From 2617de848ea6f8e209c871dd1ac488401f1aace7 Mon Sep 17 00:00:00 2001
From: Sarot Busala <sabuza97@gmail.com>
Date: Fri, 20 Oct 2017 18:47:06 +0700
Subject: [PATCH] Add Lazy Segment Tree

Add Lazy Segment Tree with Lazy Approach
---
 .../Binary Tree/LazySegmentTree.py            | 90 +++++++++++++++++++
 1 file changed, 90 insertions(+)
 create mode 100644 data_structures/Binary Tree/LazySegmentTree.py

diff --git a/data_structures/Binary Tree/LazySegmentTree.py b/data_structures/Binary Tree/LazySegmentTree.py
new file mode 100644
index 000000000..bbd880a06
--- /dev/null
+++ b/data_structures/Binary Tree/LazySegmentTree.py	
@@ -0,0 +1,90 @@
+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()