find-in-tree.js

const tree = {
    "type": "",
    "children": [
        {
            "type": "1",
            "children": [
                {
                    "type": "1.1",
                    "children": [
                        { "type": "1.1.1", "children": [] },
                        { "type": "1.1.2", "children": [] }
                    ]
                },
                {
                    "type": "1.2",
                    "children": [
                        { "type": "1.2.1", "children": [] }
                    ]
                }
            ]
        },
        { "type": "2", "children": [] }
    ]
};

function find(tree, path = '', index = 0) {

    // test if found
    if (tree.type === path) return tree

    // uses 'index' to compute child key
    const parts = path.split('.')
    const childKey = parts.filter((e, i) => i <= index).join('.')

    // find the child or throw
    const child = tree.children.find(e => e.type === childKey)
    if (!child) throw "Not Found"

    // recursively look for path with string comparison
    return find(child, path, index + 1)
}

// compute the children indexes converting the path to number (and subtracting 1)
const find2 = (tree, path = '') => path	.split('.')
                                        .map(e => Number(e) - 1)
                                        .reduce((e, i) => e.children[i] || tree, tree)

console.log('tests: find recursively');
console.log(find(tree) === tree)
console.log(find(tree, '') === tree)
console.log(find(tree, '1') === tree.children[0])
console.log(find(tree, '2') === tree.children[1])
console.log(find(tree, '1.1') === tree.children[0].children[0])
console.log(find(tree, '1.2') === tree.children[0].children[1])
console.log(find(tree, '1.2.1') === tree.children[0].children[1].children[0])

console.log('tests: find by computing indexes');
console.log(find2(tree) === tree)
console.log(find2(tree, '') === tree)
console.log(find2(tree, '1') === tree.children[0])
console.log(find2(tree, '2') === tree.children[1])
console.log(find2(tree, '1.1') === tree.children[0].children[0])
console.log(find2(tree, '1.2') === tree.children[0].children[1])
console.log(find2(tree, '1.2.1') === tree.children[0].children[1].children[0])