clue paths

Clue Paths

Memory Alias Review• Remember that it’s possible for two unique variables to point

to the same memory location

myList

MyClass mc

0x100someFn (in another class){ localVar = mc.getMyList();}

localVar

If I modify localVar, it also changes myList!

Memory Alias Continued• In C++, what was the purpose of the copy constructor?• In Java, we also use copy constructor, to avoid shallow copy.

myList

MyClass mc

myList

MyClass mc3 (created using copy, e.g., mc3 = new LinkedList<>(mc); )

myList

MyClass mc2 (created by assignment, e.g., mc2 =mc; )

0x200 0x300 0x0

0x200 0x3000x100

0x600 0x700 0x0

0x600 0x7000x500

Recursion Review*

• Base case – causes recursion to end• Recursive call – to same function• Progress toward base case

* the algorithm I describe uses recursion. Recursion is not absolutely required, but this is a good opportunity for review.

Simple Examplepublic static int factorial(int n) { if(n==1) return 1; return factorial(n-1) * n; }

public static void main(String[] args) { System.out.println(factorial(3));}

Very Quick Ex: How would factorial(3) be calculated? (trace the code)

Sometimes need “setup” first

• Example: drawing a fractal – drawFractal: setup center x, center y, x0 and y0

• Call drawFractalLine with length, theta, order

– drawFractalLine – draws a line, does a recursive call with order-1

• What’s the point? – User calls drawFractal– recursive function is drawFractalLine.

• Our algorithm has similar structure

from: Thinking Recursively in Java, Eric Roberts

The Challenge

Room Room Walk Walk Room

Room Door Walk Walk Room

Walk Walk Walk Walk Room

Walk Player Walk Walk Walk

Walk Walk Walk Walk Walk

Roll a 1

Highlight all the squares that can be reached in # of steps shown on one dieMove only up/down/left/right (no diagonal)Do not touch any location more than one timeHighlight only the final squares, not the paths

The Challenge

Roll a 2

A clarification

Roll a 4. (this is just one target)Note that the person CANNOT backtrack… that is, visit the same cell twice. But the person is NOT required to go in a straight line. So you CANNOT just include all squares that are n away from the initial point.

Simplify for nowForget about doors and rooms. Let’s do a simple 4x4 gridNumber the rows and columns. Assume a 2D grid, each containing a board cell.Create an adjacency list. NOTE: adjacency lists will be even more handy in the clue layout, because a square is not necessarily attached to each of its neighbors. By creating the adjacency list when the board is loaded, we can simplify the code for the path-finding algorithm.

With your partner: What is this? How would you write a program to create?

0 1 2 3

Adjacency List (sample entries)[0][0] => { [0][1], [1][0] }

[1][1] => { [0][1], [1][0], [1][2], [2][1] }

Calculating the Adjacency Lists

Notice that for each cell, you have at most 4 neighbors.

To calculate the adjacency list:for each cell look at each neighbor if it is a valid index add it to the adjacency list

What data structure would you use for the adjacency list?(we’ll use a common structure – covered in a minute)

0 1 2 3

Calculating Neighbors

Choose Data Structures

We want to be able to look up all the adjacencies for a given cell. This is a good application of a map:private Map<BoardCell, LinkedList<BoardCell>> adjMtx;

What is a BoardCell? For now, a simple class with a row and column. More will be added in the Clue game.

Why is the adjacency stored as a linked list? I wanted to add/remove easily at the end of the list. LinkedList supports easily. But there’s no insert/remove in the middle of the list, so LinkedList choice is somewhat arbitrary.

What are some other alternatives? •To facilitate code swap, we will use the same data types – but others might be equally valid.

Adjacency List (sample entries)[0][0] => { [0][1]->[1][0] }

[1][1] => { [0][1]->[1][0]->[1][2]->[2][1] }

0 1 2 3

Goal: Targets with paths of length 2 from cell 4Answer: Shown in green below

adjacency matrix should have been calculated prior to calling calcTargets

calcTargets: Set up for recursive call•visited list is used to avoid backtracking. Set to empty list.•targets will ultimately contain the list of cells (e.g., [0][1], [1][2], [2][1], [3][0]) . Initially set to empty list.•add the start location to the visited list (so no cycle through this cell)•call recursive function

• what will you name this function? I did findAllTargets• what parameters does it need?

Why can’t these steps be in recursive fn?

