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| 1 | +# https://en.wikipedia.org/wiki/Tree_traversal |
| 2 | + |
| 3 | + |
| 4 | +class Node: |
| 5 | + """ |
| 6 | + A Node has data variable and pointers to its left and right nodes. |
| 7 | + """ |
| 8 | + |
| 9 | + def __init__(self, data): |
| 10 | + self.left = None |
| 11 | + self.right = None |
| 12 | + self.data = data |
| 13 | + |
| 14 | + |
| 15 | +def make_tree() -> Node: |
| 16 | + root = Node(1) |
| 17 | + root.left = Node(2) |
| 18 | + root.right = Node(3) |
| 19 | + root.left.left = Node(4) |
| 20 | + root.left.right = Node(5) |
| 21 | + return root |
| 22 | + |
| 23 | + |
| 24 | +def preorder(root: Node): |
| 25 | + """ |
| 26 | + Pre-order traversal visits root node, left subtree, right subtree. |
| 27 | + >>> preorder(make_tree()) |
| 28 | + [1, 2, 4, 5, 3] |
| 29 | + """ |
| 30 | + return [root.data] + preorder(root.left) + preorder(root.right) if root else [] |
| 31 | + |
| 32 | + |
| 33 | +def postorder(root: Node): |
| 34 | + """ |
| 35 | + Post-order traversal visits left subtree, right subtree, root node. |
| 36 | + >>> postorder(make_tree()) |
| 37 | + [4, 5, 2, 3, 1] |
| 38 | + """ |
| 39 | + return postorder(root.left) + postorder(root.right) + [root.data] if root else [] |
| 40 | + |
| 41 | + |
| 42 | +def inorder(root: Node): |
| 43 | + """ |
| 44 | + In-order traversal visits left subtree, root node, right subtree. |
| 45 | + >>> inorder(make_tree()) |
| 46 | + [4, 2, 5, 1, 3] |
| 47 | + """ |
| 48 | + return inorder(root.left) + [root.data] + inorder(root.right) if root else [] |
| 49 | + |
| 50 | + |
| 51 | +def height(root: Node): |
| 52 | + """ |
| 53 | + Recursive function for calculating the height of the binary tree. |
| 54 | + >>> height(None) |
| 55 | + 0 |
| 56 | + >>> height(make_tree()) |
| 57 | + 3 |
| 58 | + """ |
| 59 | + return (max(height(root.left), height(root.right)) + 1) if root else 0 |
| 60 | + |
| 61 | + |
| 62 | +def level_order_1(root: Node): |
| 63 | + """ |
| 64 | + Print whole binary tree in Level Order Traverse. |
| 65 | + Level Order traverse: Visit nodes of the tree level-by-level. |
| 66 | + """ |
| 67 | + if not root: |
| 68 | + return |
| 69 | + temp = root |
| 70 | + que = [temp] |
| 71 | + while len(que) > 0: |
| 72 | + print(que[0].data, end=" ") |
| 73 | + temp = que.pop(0) |
| 74 | + if temp.left: |
| 75 | + que.append(temp.left) |
| 76 | + if temp.right: |
| 77 | + que.append(temp.right) |
| 78 | + return que |
| 79 | + |
| 80 | + |
| 81 | +def level_order_2(root: Node, level: int): |
| 82 | + """ |
| 83 | + Level-wise traversal: Print all nodes present at the given level of the binary tree |
| 84 | + """ |
| 85 | + if not root: |
| 86 | + return root |
| 87 | + if level == 1: |
| 88 | + print(root.data, end=" ") |
| 89 | + elif level > 1: |
| 90 | + level_order_2(root.left, level - 1) |
| 91 | + level_order_2(root.right, level - 1) |
| 92 | + |
| 93 | + |
| 94 | +def print_left_to_right(root: Node, level: int): |
| 95 | + """ |
| 96 | + Print elements on particular level from left to right direction of the binary tree. |
| 97 | + """ |
| 98 | + if not root: |
| 99 | + return |
| 100 | + if level == 1: |
| 101 | + print(root.data, end=" ") |
| 102 | + elif level > 1: |
| 103 | + print_left_to_right(root.left, level - 1) |
| 104 | + print_left_to_right(root.right, level - 1) |
| 105 | + |
| 106 | + |
| 107 | +def print_right_to_left(root: Node, level: int): |
| 108 | + """ |
| 109 | + Print elements on particular level from right to left direction of the binary tree. |
| 110 | + """ |
| 111 | + if not root: |
| 112 | + return |
| 113 | + if level == 1: |
| 114 | + print(root.data, end=" ") |
| 115 | + elif level > 1: |
| 116 | + print_right_to_left(root.right, level - 1) |
| 117 | + print_right_to_left(root.left, level - 1) |
| 118 | + |
| 119 | + |
| 120 | +def zigzag(root: Node): |
| 121 | + """ |
| 122 | + ZigZag traverse: Print node left to right and right to left, alternatively. |
| 123 | + """ |
| 124 | + flag = 0 |
| 125 | + height_tree = height(root) |
| 126 | + for h in range(1, height_tree + 1): |
| 127 | + if flag == 0: |
| 128 | + print_left_to_right(root, h) |
| 129 | + flag = 1 |
| 130 | + else: |
| 131 | + print_right_to_left(root, h) |
| 132 | + flag = 0 |
| 133 | + |
| 134 | + |
| 135 | +def main(): # Main function for testing. |
| 136 | + """ |
| 137 | + Create binary tree. |
| 138 | + """ |
| 139 | + root = make_tree() |
| 140 | + """ |
| 141 | + All Traversals of the binary are as follows: |
| 142 | + """ |
| 143 | + print(f" In-order Traversal is {inorder(root)}") |
| 144 | + print(f" Pre-order Traversal is {preorder(root)}") |
| 145 | + print(f"Post-order Traversal is {postorder(root)}") |
| 146 | + print(f"Height of Tree is {height(root)}") |
| 147 | + print("Complete Level Order Traversal is : ") |
| 148 | + level_order_1(root) |
| 149 | + print("\nLevel-wise order Traversal is : ") |
| 150 | + for h in range(1, height(root) + 1): |
| 151 | + level_order_2(root, h) |
| 152 | + print("\nZigZag order Traversal is : ") |
| 153 | + zigzag(root) |
| 154 | + print() |
| 155 | + |
| 156 | + |
| 157 | +if __name__ == "__main__": |
| 158 | + import doctest |
| 159 | + |
| 160 | + doctest.testmod() |
| 161 | + main() |
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