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Maze PA Explanation Mark Redekopp 2 Maze Solver Consider this - PowerPoint PPT Presentation

Jun 22, 2023 •225 likes •427 views

1 Maze PA Explanation Mark Redekopp 2 Maze Solver Consider this maze (0,0) (0,1) (0,2) (0,3) . . . . S = Start (1,0) (1,1) (1,2) (1,3) S # F # F = Finish (2,0) (2,1) (2,2) (2,3) . # . # . = Free (3,0)

  1. 1 Maze PA Explanation Mark Redekopp

  2. 2 Maze Solver • Consider this maze (0,0) (0,1) (0,2) (0,3) . . . . – S = Start (1,0) (1,1) (1,2) (1,3) S # F # – F = Finish (2,0) (2,1) (2,2) (2,3) . # . # – . = Free (3,0) (3,1) (3,2) (3,3) . . . # – # = Wall • Find the shortest path

  3. 3 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • To find a (there might be (1,0) (1,1) (1,2) (1,3) S # F # many) shortest path we use a (2,0) (2,1) (2,2) (2,3) . # . # breadth-first search (BFS) (3,0) (3,1) (3,2) (3,3) . . . # • BFS requires we visit all nearer squares before further Queue squares – A simple way to meet this requirement is to make a square "get in line" (i.e. a queue) when we encounter it – We will pull squares from the front to explore and add new squares to the back of the queue

  4. 4 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • We start by putting the (1,0) (1,1) (1,2) (1,3) S # F # starting location into the (2,0) (2,1) (2,2) (2,3) . # . # queue (3,0) (3,1) (3,2) (3,3) . . . # Queue 1,0

  5. 5 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • We start by putting the (1,0) (1,1) (1,2) (1,3) S # F # starting location into the (2,0) (2,1) (2,2) (2,3) . # . # queue (3,0) (3,1) (3,2) (3,3) . . . # • Then we enter a loop…while the queue is not empty Queue – Extract the front location, call it "curr" 1,0 Visit each neighbor (N,W,S,E) one at a – time Visited Predecessor If the neighbor is the finish – (0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3) 0 0 0 0 • Stop and trace backwards -1,-1 -1,-1 -1,-1 -1,-1 Else if the neighbor is a valid location and – (1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3) 1 0 0 0 -1,-1 -1,-1 -1,-1 -1,-1 not visited before (2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3) 0 0 0 0 Then add it to the back of the queue • -1,-1 -1,-1 -1,-1 -1,-1 • Mark it as visited so we don't add it to the (3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3) 0 0 0 0 queue again -1,-1 -1,-1 -1,-1 -1,-1 • Record its predecessor (the location [i.e. curr] that found this neighbor

  6. 6 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • We start by putting the (1,0) (1,1) (1,2) (1,3) S # F # starting location into the (2,0) (2,1) (2,2) (2,3) . # . # queue (3,0) (3,1) (3,2) (3,3) . . . # • Then we enter a loop…while curr = 1,0 the queue is not empty Queue – Extract the front location, call it "curr" 1,0 0,0 2,0 Visit each neighbor (N,W,E,S) one at a – time Visited Predecessor If the neighbor is the finish – (0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3) 1 0 0 0 • Stop and trace backwards 1,0 -1,-1 -1,-1 -1,-1 Else if the neighbor is a valid location and – (1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3) 1 0 0 0 -1,-1 -1,-1 -1,-1 -1,-1 not visited before (2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3) 1 0 0 0 Then add it to the back of the queue • 1,0 -1,-1 -1,-1 -1,-1 • Mark it as visited so we don't add it to the (3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3) 0 0 0 0 queue again -1,-1 -1,-1 -1,-1 -1,-1 • Record its predecessor (the location [i.e. curr] that found this neighbor

  7. 7 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • We start by putting the (1,0) (1,1) (1,2) (1,3) S # F # starting location into the (2,0) (2,1) (2,2) (2,3) . # . # queue (3,0) (3,1) (3,2) (3,3) . . . # • Then we enter a loop…while curr = 0,0 the queue is not empty Queue – Extract the front location, call it "curr" 1,0 0,0 2,0 0,1 Visit each neighbor (N,W,E,S) one at a – time Visited Predecessor If the neighbor is the finish – (0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3) 1 1 0 0 • Stop and trace backwards 1,0 0,0 -1,-1 -1,-1 Else if the neighbor is a valid location and – (1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3) 1 0 0 0 -1,-1 -1,-1 -1,-1 -1,-1 not visited before (2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3) 1 0 0 0 Then add it to the back of the queue • 1,0 -1,-1 -1,-1 -1,-1 • Mark it as visited so we don't add it to the (3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3) 0 0 0 0 queue again -1,-1 -1,-1 -1,-1 -1,-1 • Record its predecessor (the location [i.e. curr] that found this neighbor

