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Author: JO-Techs

Van Emde Boas Tree.py

@@ -0,0 +1,133 @@
+class VEBTree:
+    def __init__(self, u):
+        self.u = u  # Universe size (must be a power of two)
+        self.min_val = None
+        self.max_val = None
+
+        if u < 2:
+            raise ValueError("Universe size must be at least 2")
+        if (u & (u - 1)) != 0:
+            raise ValueError("Universe size must be a power of two")
+
+        self.summary = None
+        self.clusters = None
+
+        if u > 2:
+            exponent = u.bit_length() - 1
+            self.upper_sqrt = 1 << ((exponent + 1) // 2)
+            self.lower_sqrt = 1 << (exponent // 2)
+            self.summary = VEBTree(self.upper_sqrt)
+            self.clusters = [VEBTree(self.lower_sqrt) for _ in range(self.upper_sqrt)]
+
+    def member(self, x):
+        if x < 0 or x >= self.u:
+            return False
+        if x == self.min_val or x == self.max_val:
+            return True
+        if self.u == 2:
+            return False
+        cluster_idx = x // self.lower_sqrt
+        idx_in_cluster = x % self.lower_sqrt
+        return self.clusters[cluster_idx].member(idx_in_cluster)
+
+    def insert(self, x):
+        if x < 0 or x >= self.u:
+            raise ValueError("Value out of range")
+        if self.min_val is None:
+            self.min_val = self.max_val = x
+            return
+        if x < self.min_val:
+            x, self.min_val = self.min_val, x
+        if self.u > 2:
+            cluster_idx = x // self.lower_sqrt
+            idx_in_cluster = x % self.lower_sqrt
+            if self.clusters[cluster_idx].min_val is None:
+                self.summary.insert(cluster_idx)
+            self.clusters[cluster_idx].insert(idx_in_cluster)
+        if x > self.max_val:
+            self.max_val = x
+
+    def successor(self, x):
+        if x < 0 or x >= self.u:
+            return None
+        if self.u == 2:
+            if x == 0 and self.max_val == 1:
+                return 1
+            else:
+                return None
+        if self.min_val is not None and x < self.min_val:
+            return self.min_val
+        cluster_idx = x // self.lower_sqrt
+        idx_in_cluster = x % self.lower_sqrt
+        max_in_cluster = self.clusters[cluster_idx].max_val
+        if max_in_cluster is not None and idx_in_cluster < max_in_cluster:
+            offset = self.clusters[cluster_idx].successor(idx_in_cluster)
+            if offset is not None:
+                return cluster_idx * self.lower_sqrt + offset
+        else:
+            next_cluster = self.summary.successor(cluster_idx)
+            if next_cluster is not None:
+                offset = self.clusters[next_cluster].min_val
+                return next_cluster * self.lower_sqrt + offset
+            else:
+                if self.max_val is not None and x < self.max_val:
+                    return self.max_val
+        return None
+
+    def delete(self, x):
+        if x < 0 or x >= self.u:
+            raise ValueError("Value out of range")
+        if self.min_val == self.max_val:
+            if x == self.min_val:
+                self.min_val = self.max_val = None
+            return
+        if self.u == 2:
+            if x == self.min_val:
+                self.min_val = self.max_val
+            else:
+                self.max_val = self.min_val
+            return
+        if x == self.min_val:
+            first_cluster = self.summary.min_val
+            idx = self.clusters[first_cluster].min_val
+            self.min_val = first_cluster * self.lower_sqrt + idx
+            self.clusters[first_cluster].delete(idx)
+            if self.clusters[first_cluster].min_val is None:
+                self.summary.delete(first_cluster)
+        else:
+            cluster_idx = x // self.lower_sqrt
+            idx = x % self.lower_sqrt
+            self.clusters[cluster_idx].delete(idx)
+            if self.clusters[cluster_idx].min_val is None:
+                self.summary.delete(cluster_idx)
+        # Update max_val
+        if self.summary.max_val is None:
+            self.max_val = self.min_val
+        else:
+            last_cluster = self.summary.max_val
+            self.max_val = last_cluster * self.lower_sqrt + self.clusters[last_cluster].max_val
+
+    def get_min(self):
+        return self.min_val
+
+    def get_max(self):
+        return self.max_val
+
+# Example usage
+if __name__ == "__main__":
+    veb = VEBTree(16)
+    veb.insert(2)
+    veb.insert(3)
+    veb.insert(7)
+    veb.insert(14)
+    
+    print("Member 3:", veb.member(3))  # True
+    print("Member 4:", veb.member(4))  # False
+    
+    print("Successor of 3:", veb.successor(3))  # 7
+    print("Min:", veb.get_min())  # 2
+    print("Max:", veb.get_max())  # 14
+    
+    veb.delete(3)
+    print("Member 3 after delete:", veb.member(3))  # False
+    print("Successor of 2:", veb.successor(2))  # 7