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2D Segment Tree.py
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171 lines (149 loc) · 5.79 KB
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#2D Segment Tree
from operator import add
class CommonFunctions(object):
def treeSize(self, array):
n = 0
while(len(array) > (2**n)):
n = n+1
return 2*(2**n) - 1
def partialOverlap(self, queryRange, currentRange):
if(queryRange[0] > currentRange[0] and queryRange[1] < currentRange[1]):
return True
if(queryRange[0] <= currentRange[0] and queryRange[1] >= currentRange[0] and queryRange[1] <= currentRange[1]):
return True
if(queryRange[0] >= currentRange[0] and queryRange[0] <= currentRange[1] and queryRange[1] >= currentRange[1]):
return True
def completeOverlap(self, queryRange, currentRange):
if(queryRange == currentRange):
return True
if(queryRange[0] <= currentRange[0] and queryRange[1] >= currentRange[1]):
return True
def typeOfOverlap(self, queryRange, currentRange):
if(self.completeOverlap(queryRange, currentRange)):
return "Complete"
if(self.partialOverlap(queryRange, currentRange)):
return "Partial"
return None
class OneDSegmentTree(object):
def __init__(self, array):
self.array = array
self.tree = []
self.cf = CommonFunctions()
def treeOperation(self, left, right, index):
self.tree[index] = self.tree[left]+self.tree[right]
def createTree(self, low, high, parentIndex):
if(low == high):
self.tree[parentIndex] = self.array[low]
return
mid = (low+high)/2
#go left
self.createTree(low, mid, (2*parentIndex)+1)
#go right
self.createTree(mid+1, high, (2*parentIndex)+2)
#perform tree operation
self.treeOperation((2*parentIndex)+1, (2*parentIndex)+2, parentIndex)
def findQuery(self, queryRange, currentRange, treeIndex):
overlap = self.cf.typeOfOverlap(queryRange, currentRange)
if(overlap == "Complete"):
return self.tree[treeIndex]
if(overlap == "Partial"):
mid = (currentRange[0]+currentRange[1])/2
left = self.findQuery(queryRange, [currentRange[0], mid], (2*treeIndex)+1)
right = self.findQuery(queryRange, [mid+1, currentRange[1]], (2*treeIndex)+2)
return left+right
if(overlap == None):
return 0
def find(self, queryRange):
return self.findQuery(queryRange, [0, len(self.array)-1], 0)
def logic(self):
size = self.cf.treeSize(self.array)
self.tree = [0 for i in range(size)]
self.createTree(0, len(self.array)-1, 0)
class TwoDSegmentTree(object):
def __init__(self, matrix):
self.matrix = matrix
#this array will hold rows of 1d segment tree
self.array = [matrix[i] for i in range(len(matrix))]
self.tree = []
self.cf = CommonFunctions()
def add2Lists(self, list1, list2):
return list( map(add, list1, list2) )
def treeOperation(self, left, right, index):
obj = OneDSegmentTree([])
obj.array = self.add2Lists(self.tree[left].array, self.tree[right].array)
obj.tree = self.add2Lists(self.tree[left].tree, self.tree[right].tree)
self.tree[index] = obj
def createRowTree(self, row):
obj = OneDSegmentTree(self.array[row])
obj.logic()
return obj
def createTree(self, low, high, parentIndex):
if(low == high):
self.tree[parentIndex] = self.createRowTree(low)
return
mid = (low+high)/2
#go left
self.createTree(low, mid, (2*parentIndex)+1)
#go right
self.createTree(mid+1, high, (2*parentIndex)+2)
#perform tree operation
self.treeOperation((2*parentIndex)+1, (2*parentIndex)+2, parentIndex)
def flattenList(self, array, output):
for item in array:
if isinstance(item, (list,)):
self.flattenList(item, output)
elif(item != None):
output.append(item)
return output
def findRows(self, queryRange, currentRange, treeIndex):
print queryRange, currentRange, treeIndex,
overlap = self.cf.typeOfOverlap(queryRange, currentRange)
print overlap
if(overlap == "Complete"):
return self.tree[treeIndex]
if(overlap == "Partial"):
mid = (currentRange[0]+currentRange[1])/2
left = self.findRows(queryRange, [currentRange[0], mid], (2*treeIndex)+1)
right = self.findRows(queryRange, [mid+1, currentRange[1]], (2*treeIndex)+2)
return [left, right]
if(overlap == None):
return None
def find(self, queryRange):
rowQueryRange = [queryRange[0][0], queryRange[1][0]]
colQueryRange = [queryRange[0][1], queryRange[1][1]]
queryRows = self.findRows(rowQueryRange, [0, len(self.matrix)-1], 0)
#flatten the list
rows = self.flattenList(queryRows, [])
total = 0
for row in rows:
if(row):
total = total + row.find(colQueryRange)
return total
def logic(self):
size = self.cf.treeSize(self.array)
self.tree = [None for i in range(size)]
self.createTree(0, len(self.array)-1, 0)
print self.tree
for tree in self.tree:
if(tree):
print tree.tree
#Main
m1 = [
[1,2,3,4],
[5,6,7,8],
[1,7,5,9],
[3,0,6,2]
]
obj1 = TwoDSegmentTree(m1)
obj1.logic()
print obj1.find([[1,1], [2,2]])
m2 = [
[3, 0, 1, 4, 2],
[5, 6, 3, 2, 1],
[1, 2, 0, 1, 5],
[4, 1, 0, 1, 7],
[1, 0, 3, 0, 5]
]
obj2 = TwoDSegmentTree(m2)
obj2.logic()
print obj2.find([[2,1], [4,3]])