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

adjacencies (in condensed form, 0 is [0][0] etc.) findAllTargets pseudocode

Parameters: thisCell and numSteps

Set adjacentCells to all cells adjacent to thisCell that have not been visitedNOTE: do not modify adjacencies, create a new list!Suggest: helper function, keep code cleaner

for each adjCell in adjacentCells -- add adjCell to visited list -- if numSteps == 1, add adjCell to Targets-- else call findAllTargets with adjCell, numSteps-1-- remove adjCell from visited list

findAllTargets

recursive call!

visited: [1][0]

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacenciesTargets: (none yet)

findAllTargets call: thisCell =[1][0], numSteps=2

Set adjacentCells to all cells adjacent to [1][0] that have not been visited… [[2][0], [1][1], [0][0]]

(for each cell in adjacentCells)-- add adjCell to visited -- (if number of steps == 1 … )-- else call findAllTargets with adjCell , numStep-1 -- (when we return….remove adjCell from visited)

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacenciesTargets: (none yet)

Set adjacentCells to all cells adjacent to 4 that have not been visited… [8, 5, 0]

(for each cell in adjacentCells… current is [2][0])-- add [2][0] to visited list-- (if number of steps == 1 … )-- else call findAllTargets with adjCell, numStep-1 -- (when we return….remove from visited)

visited: [1][0][2][0]

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: (none yet)

(for each cell in adjacentCells… current is [2][0])-- add adjCell to visited -- (if number of steps == 1 … it’s not)-- else call findAllTargets with adjCell ([2][0]), numStep-1 -- (when we return….set visited to False)

recursive call! next slide

visited: [1][0][2][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: none yet

Set adjacentCells to all cells adjacent to [2][0] that have not been visited… [[3][0], [2][1]] not [1][0](but remember, don’t modify list of all adjacencies!)

(for each cell in adjacentCells)-- set visited[12] to True-- if number of steps == 1… yes! update Targets-- (else call calcTargets with adjCell, numSteps--)-- set visited to False

visited: [1][0][2][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: none yet

Set adjacentCells to all cells adjacent to 8 that have not been visited… [12, 9] not 4

(for each cell in adjacentCells, current is [3][0])-- add [3][0] to visited-- if number of steps == 1… yes! update Targets-- (else call calcTargets with adjCell, numSteps--)-- set visited to False

findAllTargets call: thisCell = =[2][0], numSteps=1

visited: [1][0][2][0][3][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0]

(for each cell in adjacentCells, current is [3][0])-- set visited[12] to True-- if number of steps == 1… yes! update Targets-- (else call calcTargets with adjCell, numSteps--)-- set visited to False

visited: [1][0][2][0][3][0

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0]

(for each cell in adjacentCells, current is [3][0])-- set visited[12] to True-- if number of steps == 1… yes! update Targets-- (else call findAllTargets with adjCell, numSteps-1)-- remove [3][0] from visited

then move to next cell in for loop, next slide

visited: [1][0][2][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

With your partner

• Continue to trace this code• You may want to start tracing from the

beginning• From past time surveys, people who

understand algorithm tend to take <4 hours for CluePaths

• Some students may be >8 hours

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0]

(for each cell in adjacentCells, current is [2][1])-- add [2][1] to visited-- if number of steps == 1… yes! update Targets-- (else call findAllTargets with adjCell, numSteps-1)-- set visited to False

visited: [1][0][2][0][2][1]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1]

(for each cell in adjacentCells, current is 9)-- set visited[9] to True-- if number of steps == 1… yes! update Targets-- (else call findAllTargets with adjCell, numSteps-1)-- set visited to False

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1]

(for each cell in adjacentCells, current is 9)-- set visited[9] to True-- if number of steps == 1… yes! update Targets-- (else call findAllTargets with adjCell, numSteps-1)-- remove [2][1] from visited

then move to next cell in for loop

visited: [1][0][2][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1]

(for each cell in adjacentCells, current is END)-- set visited[9] to True-- if number of steps == 1… yes! update Targets-- (else call findAllTargets with adjCell, numSteps-1)-- set visited to False

end of for loop, return

visited: [1][0][2][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1]

(for each cell in adjacentCells, current is 8)-- set visited[9] to True-- if number of steps == 1… yes! update Targets-- (else call findAllTargets with adjCell, numSteps-1)-- when we return, remove [2][0] from visited

end of for loop, return from recursive call

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1]

(for each cell in adjacentCells, current is 5)-- add [1][1] to visited-- if number of steps == 1… it’s not-- (else call findAllTargets with adjCell, numSteps-1)-- when we return, set visited to False

next item in for loop

visited: [1][0][1][1]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1]

(for each cell in adjacentCells, current is [1][1])-- set visited[5] to True-- if number of steps == 1… it’s not-- (else call FindAllTargets with adjCell ([1][1]), numSteps-1)-- when we return, set visited to False

recursive call

visited: [1][0][1][1]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1]

Set adjacentCells to all cells adjacent to [1][1] that have not been visited… [[0][1], [1][2], [2][1]]… not [1][0]!

