The shortest path in a grid with obstacles elimination problem adds a strategic layer to classic pathfinding. Unlike standard BFS, reaching a cell with varying remaining eliminations creates distinct states that must be tracked separately.

Traditional breadth-first search falls short because it doesn't account for resource constraints. A longer path early on might preserve eliminations needed for shorter overall solutions later. The key is treating position and remaining eliminations as a combined state.

BFS still works but operates on an expanded state space. Each node tracks row, column, and eliminations left. Transitions consume an elimination when moving through an obstacle. Dominance pruning ensures only the most efficient paths are explored, preventing redundant computations.

This approach guarantees correctness by exploring states in increasing step order. It's a staple in coding interviews because it tests adaptability and deep understanding of graph traversal under constraints, not just algorithmic recall.