Port lazysegtree

README.md

@@ -16,6 +16,7 @@ ac-library-python is a Python port of [AtCoder Library (ACL)](https://atcoder.jp
 
 + [Fenwick Tree](https://github.com/atcoder/ac-library/blob/master/document_en/fenwicktree.md)
 + segtree
++ lazysegtree
 
 #### Math
 
@@ -34,7 +35,6 @@ ac-library-python is a Python port of [AtCoder Library (ACL)](https://atcoder.jp
 
 #### Data structure
 
-+ lazysegtree
 + string
 
 #### Math

README_ja.md

@@ -14,6 +14,7 @@ ac-library-pythonは、[AtCoder Library (ACL)](https://atcoder.jp/posts/517)のP
 
 + [Fenwick Tree](https://github.com/atcoder/ac-library/blob/master/document_ja/fenwicktree.md)
 + segtree
++ lazysegtree
 
 #### 数学
 
@@ -32,7 +33,6 @@ ac-library-pythonは、[AtCoder Library (ACL)](https://atcoder.jp/posts/517)のP
 
 #### データ構造
 
-+ lazysegtree
 + string
 
 #### 数学

atcoder/lazysegtree.py

@@ -0,0 +1,204 @@
+import typing
+
+import atcoder._bit
+
+
+class LazySegTree:
+    def __init__(
+            self,
+            op: typing.Callable[[typing.Any, typing.Any], typing.Any],
+            e: typing.Any,
+            mapping: typing.Callable[[typing.Any, typing.Any], typing.Any],
+            composition: typing.Callable[[typing.Any, typing.Any], typing.Any],
+            id_: typing.Any,
+            v: typing.Union[int, typing.List[typing.Any]]) -> None:
+        self._op = op
+        self._e = e
+        self._mapping = mapping
+        self._composition = composition
+        self._id = id_
+
+        if isinstance(v, int):
+            v = [e] * v
+
+        self._n = len(v)
+        self._log = atcoder._bit._ceil_pow2(self._n)
+        self._size = 1 << self._log
+        self._d = [e] * (2 * self._size)
+        self._lz = [self._id] * self._size
+        for i in range(self._n):
+            self._d[self._size + i] = v[i]
+        for i in range(self._size - 1, 0, -1):
+            self._update(i)
+
+    def set(self, p: int, x: typing.Any) -> None:
+        assert 0 <= p < self._n
+
+        p += self._size
+        for i in range(self._log, 0, -1):
+            self._push(p >> i)
+        self._d[p] = x
+        for i in range(1, self._log + 1):
+            self._update(p >> i)
+
+    def get(self, p: int) -> typing.Any:
+        assert 0 <= p < self._n
+
+        p += self._size
+        for i in range(self._log, 0, -1):
+            self._push(p >> i)
+        return self._d[p]
+
+    def prod(self, left: int, right: int) -> typing.Any:
+        assert 0 <= left <= right <= self._n
+
+        if left == right:
+            return self._e
+
+        left += self._size
+        right += self._size
+
+        for i in range(self._log, 0, -1):
+            if ((left >> i) << i) != left:
+                self._push(left >> i)
+            if ((right >> i) << i) != right:
+                self._push(right >> i)
+
+        sml = self._e
+        smr = self._e
+        while left < right:
+            if left & 1:
+                sml = self._op(sml, self._d[left])
+                left += 1
+            if right & 1:
+                right -= 1
+                smr = self._op(self._d[right], smr)
+            left >>= 1
+            right >>= 1
+
+        return self._op(sml, smr)
+
+    def all_prod(self) -> typing.Any:
+        return self._d[1]
+
+    def apply(self, left: int, right: typing.Optional[int] = None,
+              f: typing.Optional[typing.Any] = None):
+        assert f is not None
+
+        if right is None:
+            p = left
+            assert 0 <= left < self._n
+
+            p += self._size
+            for i in range(self._log, 0, -1):
+                self._push(p >> i)
+            self._d[p] = self._mapping(f, self._d[p])
+            for i in range(1, self._log + 1):
+                self._update(p >> i)
+        else:
+            assert 0 <= left <= right <= self._n
+            if left == right:
+                return
+
+            left += self._size
+            right += self._size
+
+            for i in range(self._log, 0, -1):
+                if ((left >> i) << i) != left:
+                    self._push(left >> i)
+                if ((right >> i) << i) != right:
+                    self._push((right - 1) >> i)
+
+            l2 = left
+            r2 = right
+            while left < right:
+                if left & 1:
+                    self._all_apply(left, f)
+                    left += 1
+                if right & 1:
+                    right -= 1
+                    self._all_apply(right, f)
+                left >>= 1
+                right >>= 1
+            left = l2
+            right = r2
+
+            for i in range(1, self._log + 1):
+                if ((left >> i) << i) != left:
+                    self._update(left >> i)
+                if ((right >> i) << i) != right:
+                    self._update((right - 1) >> i)
+
+    def max_right(
+            self, left: int, g: typing.Callable[[typing.Any], bool]) -> int:
+        assert 0 <= left <= self._n
+        assert g(self._e)
+
+        if left == self._n:
+            return self._n
+
+        left += self._size
+        for i in range(self._log, 0, -1):
+            self._push(left >> i)
+
+        sm = self._e
+        first = True
+        while first or (left & -left) != left:
+            first = False
+            while left % 2 == 0:
+                left >>= 1
+            if not g(self._op(sm, self._d[left])):
+                while left < self._size:
+                    self._push(left)
+                    left *= 2
+                    if g(self._op(sm, self._d[left])):
+                        sm = self._op(sm, self._d[left])
+                        left += 1
+                return left - self._size
+            sm = self._op(sm, self._d[left])
+            left += 1
+
+        return self._n
+
+    def min_left(self, right: int, g: typing.Any) -> int:
+        assert 0 <= right <= self._n
+        assert g(self._e)
+
+        if right == 0:
+            return 0
+
+        right += self._size
+        for i in range(self._log, 0, -1):
+            self._push((right - 1) >> i)
+
+        sm = self._e
+        first = True
+        while first or (right & -right) != right:
+            first = False
+            right -= 1
+            while right > 1 and right % 2:
+                right >>= 1
+            if not g(self._op(self._d[right], sm)):
+                while right < self._size:
+                    self._push(right)
+                    right = 2 * right + 1
+                    if g(self._op(self._d[right], sm)):
+                        sm = self._op(self._d[right], sm)
+                        right -= 1
+                return right + 1 - self._size
+            sm = self._op(self._d[right], sm)
+
+        return 0
+
+    def _update(self, k: int) -> None:
+        self._d[k] = self._op(self._d[2 * k], self._d[2 * k + 1])
+
+    def _all_apply(self, k: int, f: typing.Any) -> None:
+        self._d[k] = self._mapping(f, self._d[k])
+        if k < self._size:
+            self._lz[k] = self._composition(f, self._lz[k])
+
+    def _push(self, k: int) -> None:
+        self._all_apply(2 * k, self._lz[k])
+        self._all_apply(2 * k + 1, self._lz[k])
+        self._lz[k] = self._id