  8. 8 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • We start by putting the (1,0) (1,1) (1,2) (1,3) S # F # starting location into the (2,0) (2,1) (2,2) (2,3) . # . # queue (3,0) (3,1) (3,2) (3,3) . . . # • Then we enter a loop…while curr = 2,0 the queue is not empty Queue – Extract the front location, call it "curr" 1,0 0,0 2,0 0,1 3,0 Visit each neighbor (N,W,E,S) one at a – time Visited Predecessor If the neighbor is the finish – (0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3) 1 1 0 0 • Stop and trace backwards 1,0 0,0 -1,-1 -1,-1 Else if the neighbor is a valid location and – (1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3) 1 0 0 0 -1,-1 -1,-1 -1,-1 -1,-1 not visited before (2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3) 1 0 0 0 Then add it to the back of the queue • 1,0 -1,-1 -1,-1 -1,-1 • Mark it as visited so we don't add it to the (3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3) 1 0 0 0 queue again 2,0 -1,-1 -1,-1 -1,-1 • Record its predecessor (the location [i.e. curr] that found this neighbor

  9. 9 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • We start by putting the (1,0) (1,1) (1,2) (1,3) S # F # starting location into the (2,0) (2,1) (2,2) (2,3) . # . # queue (3,0) (3,1) (3,2) (3,3) . . . # • Then we enter a loop…while curr = 0,1 the queue is not empty Queue – Extract the front location, call it "curr" 1,0 0,0 2,0 0,1 3,0 0,2 Visit each neighbor (N,W,E,S) one at a – time Visited Predecessor If the neighbor is the finish – (0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3) 1 1 1 0 • Stop and trace backwards 1,0 0,0 0,1 -1,-1 Else if the neighbor is a valid location and – (1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3) 1 0 0 0 -1,-1 -1,-1 -1,-1 -1,-1 not visited before (2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3) 1 0 0 0 Then add it to the back of the queue • 1,0 -1,-1 -1,-1 -1,-1 • Mark it as visited so we don't add it to the (3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3) 1 0 0 0 queue again 2,0 -1,-1 -1,-1 -1,-1 • Record its predecessor (the location [i.e. curr] that found this neighbor

  10. 10 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • We start by putting the (1,0) (1,1) (1,2) (1,3) S # F # starting location into the (2,0) (2,1) (2,2) (2,3) . # . # queue (3,0) (3,1) (3,2) (3,3) . . . # • Then we enter a loop…while curr = 3,0 the queue is not empty Queue – Extract the front location, call it "curr" 1,0 0,0 2,0 0,1 3,0 0,2 3,1 Visit each neighbor (N,W,E,S) one at a – time Visited Predecessor If the neighbor is the finish – (0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3) 1 1 1 0 • Stop and trace backwards 1,0 0,0 0,1 -1,-1 Else if the neighbor is a valid location and – (1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3) 1 0 0 0 -1,-1 -1,-1 -1,-1 -1,-1 not visited before (2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3) 1 0 0 0 Then add it to the back of the queue • 1,0 -1,-1 -1,-1 -1,-1 • Mark it as visited so we don't add it to the (3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3) 1 1 0 0 queue again 2,0 3,0 -1,-1 -1,-1 • Record its predecessor (the location [i.e. curr] that found this neighbor

  11. 11 Maze Solver (0,0) (0,1) (0,2) (0,3) . . . . Maze array: • We start by putting the (1,0) (1,1) (1,2) (1,3) S # F # starting location into the (2,0) (2,1) (2,2) (2,3) . # . # queue (3,0) (3,1) (3,2) (3,3) . . . # • Then we enter a loop…while curr = 0,2 the queue is not empty Found the Finish at (1,2) Queue – Extract the front location, call it "curr" 1,0 0,0 2,0 0,1 3,0 0,2 3,1 Visit each neighbor (N,W,E,S) one at a – time Visited Predecessor If the neighbor is the finish – (0,0) (0,1) (0,2) (0,3) (0,0) (0,1) (0,2) (0,3) 1 1 1 0 • Stop and trace backwards 1,0 0,0 0,1 -1,-1 Else if the neighbor is a valid location and – (1,0) (1,1) (1,2) (1,3) (1,0) (1,1) (1,2) (1,3) 1 0 0 0 -1,-1 -1,-1 -1,-1 -1,-1 not visited before (2,0) (2,1) (2,2) (2,3) (2,0) (2,1) (2,2) (2,3) 1 0 0 0 Then add it to the back of the queue • 1,0 -1,-1 -1,-1 -1,-1 • Mark it as visited so we don't add it to the (3,0) (3,1) (3,2) (3,3) (3,0) (3,1) (3,2) (3,3) 1 1 0 0 queue again 2,0 3,0 -1,-1 -1,-1 • Record its predecessor (the location [i.e. curr] that found this neighbor

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