Matrices mind map
2-D grids, traversal, and matrix manipulation.
Core idea: Make coordinates explicit: bounds, neighbors, visited state, and direction.
Mnemonic: Coordinate → bound → visit · Cost: O(rows × cols) typical
Walk: Direction & boundaries
Signal: Traversal follows layers, diagonals, or turns at an edge.
Move: Encode direction deltas and shrink boundaries or rotate direction when blocked.
Examples: Spiral Matrix, Diagonal Traverse, Robot Simulation
Connect: Flood fill
Signal: Cells form components through allowed neighbor moves.
Move: Start at each unseen cell, mark on entry, and explore every valid neighbor once.
Examples: Number of Islands, Max Area of Island, Flood Fill
Transform: Markers, order & index math
Signal: The matrix changes in place or sorted rows/columns can discard search space.
Move: Reuse boundary markers, transpose + reverse, or start at a corner that eliminates a line.
Examples: Set Matrix Zeroes, Rotate Image, Search 2D Matrix
Explore: Path state
Signal: The answer depends on moves through the grid and possibly prior choices.
Move: Use DP for acyclic moves; use memoized DFS or backtracking when choices branch.
Examples: Unique Paths, Longest Increasing Path, Word Search