Minimum Depth Of Binary Tree
You have been given a Binary Tree of integers, find the minimum depth of this Binary Tree. The minimum depth of a Binary Tree is the number of nodes along the shortest path from the root node down to the nearest leaf node.

Note:

A leaf is a node with no children.

For example:

For the given binary tree

Output: 2 The shortest path is from root node 1 to leaf node 2 which contains 2 nodes in the path. Hence, the minimum depth is 2.

Input Format:

The first line contains an integer 'T' which denotes the number of test cases or queries to be run. Then the test cases follow. The only line of each test case contains elements in the level order form. The line consists of values of nodes separated by a single space. In case a node is null, we take -1 in its place. For example, the input for the tree depicted in the below image would be :

1 2 3 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1

Explanation :

Level 1 : The root node of the tree is 1 Level 2 : Left child of 1 = 2 Right child of 1 = 3 Level 3 : Left child of 2 = 4 Right child of 2 = null (-1) Left child of 3 = 5 Right child of 3 = 6 Level 4 : Left child of 4 = null (-1) Right child of 4 = 7 Left child of 5 = null (-1) Right child of 5 = null (-1) Left child of 6 = null (-1) Right child of 6 = null (-1) Level 5 : Left child of 7 = null (-1) Right child of 7 = null (-1) The first not-null node (of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on. The input ends when all nodes at the last level are null (-1).

Note :

The above format was just to provide clarity on how the input is formed for a given tree. The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as: 1 2 3 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1

Output Format:

For each test case: Print an integer i.e. Minimum depth of the BInary Tree. Print output of each test case in a separate line.

Note:

You are not required to print the expected output, it has already been taken care of. Just implement the function.

Constraints:

1

Question

Minimum Depth Of Binary Tree

You have been given a Binary Tree of integers, find the minimum depth of this Binary Tree. The minimum depth of a Binary Tree is the number of nodes along the shortest path from the root node down to the nearest leaf node.

Note:

A leaf is a node with no children.

For example:

For the given binary tree

alt text

Output: 2
The shortest path is from root node 1 to leaf node 2 which contains 2 nodes in the path. Hence, the minimum depth is 2.

Input Format:

The first line contains an integer 'T' which denotes the number of test cases or queries to be run. Then the test cases follow.

The only line of each test case contains elements in the level order form. The line consists of values of nodes separated by a single space. In case a node is null, we take -1 in its place.

For example, the input for the tree depicted in the below image would be :

alt text

1
2 3
4 -1 5 6
-1 7 -1 -1 -1 -1
-1 -1

Explanation :

Level 1 :
The root node of the tree is 1

Level 2 :
Left child of 1 = 2
Right child of 1 = 3

Level 3 :
Left child of 2 = 4
Right child of 2 = null (-1)
Left child of 3 = 5
Right child of 3 = 6

Level 4 :
Left child of 4 = null (-1)
Right child of 4 = 7
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 6 = null (-1)
Right child of 6 = null (-1)

Level 5 :
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node (of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.
The input ends when all nodes at the last level are null (-1).

Note :

The above format was just to provide clarity on how the input is formed for a given tree. 

The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as:

1 2 3 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1

Output Format:

For each test case:

Print an integer i.e. Minimum depth of the BInary Tree.

Print output of each test case in a separate line.

Note:

You are not required to print the expected output, it has already been taken care of. Just implement the function.

Constraints:

1 <= T <= 10^2
0 <= N <= 10^3  

Time Limit: 1 sec

Accepted Answer

Depth-First-Search

We can write a recursive solution for finding the minimum depth in a Binary Tree. The idea here is to first find the minimum depths of left and right subtrees and then the minimum depth of the current node will be 1 + min(minDepthLeftSubtree, minDepthRightSubtree).

Here is the complete algorithm:

Traverse in given Binary Tree.
If currentNode is NULL, terminate recursion (return 0)
If currentNode is a leaf node, return 1.
If currentNode only has a left child, return 1 + the minimum depth of the left subtree.
If currentNode only has a right child, return 1 + the minimum depth of the right subtree.
If currentNode has both children, find the minimum depth of both subtrees and return 1 + min(minDepthLeftSubtree, minDepthRightSubtree).

Space Complexity: O(n)Explanation:

O(N), Where N is the number of nodes in the Binary Tree.

The size of the recursion stack during an inorder traversal can be at most the height of the tree. In the worst case, the height of a binary tree can be at most ‘N’ i.e. number of nodes (in case of a skewed tree).

Time Complexity: O(n)Explanation:

O(N), Where N is the number of nodes in the Binary Tree.

We will perform a full Depth-First-Search of the Binary Tree. Hence, complexity is linear.

Accepted Answer

Breadth-First-Search

A Depth-First-Search solution ends up with a complete traversal of the Binary Tree, even if the topmost leaf node is close to the root.

Now, the idea is to use a Level Order Traversal or Breadth-First-Search from the root node so that as soon as we encounter the closest leaf node, we can terminate the search. This will ensure that we will not traverse beyond the level of the closest leaf node and hence, reduce the time in finding the depth of the BInary Tree.

Space Complexity: O(logn)Explanation:

O(2 ^ D), Where D is the minimum depth of the Binary tree or the depth of the closet leaf node from the root.

As we will not traverse the tree beyond the level of the nearest leaf node, we can have at most 2^D nodes present in the level of this closest leaf node in the Queue (used for level order traversal).

Time Complexity: O(n)Explanation:

O(N), Where N is the number of nodes in the Binary Tree.

In the case of a complete Binary Tree, we still have to traverse all the nodes of the tree. Hence, the time complexity is linear.

You have been given a Binary Tree of integers, find the minimum depth of this Binary Tree. The minimum depth of a Binary Tree is the number of nodes along the shortest path from the root node down to the nearest leaf node.

Note:

For example:

Input Format:

Explanation :

Note :

Output Format:

Note:

Constraints:

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