Introduction to Algorithms learning Notes--12th Chapter two fork Find tree

Binary Search Tree Properties

Set X is a node in the two-fork lookup tree, and if Y is a node in the left subtree of x, then k[y]<=key[x]; if Y is a node in the right subtree k[y]>=k[x]

1 // Middle sequence traversal algorithm, output binary find all elements in tree T 2 inorder-tree-WALK (x)3if x!=nil4then     inorder-tree- WALK (left[x]) 5             print key[x]6             Inorder-tree-walk (Right[x])

Find

1 //Recursive version2tree-SEARCH (x,k)3 ifX=nil or k=Key[x]4Thenreturnx5 ifk<Key[x]6Thenreturntree-SEARCH (left[x],k)7     Else returntree-SEARCH (right[x],k)8 9 //non-recursive versionTeniterative-tree-SEARCH (x,k) One  whileX!=nil and k!=Key[x] A      Do ifk<Key[x] - Then X←left[x] -         ElseX←right[x] the returnX

Maximum elements, minimum elements, next and Prev

1 treeminimum (x)2  whileleft[x]!=Nil3      DoX←left[x]4 returnx5 6tree-MAXIMUM (x)7  whileright[x]!=Nil8      DoX←right[x]9 returnxTen  Onetree-successor (x) A ifright[x]!=Nil -Thenreturntree-Nimimum (right[x]) - Y←p[x] the  whileY!=nil and x=Right[y] -      DoX←y - Y←p[y] - returnY

Insert

1tree-INSERT (t,z)2 Y←nil3 X←root[t]4  whilex!=Nil5      Doy←x6         ifkey[z]<Key[x]7 Then X←left[x]8             ElseX←right[x]9 P[z]←yTen ify=Nil One Then root[t]←z A     Else ifKey[z]←key[y] - Then left[y]←z -         ElseRight[y]←z

Delete

1tree-DELETE (t,z)2 ifLeft[z]=nil or right[z]=Nil3 Then y←z4     Elsey←tree-successor (z)5 ifleft[y]!=Nil6 Then X←left[y]7     ElseX←right[y]8 ifx!=Nil9 Then P[x]←p[y]Ten ifp[y]=Nil One Then root[t]←x A     Else ify=Left[p[y]] - Then left[p[y]]←x -         Elseright[p[y]]←x the ify!=x - Then Key[z]←key[y] -Copy y's satellite data into Z - returnY

Introduction to Algorithms learning Notes--12th Chapter two fork Find tree