From c23f6b585f5b351a47da080cbbb0bd3dde897409 Mon Sep 17 00:00:00 2001
From: Ankan Mahapatra <69568975+ankan2526@users.noreply.github.com>
Date: Wed, 9 Oct 2024 14:12:35 +0530
Subject: [PATCH 1/3] Create binary_trie.py

Useful in Competitive Programming.

Contains method to find maximum and minimum XOR value.
---
 data_structures/trie/binary_trie.py | 65 +++++++++++++++++++++++++++++
 1 file changed, 65 insertions(+)
 create mode 100644 data_structures/trie/binary_trie.py

diff --git a/data_structures/trie/binary_trie.py b/data_structures/trie/binary_trie.py
new file mode 100644
index 000000000000..2796d97b0bd2
--- /dev/null
+++ b/data_structures/trie/binary_trie.py
@@ -0,0 +1,65 @@
+class BinaryTrie:
+    def __init__(self, max_bit_len=31):
+        self.inf = 1 << 63
+        self.cc = [0]
+        self.to = [[-1], [-1]]
+        self.mb = max_bit_len
+
+    def add(self, a):
+        u = 0
+        self.cc[u] += 1
+        for i in range(self.mb-1, -1, -1):
+            d = a >> i & 1
+            if self.to[d][u] == -1:
+                self.to[d][u] = len(self.cc)
+                self.to[0].append(-1)
+                self.to[1].append(-1)
+                self.cc.append(0)
+            u = self.to[d][u]
+            self.cc[u] += 1
+
+    def remove(self, a):
+        if self.cc[0] == 0: return False
+        uu = [0]
+        u = 0
+        for i in range(self.mb-1, -1, -1):
+            d = a >> i & 1
+            u = self.to[d][u]
+            if u == -1 or self.cc[u] == 0: return False
+            uu.append(u)
+        for u in uu: self.cc[u] -= 1
+        return True
+
+    def cnt(self, a):
+        u = 0
+        for i in range(self.mb-1, -1, -1):
+            d = a >> i & 1
+            u = self.to[d][u]
+            if u == -1 or self.cc[u] == 0: return 0
+        return self.cc[u]
+
+    def min_xor(self, a):
+        if self.cc[0] == 0: return self.inf
+        u, res = 0, 0
+        for i in range(self.mb-1, -1, -1):
+            d = a >> i & 1
+            v = self.to[d][u]
+            if v == -1 or self.cc[v] == 0:
+                res |= 1 << i
+                u = self.to[d ^ 1][u]
+            else:
+                u = v
+        return res
+
+    def max_xor(self, a):
+        if self.cc[0] == 0: return -self.inf
+        u, res = 0, 0
+        for i in range(self.mb-1, -1, -1):
+            d = a >> i & 1
+            v = self.to[d ^ 1][u]
+            if v == -1 or self.cc[v] == 0:
+                u = self.to[d][u]
+            else:
+                u = v
+                res |= 1 << i
+        return res

From 61d3a55474423ce9536ca323299fd4d42a37f71d Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 9 Oct 2024 08:48:59 +0000
Subject: [PATCH 2/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 data_structures/trie/binary_trie.py | 28 +++++++++++++++++-----------
 1 file changed, 17 insertions(+), 11 deletions(-)

diff --git a/data_structures/trie/binary_trie.py b/data_structures/trie/binary_trie.py
index 2796d97b0bd2..bf4aae2752e0 100644
--- a/data_structures/trie/binary_trie.py
+++ b/data_structures/trie/binary_trie.py
@@ -8,7 +8,7 @@ def __init__(self, max_bit_len=31):
     def add(self, a):
         u = 0
         self.cc[u] += 1
-        for i in range(self.mb-1, -1, -1):
+        for i in range(self.mb - 1, -1, -1):
             d = a >> i & 1
             if self.to[d][u] == -1:
                 self.to[d][u] = len(self.cc)
@@ -19,29 +19,34 @@ def add(self, a):
             self.cc[u] += 1
 
     def remove(self, a):
-        if self.cc[0] == 0: return False
+        if self.cc[0] == 0:
+            return False
         uu = [0]
         u = 0
-        for i in range(self.mb-1, -1, -1):
+        for i in range(self.mb - 1, -1, -1):
             d = a >> i & 1
             u = self.to[d][u]
-            if u == -1 or self.cc[u] == 0: return False
+            if u == -1 or self.cc[u] == 0:
+                return False
             uu.append(u)
-        for u in uu: self.cc[u] -= 1
+        for u in uu:
+            self.cc[u] -= 1
         return True
 
     def cnt(self, a):
         u = 0
-        for i in range(self.mb-1, -1, -1):
+        for i in range(self.mb - 1, -1, -1):
             d = a >> i & 1
             u = self.to[d][u]
-            if u == -1 or self.cc[u] == 0: return 0
+            if u == -1 or self.cc[u] == 0:
+                return 0
         return self.cc[u]
 
     def min_xor(self, a):
-        if self.cc[0] == 0: return self.inf
+        if self.cc[0] == 0:
+            return self.inf
         u, res = 0, 0
-        for i in range(self.mb-1, -1, -1):
+        for i in range(self.mb - 1, -1, -1):
             d = a >> i & 1
             v = self.to[d][u]
             if v == -1 or self.cc[v] == 0:
@@ -52,9 +57,10 @@ def min_xor(self, a):
         return res
 
     def max_xor(self, a):
-        if self.cc[0] == 0: return -self.inf
+        if self.cc[0] == 0:
+            return -self.inf
         u, res = 0, 0
-        for i in range(self.mb-1, -1, -1):
+        for i in range(self.mb - 1, -1, -1):
             d = a >> i & 1
             v = self.to[d ^ 1][u]
             if v == -1 or self.cc[v] == 0:

From d44b3787e2106b1225bfbec4db9d8808876ca68b Mon Sep 17 00:00:00 2001
From: cclauss <cclauss@users.noreply.github.com>
Date: Wed, 23 Sep 2026 12:46:37 +0000
Subject: [PATCH 3/3] updating DIRECTORY.md

---
 DIRECTORY.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 123f61d1b40b..9b32dd71cbef 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -402,6 +402,7 @@
     * Tests
       * [Test Suffix Tree](data_structures/suffix_tree/tests/test_suffix_tree.py)
   * Trie
+    * [Binary Trie](data_structures/trie/binary_trie.py)
     * [Radix Tree](data_structures/trie/radix_tree.py)
     * [Trie](data_structures/trie/trie.py)