# AI solution for JavaScript Coding Question on BFE.dev

19. find corresponding node in two identical DOM tree

Solution:

Recursive solution:

We can use a recursive approach to solve this problem. For each node in tree A, we check if it matches the given element 'a'. If it does match, we return the corresponding node in tree B. Otherwise, we recurse on all of its children nodes in tree A, trying to find a match for 'a'. If we do find a match, we return the corresponding node in tree B. Otherwise, we continue recursing through the children nodes until we reach a leaf node.

Here's the JavaScript code for the recursive solution:

```
function findCorrespondingNodeRecursively(a, bA, bB) {
if (a === bA) {
return bB;
}
for (let i = 0; i < bA.children.length; i++) {
const childB = bB.children[i];
const result = findCorrespondingNodeRecursively(a, bA.children[i], childB);
if (result) {
return result;
}
}
return null;
}
```

Time complexity: O(nlogn) - since we're traversing through a tree with n nodes, and for each node, we're iterating through its children (worst case, logn) to find a match.

Iterative solution:

We could also use an iterative approach to solve the problem. We can start by adding the root nodes of the trees A and B to two separate stacks. We then iterate through the stacks, popping nodes from each stack and comparing them. If we find a match, we return it. Otherwise, we push the children nodes of each node onto their corresponding stack, and continue iterating until we've traversed the entire tree.

Here's the JavaScript code for the iterative solution:

```
function findCorrespondingNodeIteratively(a, bA, bB) {
const stackA = [bA];
const stackB = [bB];
while (stackA.length) {
const nodeA = stackA.pop();
const nodeB = stackB.pop();
if (nodeA === a) {
return nodeB;
}
for (let i = nodeA.children.length - 1; i >= 0; i--) {
stackA.push(nodeA.children[i]);
stackB.push(nodeB.children[i]);
}
}
return null;
}
```

Time complexity: O(n) - since we're traversing through the entire tree once, with a constant amount of work done for each node.

DOM API solution:

Finally, we could use the DOM API to solve the problem. We could first get the XPath for the given element 'a', and then use the DOM API to find the corresponding node 'b' in tree B using the same XPath.

Here's the JavaScript code for the DOM API solution:

```
function findCorrespondingNodeWithDOM(a, bA, bB) {
const xpath = getXPathFromElement(a);
const result = document.evaluate(xpath, bB, null, XPathResult.FIRST_ORDERED_NODE_TYPE, null);
return result.singleNodeValue;
}
function getXPathFromElement(element) {
const paths = [];
for (; element && element.nodeType === Node.ELEMENT_NODE; element = element.parentNode) {
let index = 0;
const siblings = element.parentNode.childNodes;
for (let i = 0; i < siblings.length; i++) {
const sibling = siblings[i];
if (sibling === element) {
paths.unshift(element.nodeName + '[' + (index + 1) + ']');
break;
} else if (sibling.nodeType === Node.ELEMENT_NODE && sibling.nodeName === element.nodeName) {
index++;
}
}
}
return paths.length ? '/' + paths.join('/') : null;
}
```

Time complexity: O(nlogn) - since we're using a DOM API call to find the corresponding node, the time complexity depends on how the DOM is implemented and the size of the tree. The getXPathFromElement() function has a time complexity of O(logn), since we're traversing up the tree hierarchy. The document.evaluate() function has a worst-case time complexity of O(n), since it needs to traverse the entire DOM tree. However, in practice, the time cost of using the DOM API might be faster due to optimizations made by modern browsers.