Answer 1

const data = [{
  id: '1',
  name: 'test1',
  children: [
      {
          id: '11',
          name: 'test11',
          children: [
              {
                  id: '111',
                  name: 'test111'
              },
              {
                  id: '112',
                  name: 'test112'
              }
          ]

      },
      {
          id: '12',
          name: 'test12',
          children: [
              {
                  id: '121',
                  name: 'test121'
              },
              {
                  id: '122',
                  name: 'test122'
              }
          ]
      }
  ]
}];

// 通过递归来实现
function find(arr, value) {
  const result = [];
  for(let i = 0; i < arr.length; i++) {
    const item = arr[i];
    if(item.id === value) {
      return [value]
    }

    if(item.children) {
      const ids = find(item.children, value);
      if(ids.length > 0) {
        result.push(item.id, ...ids);
      }
    }
  }
  return result;
}

console.log(find(data, '11'));