Port segtree

README.md

@@ -15,6 +15,7 @@ ac-library-python is a Python port of [AtCoder Library (ACL)](https://atcoder.jp
 #### Data structure
 
 + [Fenwick Tree](https://github.com/atcoder/ac-library/blob/master/document_en/fenwicktree.md)
++ segtree
 
 #### Math
 
@@ -32,7 +33,6 @@ ac-library-python is a Python port of [AtCoder Library (ACL)](https://atcoder.jp
 
 #### Data structure
 
-+ segtree
 + lazysegtree
 + string
 

README_ja.md

@@ -13,6 +13,7 @@ ac-library-pythonは、[AtCoder Library (ACL)](https://atcoder.jp/posts/517)のP
 #### データ構造
 
 + [Fenwick Tree](https://github.com/atcoder/ac-library/blob/master/document_ja/fenwicktree.md)
++ segtree
 
 #### 数学
 
@@ -30,7 +31,6 @@ ac-library-pythonは、[AtCoder Library (ACL)](https://atcoder.jp/posts/517)のP
 
 #### データ構造
 
-+ segtree
 + lazysegtree
 + string
 

atcoder/_bit.py

@@ -0,0 +1,15 @@
+def _ceil_pow2(n: int) -> int:
+    x = 0
+    while (1 << x) < n:
+        x += 1
+
+    return x
+
+
+def _bsf(n: int) -> int:
+    x = 0
+    while n % 2 == 0:
+        x += 1
+        n //= 2
+
+    return x

atcoder/segtree.py

@@ -0,0 +1,119 @@
+import typing
+
+import atcoder._bit
+
+
+class SegTree:
+    def __init__(self,
+                 op: typing.Callable[[typing.Any, typing.Any], typing.Any],
+                 e: typing.Any,
+                 v: typing.Union[int, typing.List[typing.Any]]) -> None:
+        self._op = op
+        self._e = e
+
+        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)
+
+        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
+        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
+
+        return self._d[p + self._size]
+
+    def prod(self, left: int, right: int) -> typing.Any:
+        assert 0 <= left <= right <= self._n
+        sml = self._e
+        smr = self._e
+        left += self._size
+        right += self._size
+
+        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 max_right(self, left: int,
+                  f: typing.Callable[[typing.Any], bool]) -> int:
+        assert 0 <= left <= self._n
+        assert f(self._e)
+
+        if left == self._n:
+            return self._n
+
+        left += self._size
+        sm = self._e
+
+        first = True
+        while first or (left & -left) != left:
+            first = False
+            while left % 2 == 0:
+                left >>= 1
+            if not f(self._op(sm, self._d[left])):
+                while left < self._size:
+                    left *= 2
+                    if f(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,
+                 f: typing.Callable[[typing.Any], bool]) -> int:
+        assert 0 <= right <= self._n
+        assert f(self._e)
+
+        if right == 0:
+            return 0
+
+        right += self._size
+        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 f(self._op(self._d[right], sm)):
+                while right < self._size:
+                    right = 2 * right + 1
+                    if f(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])

example/segtree_practice.py

@@ -0,0 +1,25 @@
+# https://atcoder.jp/contests/practice2/tasks/practice2_j
+
+import sys
+
+from atcoder.segtree import SegTree
+
+
+def main() -> None:
+    n, q = map(int, sys.stdin.readline().split())
+    a = list(map(int, sys.stdin.readline().split()))
+
+    segtree = SegTree(max, -1, a)
+
+    for _ in range(q):
+        t, x, y = map(int, sys.stdin.readline().split())
+        if t == 1:
+            segtree.set(x - 1, y)
+        elif t == 2:
+            print(segtree.prod(x - 1, y))
+        else:
+            print(segtree.max_right(x - 1, lambda v: v < y) + 1)
+
+
+if __name__ == '__main__':
+    main()

example/segtree_practice_reversed.py

@@ -0,0 +1,25 @@
+# https://atcoder.jp/contests/practice2/tasks/practice2_j
+
+import sys
+
+from atcoder.segtree import SegTree
+
+
+def main() -> None:
+    n, q = map(int, sys.stdin.readline().split())
+    a = list(map(int, sys.stdin.readline().split()))[::-1]
+
+    segtree = SegTree(max, -1, a)
+
+    for _ in range(q):
+        t, x, y = map(int, sys.stdin.readline().split())
+        if t == 1:
+            segtree.set(n - x, y)
+        elif t == 2:
+            print(segtree.prod(n - y, n - x + 1))
+        else:
+            print(n - segtree.min_left(n - x + 1, lambda v: v < y) + 1)
+
+
+if __name__ == '__main__':
+    main()