BFS with Queue
Using a breadth-first search approach, we process nodes level by level, which can be efficient in scenarios where the tree is balanced or nearly balanced:
- A queue is used to store the nodes along with their ‘leftness’ status.
- Nodes are dequeued and checked; if a node is a left leaf, its value is added to the sum.
- This method can potentially reduce the need to visit all nodes if combined with other conditions or optimizations, such as early stopping if a certain condition is met.
Example: To demonstrate finding the sum of left leaves in Binary tree using breadth first search with queue in JavaScript.
function sumOfLeftLeavesBFS(root) {
if (!root) return 0;
let sum = 0;
const queue = [{ node: root, isLeft: false }];
while (queue.length) {
const { node, isLeft } = queue
.shift();
if (!node.left && !node.right && isLeft) {
sum += node.value;
}
if (node.right) queue
.push({ node: node.right, isLeft: false });
if (node.left) queue
.push({ node: node.left, isLeft: true });
}
return sum;
}
class TreeNode {
constructor(value = 0, left = null, right = null) {
this.value = value;
this.left = left;
this.right = right;
}
}
const root = new TreeNode(3);
root.left = new TreeNode(9);
root.right =
new TreeNode(20, new TreeNode(15), new TreeNode(7));
// Calculate sum of left leaves
console.log(sumOfLeftLeavesBFS(root));
Output
24
Time Complexity:
- Best Case: O(1) (constant time)
- Worst Case: O(n) (linear time)
Space Complexity: O(n), where n is the number of nodes in the tree.
Sum of Left leaves in Binary Tree using JavaScript
Calculating the sum of all left leaves in a binary tree is a common task that helps in understanding tree traversal techniques. A left leaf is defined as a leaf node that is the left child of its parent node. This problem can serve various purposes, such as evaluating symmetry in data structures or specific tree-based calculations.
Problem Description:
In this problem, we need to identify all the left leaves in a binary tree and calculate their cumulative sum. A leaf is a node with no children, and a left leaf is a leaf that is also a left child of its parent.
Example: Consider the following binary tree:
3
/ \
9 20
/ \
15 7
In this tree, the only left leaf is the node with value 9. Thus, the sum of the left leaves is 9.
There are several methods in JavaScript to find the sum of left leaves in Binary Tree which are as follows:
Table of Content
- Recursive Method
- Iterative Method Using Stack
- BFS with Queue