这是我创建的用于打印任何二叉树结构的函数。
它非常通用，只需要一个起始节点（root）和一个函数（或 lambda）即可获得标签和左/右子节点：
你通常会在你的 Node 类上这样使用它：
printBTree(rootNode,lambda n: (n.operand, n.left, n.right) )
# assuming the Node class has a string property named operand
# and left,right properties that return a Node or None
二次方程 (-b +/- sqrt(b**2 - 4*a*c))/(2*a) 可以这样打印：
# /
# ___/ \__
# +/- *
# / \ / \
# - sqrt 2 a
# \ \
# b -
# __/ \_
# ** *
# / \ / \
# b 2 4 *
# / \
# a c
这里是 printBTree 函数：
import functools as fn
def printBTree(node, nodeInfo=None, inverted=False, isTop=True):
# node value string and sub nodes
stringValue, leftNode, rightNode = nodeInfo(node)
stringValueWidth = len(stringValue)
# recurse to sub nodes to obtain line blocks on left and right
leftTextBlock = [] if not leftNode else printBTree(leftNode,nodeInfo,inverted,False)
rightTextBlock = [] if not rightNode else printBTree(rightNode,nodeInfo,inverted,False)
# count common and maximum number of sub node lines
commonLines = min(len(leftTextBlock),len(rightTextBlock))
subLevelLines = max(len(rightTextBlock),len(leftTextBlock))
# extend lines on shallower side to get same number of lines on both sides
leftSubLines = leftTextBlock + [""] * (subLevelLines - len(leftTextBlock))
rightSubLines = rightTextBlock + [""] * (subLevelLines - len(rightTextBlock))
# compute location of value or link bar for all left and right sub nodes
# * left node's value ends at line's width
# * right node's value starts after initial spaces
leftLineWidths = [ len(line) for line in leftSubLines ]
rightLineIndents = [ len(line)-len(line.lstrip(" ")) for line in rightSubLines ]
# top line value locations, will be used to determine position of current node & link bars
firstLeftWidth = (leftLineWidths + [0])[0]
firstRightIndent = (rightLineIndents + [0])[0]
# width of sub node link under node value (i.e. with slashes if any)
# aims to center link bars under the value if value is wide enough
#
# ValueLine: v vv vvvvvv vvvvv
# LinkLine: / \ / \ / \ / \
#
linkSpacing = min(stringValueWidth, 2 - stringValueWidth % 2)
leftLinkBar = 1 if leftNode else 0
rightLinkBar = 1 if rightNode else 0
minLinkWidth = leftLinkBar + linkSpacing + rightLinkBar
valueOffset = (stringValueWidth - linkSpacing) // 2
# find optimal position for right side top node
# * must allow room for link bars above and between left and right top nodes
# * must not overlap lower level nodes on any given line (allow gap of minSpacing)
# * can be offset to the left if lower subNodes of right node
# have no overlap with subNodes of left node
minSpacing = 2
rightNodePosition = fn.reduce(lambda r,i: max(r,i[0] + minSpacing + firstRightIndent - i[1]), \
zip(leftLineWidths,rightLineIndents[0:commonLines]), \
firstLeftWidth + minLinkWidth)
