQ
What does 'board coloring' really mean here?+
You're assigning colors (usually integers) to positions on a board such that adjacent positions don't share the same color. Think of it like graph coloring where each cell is a node and edges connect adjacent cells. You build the coloring once, then answer queries about the colors.
Do I need to recolor for each query?+
No. Build the coloring upfront in one pass (greedy or BFS works). Store it in an array or map. Queries read from that precomputed state. If queries include updates, you may need a segment tree or lazy propagation, but often updates are rare.
What's the greedy approach?+
Iterate through the board. For each cell, assign the smallest color not used by any adjacent cell. This is O(n * degree), where degree is the max number of neighbors. It always works for planar graphs (like a grid).
How do I represent the board graph?+
If it's a grid, adjacency is implicit: each cell (i, j) touches (i-1, j), (i+1, j), (i, j-1), (i, j+1). You don't need an explicit adjacency list unless the board structure is irregular. For irregular boards, use a hash map of neighbors.
Will PayPay ask for the minimum number of colors used?+
Probably. Track the maximum color assigned during greedy coloring. For a grid, you'll never need more than 4 colors. For bipartite boards, you'll need 2. The problem may ask you to output this count alongside query answers.