From 335bf5b23acf19fe5c2b1b011579ab5d45782dd6 Mon Sep 17 00:00:00 2001
From: Mukundan314 <mukundan314@gmail.com>
Date: Wed, 6 Nov 2024 20:33:29 +0530
Subject: [PATCH] Refactor LazySegmentTree to be easier to modify

---
 pyrival/data_structures/LazySegmentTree.py | 76 ++++++++++++++--------
 1 file changed, 48 insertions(+), 28 deletions(-)

diff --git a/pyrival/data_structures/LazySegmentTree.py b/pyrival/data_structures/LazySegmentTree.py
index f6a5221..842578f 100644
--- a/pyrival/data_structures/LazySegmentTree.py
+++ b/pyrival/data_structures/LazySegmentTree.py
@@ -1,56 +1,74 @@
 class LazySegmentTree:
-    def __init__(self, data, default=0, func=max):
+    def __init__(self, data):
         """initialize the lazy segment tree with data"""
-        self._default = default
-        self._func = func
-
         self._len = len(data)
         self._size = _size = 1 << (self._len - 1).bit_length()
-        self._lazy = [0] * (2 * _size)
+        self._buffer_idx = 2 * _size
 
-        self.data = [default] * (2 * _size)
+        self.lazy = [0] * (2 * _size + 1)
+        self.data = [0] * (2 * _size + 1)
         self.data[_size:_size + self._len] = data
         for i in reversed(range(_size)):
-            self.data[i] = func(self.data[i + i], self.data[i + i + 1])
+            self._merge_data(i + i, i + i + 1, i)
 
     def __len__(self):
         return self._len
 
-    def _push(self, idx):
-        """push query on idx to its children"""
-        # Let the children know of the queries
-        q, self._lazy[idx] = self._lazy[idx], 0
+    def _get_range(self, a):
+        shift = self._size.bit_length() - a.bit_length()
+        return a << shift, (a << shift) + (1 << shift)
+
+    def _unset_lazy(self, a):
+        """a: lazy_idx; unset a"""
+        self.lazy[a] = 0
+
+    def _apply_to_data(self, a, b):
+        """a: lazy_idx, b: data_idx; apply a to b"""
+        l, r = self._get_range(b)
+        self.data[b] += self.lazy[a] * (r - l)
+
+    def _apply_to_lazy(self, a, b):
+        """a: lazy_idx, b: lazy_idx; apply a to b"""
+        self.lazy[b] += self.lazy[a]
 
-        self._lazy[2 * idx] += q
-        self._lazy[2 * idx + 1] += q
-        self.data[2 * idx] += q
-        self.data[2 * idx + 1] += q
+    def _merge_data(self, a, b, c):
+        """a: data_idx, b: data_idx, c: data_idx; merge a and b store result in c"""
+        self.data[c] = self.data[a] + self.data[b]
 
     def _update(self, idx):
         """updates the node idx to know of all queries applied to it via its ancestors"""
         for i in reversed(range(1, idx.bit_length())):
-            self._push(idx >> i)
+            _idx = idx >> i
+            self._apply_to_data(_idx, 2 * _idx)
+            self._apply_to_lazy(_idx, 2 * _idx)
+            self._apply_to_data(_idx, 2 * _idx + 1)
+            self._apply_to_lazy(_idx, 2 * _idx + 1)
+            self._unset_lazy(_idx)
 
     def _build(self, idx):
         """make the changes to idx be known to its ancestors"""
         idx >>= 1
         while idx:
-            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) + self._lazy[idx]
+            self._merge_data(2 * idx, 2 * idx + 1, idx)
+            self._apply_to_data(idx, idx)
             idx >>= 1
 
-    def add(self, start, stop, value):
-        """lazily add value to [start, stop)"""
+    def apply(self, start, stop, value):
+        """lazily apply value to [start, stop)"""
         start = start_copy = start + self._size
         stop = stop_copy = stop + self._size
+
+        self.lazy[self._buffer_idx] = value
+
         while start < stop:
             if start & 1:
-                self._lazy[start] += value
-                self.data[start] += value
+                self._apply_to_lazy(self._buffer_idx, start)
+                self._apply_to_data(self._buffer_idx, start)
                 start += 1
             if stop & 1:
                 stop -= 1
-                self._lazy[stop] += value
-                self.data[stop] += value
+                self._apply_to_lazy(self._buffer_idx, stop)
+                self._apply_to_data(self._buffer_idx, stop)
             start >>= 1
             stop >>= 1
 
@@ -58,7 +76,7 @@ def add(self, start, stop, value):
         self._build(start_copy)
         self._build(stop_copy - 1)
 
-    def query(self, start, stop, default=0):
+    def query(self, start, stop):
         """func of data[start, stop)"""
         start += self._size
         stop += self._size
@@ -67,17 +85,19 @@ def query(self, start, stop, default=0):
         self._update(start)
         self._update(stop - 1)
 
-        res = default
+        self.data[self._buffer_idx] = 0
+
         while start < stop:
             if start & 1:
-                res = self._func(res, self.data[start])
+                self._merge_data(self._buffer_idx, start, self._buffer_idx)
                 start += 1
             if stop & 1:
                 stop -= 1
-                res = self._func(res, self.data[stop])
+                self._merge_data(self._buffer_idx, stop, self._buffer_idx)
             start >>= 1
             stop >>= 1
-        return res
+
+        return self.data[self._buffer_idx]
 
     def __repr__(self):
         return "LazySegmentTree({0})".format(self.data)