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