# extend basic link bars (slashes) with underlines to reach left and right
# top nodes.
#
# vvvvv
# __/ \__
# L R
#
linkExtraWidth = max(0, rightNodePosition - firstLeftWidth - minLinkWidth )
rightLinkExtra = linkExtraWidth // 2
leftLinkExtra = linkExtraWidth - rightLinkExtra
# build value line taking into account left indent and link bar extension (on left side)
valueIndent = max(0, firstLeftWidth + leftLinkExtra + leftLinkBar - valueOffset)
valueLine = " " * max(0,valueIndent) + stringValue
slash = "\\" if inverted else "/"
backslash = "/" if inverted else "\\"
uLine = "¯" if inverted else "_"
# build left side of link line
leftLink = "" if not leftNode else ( " " * firstLeftWidth + uLine * leftLinkExtra + slash)
# build right side of link line (includes blank spaces under top node value)
rightLinkOffset = linkSpacing + valueOffset * (1 - leftLinkBar)
rightLink = "" if not rightNode else ( " " * rightLinkOffset + backslash + uLine * rightLinkExtra )
# full link line (will be empty if there are no sub nodes)
linkLine = leftLink + rightLink
# will need to offset left side lines if right side sub nodes extend beyond left margin
# can happen if left subtree is shorter (in height) than right side subtree
leftIndentWidth = max(0,firstRightIndent - rightNodePosition)
leftIndent = " " * leftIndentWidth
indentedLeftLines = [ (leftIndent if line else "") + line for line in leftSubLines ]
# compute distance between left and right sublines based on their value position
# can be negative if leading spaces need to be removed from right side
mergeOffsets = [ len(line) for line in indentedLeftLines ]
mergeOffsets = [ leftIndentWidth + rightNodePosition - firstRightIndent - w for w in mergeOffsets ]
mergeOffsets = [ p if rightSubLines[i] else 0 for i,p in enumerate(mergeOffsets) ]
# combine left and right lines using computed offsets
# * indented left sub lines
# * spaces between left and right lines
# * right sub line with extra leading blanks removed.
mergedSubLines = zip(range(len(mergeOffsets)), mergeOffsets, indentedLeftLines)
mergedSubLines = [ (i,p,line + (" " * max(0,p)) ) for i,p,line in mergedSubLines ]
mergedSubLines = [ line + rightSubLines[i][max(0,-p):] for i,p,line in mergedSubLines ]
# Assemble final result combining
# * node value string
# * link line (if any)
# * merged lines from left and right sub trees (if any)
treeLines = [leftIndent + valueLine] + ( [] if not linkLine else [leftIndent + linkLine] ) + mergedSubLines
# invert final result if requested
treeLines = reversed(treeLines) if inverted and isTop else treeLines
# return intermediate tree lines or print final result
if isTop : print("\n".join(treeLines))
else : return treeLines
这是一个使用简单 TreeNode 类产生的输出类型的示例。
class TreeNode:
def __init__(self,rootValue):
self.value = rootValue
self.left = None
self.right = None
def addValue(self,newValue):
if newValue == self.value: return self
if newValue < self.value:
if self.left : return self.left.addValue(newValue)
self.left = TreeNode(newValue)
return self.left
if self.right : return self.right.addValue(newValue)
self.right = TreeNode(newValue)
return self.right
def printTree(self):
printBTree(self,lambda n:(str(n.value),n.left,n.right))
root = TreeNode(80)
root.addValue(50)
root.addValue(90)
root.addValue(10)
root.addValue(60)
root.addValue(30)
root.addValue(70)
root.addValue(55)
root.addValue(5)
root.addValue(35)
root.addValue(85)
root.printTree()
这会产生以下输出：
# 80
# ___/ \___
# 50 90
# __/ \__ /
# 10 60 85
# / \ / \
# 5 30 55 70
# \
# 35
该函数足够通用，可以处理未存储在对象层次结构中的二叉树结构。这是一个如何使用它从包含堆树的列表中打印的示例：
def printHeapTree(tree, inverted=False):
def getNode(index):
left = index * 2 + 1
right = index * 2 + 2
left = left if left < len(tree) and tree[left] else None
right = right if right < len(tree) and tree[right] else None
return (str(tree[index]), left, right)
printBTree(0,getNode,inverted)
formula = ["+","4","*",None,None,"2","75"]
printHeapTree(formula)
# +
# / \
# 4 *
# / \
# 2 75
该功能将自动调整更宽标签的缩进：
family = [ "Me","Paul","Rosa","Vincent","Jody","John","Kate"]
printHeapTree(family)
# Me
# ___/ \___
# Paul Rosa
# / \ / \
# Vincent Jody John Kate
它还可以颠倒打印树（适合于家谱）：
printHeapTree(family,inverted=True)
# Vincent Jody John Kate
# \ / \ /
# Paul Rosa
# ¯¯¯\ /¯¯¯
# Me