Python/data_structures/Binary Tree/LazySegmentTree.py

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from __future__ import print_function
import math
class SegmentTree:
def __init__(self, N):
self.N = N
self.st = [0 for i in range(0,4*N)] # approximate the overall size of segment tree with array N
self.lazy = [0 for i in range(0,4*N)] # create array to store lazy update
self.flag = [0 for i in range(0,4*N)] # flag for lazy update
def left(self, idx):
return idx*2
def right(self, idx):
return idx*2 + 1
def build(self, idx, l, r, A):
if l==r:
self.st[idx] = A[l-1]
else :
mid = (l+r)//2
self.build(self.left(idx),l,mid, A)
self.build(self.right(idx),mid+1,r, A)
self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)])
# update with O(lg N) (Normal segment tree without lazy update will take O(Nlg N) for each update)
def update(self, idx, l, r, a, b, val): # update(1, 1, N, a, b, v) for update val v to [a,b]
if self.flag[idx] == True:
self.st[idx] = self.lazy[idx]
self.flag[idx] = False
if l!=r:
self.lazy[self.left(idx)] = self.lazy[idx]
self.lazy[self.right(idx)] = self.lazy[idx]
self.flag[self.left(idx)] = True
self.flag[self.right(idx)] = True
if r < a or l > b:
return True
if l >= a and r <= b :
self.st[idx] = val
if l!=r:
self.lazy[self.left(idx)] = val
self.lazy[self.right(idx)] = val
self.flag[self.left(idx)] = True
self.flag[self.right(idx)] = True
return True
mid = (l+r)//2
self.update(self.left(idx),l,mid,a,b,val)
self.update(self.right(idx),mid+1,r,a,b,val)
self.st[idx] = max(self.st[self.left(idx)] , self.st[self.right(idx)])
return True
# query with O(lg N)
def query(self, idx, l, r, a, b): #query(1, 1, N, a, b) for query max of [a,b]
if self.flag[idx] == True:
self.st[idx] = self.lazy[idx]
self.flag[idx] = False
if l != r:
self.lazy[self.left(idx)] = self.lazy[idx]
self.lazy[self.right(idx)] = self.lazy[idx]
self.flag[self.left(idx)] = True
self.flag[self.right(idx)] = True
if r < a or l > b:
return -math.inf
if l >= a and r <= b:
return self.st[idx]
mid = (l+r)//2
q1 = self.query(self.left(idx),l,mid,a,b)
q2 = self.query(self.right(idx),mid+1,r,a,b)
return max(q1,q2)
def showData(self):
showList = []
for i in range(1,N+1):
showList += [self.query(1, 1, self.N, i, i)]
print (showList)
if __name__ == '__main__':
A = [1,2,-4,7,3,-5,6,11,-20,9,14,15,5,2,-8]
N = 15
segt = SegmentTree(N)
segt.build(1,1,N,A)
print (segt.query(1,1,N,4,6))
print (segt.query(1,1,N,7,11))
print (segt.query(1,1,N,7,12))
segt.update(1,1,N,1,3,111)
print (segt.query(1,1,N,1,15))
segt.update(1,1,N,7,8,235)
segt.showData()