Clue Paths
Feb 10, 2016
Clue Paths
Memory Alias Review• Remember that it’s possible for two unique variables to point
to the same memory location
myList
MyClass mc
0x100
0x100someFn (in another class){ localVar = mc.getMyList();}
localVar
0x100
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
0x100
myList
MyClass mc3 (created using copy, e.g., mc3 = new LinkedList<>(mc); )
0x500
myList
MyClass mc2 (created by assignment, e.g., mc2 =mc; )
0x100
0x200 0x300 0x0
0x200 0x3000x100
0x600 0x700 0x0
0x600 0x7000x500
55
55
75
75
95
95
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
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
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
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 2
A clarification
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
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 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
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
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
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
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
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
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)
findAllTargets call: thisCell =[1][0], numSteps=2
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
0
1
2
3
Targets: (none yet)
findAllTargets call: thisCell =[1][0], numSteps=2
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 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
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
findAllTargets call: thisCell =[2][0], numSteps=1
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
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
0
1
2
3
Targets: [3][0]
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])-- set visited[12] to True-- 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
0
1
2
3
Targets: [3][0]
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])-- 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
findAllTargets call: thisCell = =[2][0], numSteps=1
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
0
1
2
3
Targets: [3][0]
Set adjacentCells to all cells adjacent to 8 that have not been visited… [12, 9] not 4
(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
findAllTargets call: thisCell = =[2][0], numSteps=1
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
0
1
2
3
Targets: [3][0], [2][1]
Set adjacentCells to all cells adjacent to 8 that have not been visited… [12, 9] not 4
(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
findAllTargets call: thisCell =[2][0], 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
0
1
2
3
Targets: [3][0], [2][1]
Set adjacentCells to all cells adjacent to 8 that have not been visited… [12, 9] not 4
(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
findAllTargets call: thisCell =[2][0], numSteps=1
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
0
1
2
3
Targets: [3][0], [2][1]
Set adjacentCells to all cells adjacent to 8 that have not been visited… [12, 9] not 4
(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
findAllTargets call: thisCell =[2][0], numSteps=1
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
0
1
2
3
Targets: [3][0], [2][1]
Set adjacentCells to all cells adjacent to 8 that have not been visited… [8, 5, 0]
(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
findAllTargets call: thisCell =[1][0], numSteps=2
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
0
1
2
3
Targets: [3][0], [2][1]
Set adjacentCells to all cells adjacent to 8 that have not been visited… [8, 5, 0]
(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
findAllTargets call: thisCell =[1][0], numSteps=2
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
0
1
2
3
Targets: [3][0], [2][1]
Set adjacentCells to all cells adjacent to 8 that have not been visited… [8, 5, 0]
(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
findAllTargets call: thisCell =[1][0], numSteps=2
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
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
findAllTargets call: thisCell =[1][1], numSteps=1
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
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
0
1
2
3
Targets: [3][0], [2][1], [0][1]
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]
(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
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
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
0
1
2
3
Targets: 12, 9, 1
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]
(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
findAllTargets call: thisCell =5, numSteps=1
then 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
0
1
2
3
Targets: 12, 9, 1
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 3]
(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
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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]
(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
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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]
(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[6] to False
findAllTargets call: thisCell =5, numSteps=1
then 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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]
(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
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
0
1
2
3
Targets: 12, 9, 1, 6… no need to add 9 again
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]
(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
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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]
(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
calcTargets call: thisCell =5, numSteps=1
then 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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 5 that have not been visited… [1, 6, 9]
(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
calcTargets call: thisCell =5, numSteps=1
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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 4 that have not been visited… [8, 5, 0]
(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
findAllTargets call: thisCell =4, numSteps=2
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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 4 that have not been visited… [8, 5, 0]
(for each cell in adjacentCells, current is 0)-- set visited[0] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell, numSteps-1)-- set visited to False
findAllTargets call: thisCell =4, numSteps=2
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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 4 that have not been visited… [8, 5, 0]
(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
findAllTargets call: thisCell =4, numSteps=2
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
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
findAllTargets call: thisCell =0, numSteps=1
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
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, 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
findAllTargets call: thisCell =0, 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
0
1
2
3
Targets: 12, 9, 1, 6 … 1 is already in the set
Set adjacentCells to all cells adjacent to 0 that have not been visited… [1] … not 4!
(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 (0), numSteps-1)-- set visited to False
findAllTargets call: thisCell =0, 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
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, current is 1)-- set visited[1] to True-- if number of steps == 1… yes! update targets-- (else call findAllTargets with adjCell (0), numSteps-1)-- set visited[1] to False
findAllTargets call: thisCell =0, numSteps=1
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
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, 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
findAllTargets call: thisCell =0, numSteps=1
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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 0 that have not been visited… [8, 5, 0]
(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
findAllTargets call: thisCell =4, numSteps=2
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
0
1
2
3
Targets: 12, 9, 1, 6
Set adjacentCells to all cells adjacent to 0 that have not been visited… [8, 5, 0]
(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
findAllTargets call: thisCell =4, numSteps=2
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
0
1
2
30123456789
101112131415
F
F
F
F
T
F
T
F
F
F
F
F
F
F
F
F
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
calcTargets call: thisCell =4, numSteps=2
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)