(for each cell in adjacentCells)-- set visited[1] to True-- if number of steps == 1… it’s not-- (else call findAllTargets with adjCell (5), numSteps-1)-- when we return, set visited to False

visited: [1][0][1][1]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1]

Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]… not 4!

(for each cell in adjacentCells, current is 1)-- add [0][1] to visited-- if number of steps == 1… it’s not-- (else call findAllTargets with adjCell (5), numSteps-1)-- when we return, set visited to False

findAllTargets call: thisCell =5, numSteps=1

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: [3][0], [2][1], [0][1]

(for each cell in adjacentCells, current is 1)-- set visited[1] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell (5), numSteps-1)-- when we return, set visited to False

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

NOTE: rest of slides will use single digits for cells.Set visited to true/false means to add/remove from visited list

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1

(for each cell in adjacentCells, current is 1)-- set visited[1] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell (5), numSteps-1)-- set visited[1] to False

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1

(for each cell in adjacentCells, current is 6)-- set visited[6] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell (5), numSteps-1)-- set visited to False

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is 9)-- set visited[9] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell, numSteps-1)-- set visited to False

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6… no need to add 9 again

calcTargets call: thisCell =5, numSteps=1

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is 9)-- set visited[9] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell, numSteps-1)-- set visited[9] to False

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is END)-- set visited[9] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell, numSteps-1)-- set visited[9] to False

end of for loop, return from recursive call

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is 5)-- set visited[5] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell, numSteps-1)-- when return from call, set visited[5] to False

move to next cell in for loop

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is 0)-- set visited[0] to True-- if number of steps == 1… it’s not-- (else call findAllTargets with adjCell (0), numSteps-1)-- set visited to False

another recursive call

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

Set adjacentCells to all cells adjacent to 0 that have not been visited… [1] … not 4!

(for each cell in adjacentCells)-- set visited[0] to True-- if number of steps == 1… it’s not-- (else call findAllTargets with adjCell (0), numSteps-1)-- set visited to False

another recursive call

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is 1)-- set visited[1] to True-- if number of steps == 1… it’s not-- (else call findAllTargets with adjCell (0), numSteps-1)-- set visited to False

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6 … 1 is already in the set

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is END)-- set visited[1] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell (0), numSteps-1)-- set visited to False

end of for loop, return from call

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is 0)-- set visited[1] to True-- if number of steps == 1… yes! update targets-- (else call FindAllTargets with adjCell (0), numSteps-1)-- set visited[0] to False

move to next item in loop

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

Targets: 12, 9, 1, 6

(for each cell in adjacentCells, current is END)-- set visited[1] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell (0), numSteps-1)-- set visited to False

end of loop, return from call

visited: [1][0]

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

All adjacencies

findAllTargets

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

0 1 2 3

30123456789

101112131415

visited

0 => [4, 1]1 => [0, 5, 2]2 => [1, 6, 3]3 => [2, 7]4 => [8, 5, 0]5 => [4, 9, 6, 1]6 => [2, 5, 10, 7]7 => [11, 3, 6]8 => [12, 9, 4]9 => [13, 10, 5, 8]10 => [14, 11, 6, 9]11 => [15, 7, 10]12 => [13, 8]13 => [14, 9, 12]14 => [15, 10, 13]15 => [11, 14]

adjacencies Targets: 12, 9, 1, 6

We have now returned to the calcTargets

instance variable targets contains answer

calcTargets

end of loop, return from call

HINT• You can use clone or a copy constructor to create a list of

adjacent cells that have not been visited. Or create a new list containing just the unvisted cells. If you just modify the existing list, your code will fail.

012345

0x1000x2000x3000x4000x5000x600

1 -> 4 get(0) gets 0x100if I remove an element, I update the list in myhash map

HINT 2

• Take a look at the javadocs for collections, maybe you’ll find some useful functions (e.g., one student use the Array.fill method)

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