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如何获得未知JSON层次结构的总深度?

我一直在努力寻找/构建一个递归函数来解析这个JSON文件并获得其子项的总深度.

该文件看起来像这样:

var input = {
    "name": "positive",
    "children": [{
        "name": "product service",
        "children": [{
            "name": "price",
            "children": [{
                "name": "cost",
                "size": 8
            }]
        }, {
            "name": "quality",
            "children": [{
                "name": "messaging",
                "size": 4
            }]
        }]
    }, {
        "name": "customer service",
        "children": [{
            "name": "Personnel",
            "children": [{
                "name": "CEO",
                "size": 7
            }]
        }]
    }, {
        "name": "product",
        "children": [{
            "name": "Apple",
            "children": [{
                "name": "iPhone 4",
                "size": 10
            }]
        }]
    }] 
}
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javascript json nested d3.js

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