Learning pathOriginal reference
Lesson 8 of 8

Trace paths and recognize reusable states

Distinguish current-path visitation from permanent visitation and memoized answers.

Understand the idea

For enumerating simple grid paths, visited means “on this path.” Mark a cell on entry and unmark it on return so another branch may use it. For unrestricted down/right grid routes, every move increases a coordinate, so no cycle is possible.

Trace a small example

A 2-by-2 open grid has two top-left to bottom-right down/right routes: right-down and down-right. Four-direction simple paths need path-local visitation. Memoization can reuse answers only when the key describes every fact affecting the future; position alone is insufficient when allowed cells depend on the current visited set.

Conditions and cost

Path enumeration can be exponential and must include output cost. Memoized counting and enumerating every path are different tasks. The PDF also develops Hanoi and merge sort as extensions of clear parameter roles and combining smaller answers.

Pause & predict

In simple-path backtracking, why unmark a cell on return?

Choose an answer
Try it yourself

Turn the idea into code

A robot must make two right moves and one down move. Enumerate its routes.

Give me a hint

Choose the position of the down move.

Show the explained solution

DRR, RDR, and RRD are the three routes. A call can track remaining right and down moves, reducing one on each branch.

Your notes

Ready for the next idea?

Mark complete when you can explain it yourself.

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