angular filter on nested object, to show both parent and children of object found

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Javascript

AngularJs

I'm trying to implement a search on a nested list. The idea is that when a search is performed on the list both the parents and children of the found element are visible.

Right now I have a list and I'm able to search for a element and return the all the parents for the element.

But I'm not able to show the children of all the elements that are visible.

Here is fiddle that filters and shows the parents of all elements that are found. plunker with the list and search--Plunker[^]

I added a piece of code that adds show property to every child of a visible parent but only if the children has few more children.

function setChildren(child) {
    var i;
    if (child) {
        for (i=0;i< child.length;i++){
            child[i].show = true;
            setChildren(child[i].children);
        }
    }
}

attempt to show children--Plunker[^]

Any thoughts on how this can be achieved?