SOURCE

let str = [{
    "id": 1,
    "name": "教育",
    "level": 1,
    "des": "指学校或培训机构为学生提供的学习技能或素质提升的商品或服务",
    "children": [{
        "id": 101,
        "name": "早教与学前教育",
        "level": 2,
        "des": "为0-6岁的儿童提供的教育，包括语言启蒙、智力开发等学前教育。智力开发类的游戏，玩具，画板也算到这里",
        "children": [{
            "id": 10101,
            "name": "语言启蒙",
            "level": 3,
            "des": "主要针对0~3岁幼儿的语言能力开发",
            "children": [],
            "count": 0
        }, {
            "id": 10102,
            "name": "智力开发",
            "level": 3,
            "des": "面向0~6岁幼儿的，对观察力、记忆力、想像力和思维能力的开发",
            "children": [],
            "count": 0
        }, {
            "id": 10103,
            "name": "幼儿园",
            "level": 3,
            "des": "为3-6岁幼儿提供的学前教育",
            "children": [],
            "count": 4999413
        }, {
            "id": 10104,
            "name": "少儿早教",
            "level": 3,
            "des": "为0-6岁儿童提供的教育，包括语言启蒙、智力开发等，寓教于乐小游戏、识字卡、画板等",
            "children": [],
            "count": 73980829
        }],
        "count": 79933157
    }],
    "count": 342830858
}]

function pushId(item) {
    let arr = [item.id]
    item.children.forEach(item => {
        arr.push(item.id)
     item.children.length

    })
     return arr
}
let a=[]
str.forEach(item=>{
    a.push(pushId(item))
})
console.log(a)