More Recursion.

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Presentation transcript:

More Recursion

Binary Strings "" 3 steps to go "0" "1" 2 steps to go "00" "01" "10" "11" 1 step to go "000" "001" "010" "011" "100" "101" "110" "111" done

Binary Strings

Towers Of Hanoi 3 Pegs & Stack of disks Get from one peg to another Can only move one disk at a time Big disks can not be on top of small disks

Decomposition To move 3 disks from A to C Move top 2 to B Move last to C Move 2 from B to C

Towers Of Hanoi 3 disks = 7 moves N disks = 2n – 1 moves

N-Queens Eight Queens Each must be on own row/col/diagonal

Representation Single array : what col is queen in?

Code Do not need to copy – moving queen overwrites old move

Flood Fill Flood Fill Color starting square Try to color square above Try to color square below Try to color square to left Try to color square to right

Shared Data Flood fill works on one copy of data Array passed as memory addresses Every recursive call uses same array

Path Finding Find a path… If goal, done = return 0 If bad square return  Else Mark square Ask left how far Ask right how far Ask up how far Ask down how far Return 1 + shortest of neighbors

Path Finding

Path Finding Want to explore different paths Each path needs own array Need to copy current maze before marking move