Many books and websites have aggressive programming challenges for top coders. The last chapter, on fractals, culminates with examples of the beautiful fractal shapes recursion can produce. The book also explains tail call optimization and memoization, concepts often employed to produce effective recursive algorithms, and the call stack, which is a critical part of how recursive functions work but is almost never explicitly pointed out in lessons on recursion. It is project-based, containing complete, runnable programs in both Python and JavaScript, and covers several common recursive algorithms for tasks like calculating factorials, producing numbers in the Fibonacci sequence, tree traversal, maze solving, binary search, quicksort and merge sort, Karatsuba multiplication, permutations and combinations, and solving the eight queens problem. This book teaches the basics of recursion, exposes the ways it's often poorly taught, and clarifies the fundamental principles behind all recursive algorithms. Its fearsome reputation is more a product of poor teaching than of the complexity of recursion itself. But there's nothing magical about recursion. Moreover, coders often perceive the use of a recursive algorithm as a sophisticated solution that only true programmers can produce. They're seen as an advanced computer science topic often brought up in coding interviews. Recursion, and recursive algorithms, have a reputation for being intimidating. Put ( '+' ) for Col in Item ' Range ( 2 ) loop if Item ( Row, Col ). Put ( "?" ) end if end loop if Item ( Row, Item ' Last ( 2 )). Put ( ' ' ) end if if Item ( Row, Col ). Walls ( West ) or else Item ( Row, Col - 1 ). Walls ( West ) and then Item ( Row, Col - 1 ). Put ( ' ' ) end if elsif Item ( Row, Col ). New_Line end if for Col in Item ' Range ( 2 ) loop if Col = Item ' First ( 2 ) then if Item ( Row, Col ). Put_Line ( "Starting generation at " & Positive ' Image ( Row ) & " x" & Positive ' Image ( Column )) Depth_First_Algorithm ( Maze, Row, Column ) end Initialize procedure Put ( Item : Maze_Grid ) is begin for Row in Item ' Range ( 1 ) loop if Row = Item ' First ( 1 ) then Ada. #VISUAL BASIC CODE MAZE GAME GENERATOR#Random ( Generator ) mod Height + 1 Column := RNG. Reset ( Dir_Generator ) - choose starting cell Row := RNG. exit when All_Tested end loop end Depth_First_Algorithm procedure Initialize ( Maze : in out Maze_Grid ) is Row, Column : Positive begin - initialize random generators RNG. Walls ( - Next_Direction ) := False Depth_First_Algorithm ( Maze, Next_Row, Next_Column ) end if end if Tested_Wall ( Next_Direction ) := True - continue as long as there are unvisited neighbours left All_Tested := True for D in Directions loop All_Tested := All_Tested and Tested_Wall ( D ) end loop - all directions are either visited (from here, - or previously visited), or invalid. Walls ( Next_Direction ) := False Maze ( Next_Row, Next_Column ). Visited then - connect the two cells Maze ( Row, Column ). Random ( Dir_Generator ) exit when not Tested_Wall ( Next_Direction ) end loop Next_Row := Row Next_Column := Column Move ( Next_Row, Next_Column, Next_Direction, Valid_Direction ) if Valid_Direction then if not Maze ( Next_Row, Next_Column ). Visited := True loop - use random direction loop Next_Direction := Random_Direction. Generator function "-" ( Dir : Directions ) return Directions is begin case Dir is when North => return South when South => return North when East => return West when West => return East end case end "-" procedure Move ( Row : in out Height_Type Column : in out Width_Type Direction : Directions Valid_Move : out Boolean ) is begin Valid_Move := False case Direction is when North => if Row > Height_Type ' First then Valid_Move := True Row := Row - 1 end if when East => if Column if Column > Width_Type ' First then Valid_Move := True Column := Column - 1 end if when South => if Row False ) All_Tested : Boolean begin - mark as visited Maze ( Row, Column ). Generator Dir_Generator : Random_Direction. With _Random with Ada.Text_IO package body Mazes is package RNG is new _Random (Positive ) package Random_Direction is new _Random (Directions ) Generator : RNG. PROC GetNeighbors(BYTE x,y BYTE ARRAY n BYTE POINTER count) BYTE POINTER ptr pointer to the screen memory
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