Add lowest common ancestor to data structures (#732)

* add longest common ancestor in data structures

* add lowest common ancestor to data structures

data_structures/LCA.py

@@ -0,0 +1,91 @@
+import queue
+
+
+def swap(a, b):
+    a ^= b
+    b ^= a
+    a ^= b
+    return a, b
+
+
+# creating sparse table which saves each nodes 2^ith parent
+def creatSparse(max_node, parent):
+    j = 1
+    while (1 << j) < max_node:
+        for i in range(1, max_node + 1):
+            parent[j][i] = parent[j - 1][parent[j - 1][i]]
+        j += 1
+    return parent
+
+
+# returns lca of node u,v
+def LCA(u, v, level, parent):
+    # u must be deeper in the tree than v
+    if level[u] < level[v]:
+        u, v = swap(u, v)
+    # making depth of u same as depth of v
+    for i in range(18, -1, -1):
+        if level[u] - (1 << i) >= level[v]:
+            u = parent[i][u]
+    # at the same depth if u==v that mean lca is found
+    if u == v:
+        return u
+    # moving both nodes upwards till lca in found
+    for i in range(18, -1, -1):
+        if parent[i][u] != 0 and parent[i][u] != parent[i][v]:
+            u, v = parent[i][u], parent[i][v]
+    # returning longest common ancestor of u,v
+    return parent[0][u]
+
+
+# runs a breadth first search from root node of the tree
+# sets every nodes direct parent
+# parent of root node is set to 0
+# calculates depth of each node from root node
+def bfs(level, parent, max_node, graph, root=1):
+    level[root] = 0
+    q = queue.Queue(maxsize=max_node)
+    q.put(root)
+    while q.qsize() != 0:
+        u = q.get()
+        for v in graph[u]:
+            if level[v] == -1:
+                level[v] = level[u] + 1
+                q.put(v)
+                parent[0][v] = u
+    return level, parent
+
+
+def main():
+    max_node = 13
+    # initializing with 0
+    parent = [[0 for _ in range(max_node + 10)] for _ in range(20)]
+    # initializing with -1 which means every node is unvisited
+    level = [-1 for _ in range(max_node + 10)]
+    graph = {
+        1: [2, 3, 4],
+        2: [5],
+        3: [6, 7],
+        4: [8],
+        5: [9, 10],
+        6: [11],
+        7: [],
+        8: [12, 13],
+        9: [],
+        10: [],
+        11: [],
+        12: [],
+        13: []
+    }
+    level, parent = bfs(level, parent, max_node, graph, 1)
+    parent = creatSparse(max_node, parent)
+    print("LCA of node 1 and 3 is: ", LCA(1, 3, level, parent))
+    print("LCA of node 5 and 6 is: ", LCA(5, 6, level, parent))
+    print("LCA of node 7 and 11 is: ", LCA(7, 11, level, parent))
+    print("LCA of node 6 and 7 is: ", LCA(6, 7, level, parent))
+    print("LCA of node 4 and 12 is: ", LCA(4, 12, level, parent))
+    print("LCA of node 8 and 8 is: ", LCA(8, 8, level, parent))
+
+
+if __name__ == "__main__":
+    main()