atcoder/modint.py

@@ -1,5 +1,4 @@
 from __future__ import annotations
-import copy
 import typing
 
 import atcoder._math
@@ -37,27 +36,36 @@ def val(self) -> int:
         return self._v
 
     def __iadd__(self, rhs: typing.Union[Modint, int]) -> Modint:
-        rhs = self._asmodint(rhs)
-        self._v += rhs._v
+        if isinstance(rhs, Modint):
+            self._v += rhs._v
+        else:
+            self._v += rhs
         if self._v >= self._mod:
             self._v -= self._mod
         return self
 
     def __isub__(self, rhs: typing.Union[Modint, int]) -> Modint:
-        rhs = self._asmodint(rhs)
-        self._v -= rhs._v
+        if isinstance(rhs, Modint):
+            self._v -= rhs._v
+        else:
+            self._v -= rhs
         if self._v < 0:
             self._v += self._mod
         return self
 
     def __imul__(self, rhs: typing.Union[Modint, int]) -> Modint:
-        rhs = self._asmodint(rhs)
-        self._v = self._v * rhs._v % self._mod
+        if isinstance(rhs, Modint):
+            self._v = self._v * rhs._v % self._mod
+        else:
+            self._v = self._v * rhs % self._mod
         return self
 
     def __ifloordiv__(self, rhs: typing.Union[Modint, int]) -> Modint:
-        rhs = self._asmodint(rhs)
-        self *= rhs.inv()
+        if isinstance(rhs, Modint):
+            inv = rhs.inv()._v
+        else:
+            inv = atcoder._math._inv_gcd(rhs, self._mod)[1]
+        self._v = self._v * inv % self._mod
         return self
 
     def __pos__(self) -> Modint:
@@ -79,42 +87,47 @@ def inv(self) -> Modint:
         return Modint(eg[1])
 
     def __add__(self, rhs: typing.Union[Modint, int]) -> Modint:
-        rhs = self._asmodint(rhs)
-        result = copy.deepcopy(self)
-        result += rhs
-        return result
+        if isinstance(rhs, Modint):
+            result = self._v + rhs._v
+            if result >= self._mod:
+                result -= self._mod
+            return raw(result)
+        else:
+            return Modint(self._v + rhs)
 
     def __sub__(self, rhs: typing.Union[Modint, int]) -> Modint:
-        rhs = self._asmodint(rhs)
-        result = copy.deepcopy(self)
-        result -= rhs
-        return result
+        if isinstance(rhs, Modint):
+            result = self._v - rhs._v
+            if result < 0:
+                result += self._mod
+            return raw(result)
+        else:
+            return Modint(self._v - rhs)
 
     def __mul__(self, rhs: typing.Union[Modint, int]) -> Modint:
-        rhs = self._asmodint(rhs)
-        result = copy.deepcopy(self)
-        result *= rhs
-        return result
+        if isinstance(rhs, Modint):
+            return Modint(self._v * rhs._v)
+        else:
+            return Modint(self._v * rhs)
 
     def __floordiv__(self, rhs: typing.Union[Modint, int]) -> Modint:
-        rhs = self._asmodint(rhs)
-        result = copy.deepcopy(self)
-        result //= rhs
-        return result
+        if isinstance(rhs, Modint):
+            inv = rhs.inv()._v
+        else:
+            inv = atcoder._math._inv_gcd(rhs, self._mod)[1]
+        return Modint(self._v * inv)
 
     def __eq__(self, rhs: typing.Union[Modint, int]) -> bool:
-        rhs = self._asmodint(rhs)
-        return self._v == rhs._v
+        if isinstance(rhs, Modint):
+            return self._v == rhs._v
+        else:
+            return self._v == rhs
 
     def __ne__(self, rhs: typing.Union[Modint, int]) -> bool:
-        rhs = self._asmodint(rhs)
-        return self._v != rhs._v
-
-    def _asmodint(self, rhs: typing.Union[Modint, int]) -> Modint:
         if isinstance(rhs, Modint):
-            return rhs
+            return self._v != rhs._v
         else:
-            return Modint(rhs)
+            return self._v != rhs
 
 
 def raw(v: int) -> Modint: