remove nodes from a binary treei based on length

Author: danrusei

README.md

@@ -71,7 +71,7 @@ WIP, the descriptions of the below `unsolved yet` problems can be found in the [
 - [] Check whether a binary tree is a full binary tree or not
 - [x] [Bottom View Binary Tree](https://github.com/danrusei/algorithms_with_Go/tree/main/binary_tree/bottom_view)
 - [] Print Nodes in Top View of Binary Tree
-- [] Remove nodes on root to leaf paths of length < K
+- [x] [Remove nodes on root to leaf paths of length < K](https://github.com/danrusei/algorithms_with_Go/tree/main/binary_tree/remove_nodes)
 - [] Lowest Common Ancestor in a Binary Search Tree
 - [] Check if a binary tree is subtree of another binary tree
 - [] Reverse alternate levels of a perfect binary tree

binary_tree/remove_nodes/README.md

@@ -0,0 +1,56 @@
+# Remove nodes on root to leaf paths of length < K
+
+Problem description: [GeeksforGeeks](https://www.geeksforgeeks.org/remove-nodes-root-leaf-paths-length-k/amp/)
+
+Given a Binary Tree and a number k, remove all nodes that lie only on root to leaf path(s) of length smaller than k. If a node X lies on multiple root-to-leaf paths and if any of the paths has path length >= k, then X is not deleted from Binary Tree. In other words a node is deleted if all paths going through it have lengths smaller than k.
+
+## Example
+
+Consider the following example Binary Tree
+
+```bash
+               1
+           /      \
+         2          3
+      /     \         \
+    4         5        6
+  /                   /
+ 7                   8 
+
+Input: Root of above Binary Tree
+       k = 4
+
+Output: The tree should be changed to following  
+           1
+        /     \
+      2          3
+     /             \
+   4                 6
+ /                  /
+7                  8
+
+There are 3 paths 
+i) 1->2->4->7      path length = 4
+ii) 1->2->5        path length = 3
+iii) 1->3->6->8    path length = 4 
+
+There is only one path " 1->2->5 " of length smaller than 4.  The node 5 is the only node that lies only on this path, so node 5 is removed. Nodes 2 and 1 are not removed as they are parts of other paths of length 4 as well.
+
+If k is 5 or greater than 5, then whole tree is deleted. 
+If k is 3 or less than 3, then nothing is deleted.
+```
+
+## Algorithm
+
+* Traverse the tree in postorder fashion so that if a leaf node path length is shorter than k, then that node and  all of its descendants till the node which are not on some other path are removed.
+* If root is a leaf node and it's level is less than k then remove this node.
+
+## Result
+
+```bash
+$ go run main.go 
+In order traversal of the original tree:
+((((7) 4) 2 (5)) 1 (3 ((8) 6)))
+In order traversal of the modified tree:
+((((7) 4) 2) 1 (3 ((8) 6)))
+```

binary_tree/remove_nodes/main.go

@@ -0,0 +1,50 @@
+package main
+
+import (
+	"fmt"
+
+	binarytree "github.com/danrusei/algorithms_with_go/binary_tree"
+)
+
+func removeShortPath(tree *binarytree.Tree, level int, k int) *binarytree.Tree {
+	if tree == nil {
+		return nil
+	}
+
+	// Traverse the tree in postorder fashion so that if a leaf
+	// node path length is shorter than k, then that node and
+	// all of its descendants till the node which are not
+	// on some other path are removed.
+	tree.Left = removeShortPath(tree.Left, level+1, k)
+	tree.Right = removeShortPath(tree.Right, level+1, k)
+
+	if tree.Left == nil && tree.Right == nil && level < k {
+		tree = nil
+	}
+
+	return tree
+}
+
+func main() {
+
+	tree := binarytree.NewTree(1)
+	tree.Left = binarytree.NewTree(2)
+	tree.Right = binarytree.NewTree(3)
+	tree.Left.Left = binarytree.NewTree(4)
+	tree.Left.Right = binarytree.NewTree(5)
+	tree.Left.Left.Left = binarytree.NewTree(7)
+	tree.Right.Right = binarytree.NewTree(6)
+	tree.Right.Right.Left = binarytree.NewTree(8)
+
+	fmt.Println("In order traversal of the original tree:")
+	fmt.Println(tree)
+
+	// this is the distance of the shortest path
+	k := 4
+
+	modifiedTree := removeShortPath(tree, 1, k)
+
+	fmt.Println("In order traversal of the modified tree:")
+	fmt.Println(modifiedTree)
+
+}