【js】json内のすべてのノードの親ノードを探し出す

例:
入力:
var nodes = {   node: 6,   left: {     node: 5,      left: {        node: 4      },      right: {        node: 3      }   },   right: {      node: 2,      right: {        node: 1      }    } }
出力:
[ { node: 1, parent: 2 },   { node: 2, parent: 6 },   { node: 3, parent: 5 },   { node: 4, parent: 5 },   { node: 5, parent: 6 },   { node: 6, parent: 0 } ]

var arr=[]
function find(obj,parent){
  for(var key in obj){
    if(key=='node'){
      var j={}
      var temp=obj[key]
      j[key]=temp
      j['parent']=parent
      arr.push(j)
    }
    else find(obj[key],temp)  
  }
}
//////////////////////////////////////  
var nodes = {
  node: 6,
  left: {
    node: 5, 
    left: { 
      node: 4 
    }, 
    right: { 
      node: 3 
    }
  },
  right: { 
    node: 2, 
    right: { 
      node: 1 
    } 
  }
}
find(nodes,0)
arr.sort(function(a,b){
  return a.node-b.node
})
console.log(arr)
// [ { node: 1, parent: 2 },
//   { node: 2, parent: 6 },
//   { node: 3, parent: 5 },
//   { node: 4, parent: 5 },
//   { node: 5, parent: 6 },
//   { node: 6, parent: 0 } ]