路由查找之Radix Tree

## 什么是Radix Tree   在计算机科学中,基数树,或称Patricia trie/tree,或crit bit tree,压缩前缀树,是一种更节省空间的Trie(前缀树)。对于基数树的每个节点,如果该节点是唯一的子树的话,就和父节点合并。 ![radix_tree.png](https://static.studygolang.com/190620/9b56abe61d0af97926c25557ee3b7e82.png)   golang的web框架`echo`和`gin`都使用了`radix tree`作为路由查找的算法,我们以gin的实现来分析一下。   在gin的路由中,每一个`Http Method`(GET, PUT, POST…)都对应了一棵 `radix tree` ``` func (engine *Engine) addRoute(method, path string, handlers HandlersChain) { // ... // 获取method对应的树,如果没有就创建 root := engine.trees.get(method) if root == nil { // 创建radix tree,只有根节点 root = new(node) engine.trees = append(engine.trees, methodTree{method: method, root: root}) } root.addRoute(path, handlers) } ``` `radix tree`可以被认为是一棵简洁版的前缀树。拥有共同前缀的节点也共享同一个父节点。下面是一个`GET`方法对应的路由树的结构: ``` Priority Path Handle 9 \ *<1> 3 ├s nil 2 |├earch\ *<2> 1 |└upport\ *<3> 2 ├blog\ *<4> 1 | └:post nil 1 | └\ *<5> 2 ├about-us\ *<6> 1 | └team\ *<7> 1 └contact\ *<8> ``` `*`是方法(handler)对应的指针,从根节点遍历到叶子节点我们就能得到完整的路由表,图中的示例实现了以下路由: ``` GET("/", func1) GET("/search/", func2) GET("/support/", func3) GET("/blog/", func4) GET("/blog/:post/", func5) GET("/about-us/", func6) GET("/about-us/team/", func7) GET("/contact/", func8) ```   `:post`是真实的`post name`的一个占位符(就是一个参数)。这里体现了radix tree相较于hash-map的一个优点,树结构允许我们的路径中存在动态的部分(参数),因为我们匹配的是路由的模式而不是hash值   为了更具扩展性,每一层的节点按照priority排序,priority是节点的子节点(儿子节点,孙子节点等)注册的handler的数量,这样做有两个好处: - 被最多路径包含的节点会被最先评估。这样可以让尽量多的路由快速被定位。 - 有点像成本补偿。最长的路径可以被最先评估,补偿体现在最长的路径需要花费更长的时间来定位,如果最长路径的节点能被优先评估(即每次拿子节点都命中),那么所花时间不一定比短路径的路由长。下面展示了节点(每个-可以看做一个节点)评估的路径:从左到右,从上到下 ``` ├------------ ├--------- ├----- ├---- ├-- ├-- └- ``` ## 节点数据结构 节点的数据结构如下: ``` type node struct { // 节点路径,比如上面的s,earch,和upport path string // 节点是否是参数节点,比如上面的:post wildChild bool // 节点类型,包括static, root, param, catchAll // static: 静态节点,比如上面的s,earch等节点 // root: 树的根节点 // catchAll: 有*匹配的节点 // param: 参数节点 nType nodeType // 路径上最大参数个数 maxParams uint8 // 和children字段对应, 保存的是分裂的分支的第一个字符 // 例如search和support, 那么s节点的indices对应的"eu" // 代表有两个分支, 分支的首字母分别是e和u indices string // 儿子节点 children []*node // 处理函数 handlers HandlersChain // 优先级,子节点注册的handler数量 priority uint32 } ``` ## 添加路由 ``` func (n *node) addRoute(path string, handlers HandlersChain) { fullPath := path n.priority++ numParams := countParams(path) // non-empty tree if len(n.path) > 0 || len(n.children) > 0 { walk: for { // Update maxParams of the current node if numParams > n.maxParams { n.maxParams = numParams } // Find the longest common prefix. // This also implies that the common prefix contains no ':' or '*' // since the existing key can't contain those chars. i := 0 max := min(len(path), len(n.path)) for i < max && path[i] == n.path[i] { i++ } // Split edge // 开始分裂,比如一开始path是search,新来了support,s是他们匹配的部分, // 那么会将s拿出来作为parent节点,增加earch和upport作为child节点 if i < len(n.path) { child := node{ path: n.path[i:], // 不匹配的部分作为child节点 wildChild: n.wildChild, indices: n.indices, children: n.children, handlers: n.handlers, priority: n.priority - 1, // 降级成子节点,priority减1 } // Update maxParams (max of all children) for i := range child.children { if child.children[i].maxParams > child.maxParams { child.maxParams = child.children[i].maxParams } } // 当前节点的子节点变成刚刚分裂的出来的节点 n.children = []*node{&child} // []byte for proper unicode char conversion, see #65 n.indices = string([]byte{n.path[i]}) n.path = path[:i] n.handlers = nil n.wildChild = false } // Make new node a child of this node // 将新来的节点插入新的parent节点作为子节点 if i < len(path) { path = path[i:] // 如果是参数节点(包含:或*) if n.wildChild { n = n.children[0] n.priority++ // Update maxParams of the child node if numParams > n.maxParams { n.maxParams = numParams } numParams-- // Check if the wildcard matches // 例如:/blog/:pp 和 /blog/:ppp,需要检查更长的通配符 if len(path) >= len(n.path) && n.path == path[:len(n.path)] { // check for longer wildcard, e.g. :name and :names if len(n.path) >= len(path) || path[len(n.path)] == '/' { continue walk } } panic("path segment '" + path + "' conflicts with existing wildcard '" + n.path + "' in path '" + fullPath + "'") } // 首字母,用来与indices做比较 c := path[0] // slash after param if n.nType == param && c == '/' && len(n.children) == 1 { n = n.children[0] n.priority++ continue walk } // Check if a child with the next path byte exists // 判断子节点中是否有和当前path有匹配的,只需要查看子节点path的第一个字母即可,即indices // 比如s的子节点现在是earch和upport,indices为eu // 如果新来的路由为super,那么就是和upport有匹配的部分u,将继续分类现在的upport节点 for i := 0; i < len(n.indices); i++ { if c == n.indices[i] { i = n.incrementChildPrio(i) n = n.children[i] continue walk } } // Otherwise insert it if c != ':' && c != '*' { // []byte for proper unicode char conversion, see #65 // 记录第一个字符,放在indices中 n.indices += string([]byte{c}) child := &node{ maxParams: numParams, } // 增加子节点 n.children = append(n.children, child) n.incrementChildPrio(len(n.indices) - 1) n = child } n.insertChild(numParams, path, fullPath, handlers) return } else if i == len(path) { // Make node a (in-path) leaf // 路径相同,如果已有handler就报错,没有就赋值 if n.handlers != nil { panic("handlers are already registered for path ''" + fullPath + "'") } n.handlers = handlers } return } } else { // Empty tree,空树,插入节点,节点种类是root n.insertChild(numParams, path, fullPath, handlers) n.nType = root } } ```   此函数的主要目的是找到插入节点的位置,如果和现有节点存在相同的前缀,那么要将现有节点进行分裂,然后再插入,下面是`insertChild`函数 ## 插入子节点 ``` // @1: 参数个数 // @2: 路径 // @3: 完整路径 // @4: 处理函数 func (n *node) insertChild(numParams uint8, path string, fullPath string, handlers HandlersChain) { var offset int // already handled bytes of the path // find prefix until first wildcard (beginning with ':'' or '*'') // 找到前缀,只要匹配到wildcard for i, max := 0, len(path); numParams > 0; i++ { c := path[i] if c != ':' && c != '*' { continue } // find wildcard end (either '/' or path end) end := i + 1 for end < max && path[end] != '/' { switch path[end] { // the wildcard name must not contain ':' and '*' case ':', '*': panic("only one wildcard per path segment is allowed, has: '" + path[i:] + "' in path '" + fullPath + "'") default: end++ } } // check if this Node existing children which would be // unreachable if we insert the wildcard here if len(n.children) > 0 { panic("wildcard route '" + path[i:end] + "' conflicts with existing children in path '" + fullPath + "'") } // check if the wildcard has a name if end-i < 2 { panic("wildcards must be named with a non-empty name in path '" + fullPath + "'") } if c == ':' { // param // split path at the beginning of the wildcard if i > 0 { n.path = path[offset:i] offset = i } child := &node{ nType: param, maxParams: numParams, } n.children = []*node{child} n.wildChild = true n = child n.priority++ numParams-- // if the path doesn't end with the wildcard, then there // will be another non-wildcard subpath starting with '/' if end < max { n.path = path[offset:end] offset = end child := &node{ maxParams: numParams, priority: 1, } n.children = []*node{child} // 下次循环这个新的child节点 n = child } } else { // catchAll if end != max || numParams > 1 { panic("catch-all routes are only allowed at the end of the path in path '" + fullPath + "'") } if len(n.path) > 0 && n.path[len(n.path)-1] == '/' { panic("catch-all conflicts with existing handle for the path segment root in path '" + fullPath + "'") } // currently fixed width 1 for '/' i-- if path[i] != '/' { panic("no / before catch-all in path '" + fullPath + "'") } n.path = path[offset:i] // first node: catchAll node with empty path child := &node{ wildChild: true, nType: catchAll, maxParams: 1, } n.children = []*node{child} n.indices = string(path[i]) n = child n.priority++ // second node: node holding the variable child = &node{ path: path[i:], nType: catchAll, maxParams: 1, handlers: handlers, priority: 1, } n.children = []*node{child} return } } // insert remaining path part and handle to the leaf n.path = path[offset:] n.handlers = handlers } ```   `insertChild`函数是根据`path`本身进行分割, 将/分开的部分分别作为节点保存, 形成一棵树结构. 注意参数匹配中的`:`和`*`的区别, 前者是匹配一个字段, 后者是匹配后面所有的路径 ## 路径查找   匹配每个children的path,最长匹配 ``` // Returns the handle registered with the given path (key). The values of // wildcards are saved to a map. // If no handle can be found, a TSR (trailing slash redirect) recommendation is // made if a handle exists with an extra (without the) trailing slash for the // given path. func (n *node) getValue(path string, po Params, unescape bool) (handlers HandlersChain, p Params, tsr bool) { p = po walk: // Outer loop for walking the tree for { // 尚未到达path的终点 if len(path) > len(n.path) { // 前面一段需要一致 if path[:len(n.path)] == n.path { path = path[len(n.path):] // If this node does not have a wildcard (param or catchAll) // child, we can just look up the next child node and continue // to walk down the tree if !n.wildChild { c := path[0] for i := 0; i < len(n.indices); i++ { if c == n.indices[i] { n = n.children[i] continue walk } } // Nothing found. // We can recommend to redirect to the same URL without a // trailing slash if a leaf exists for that path. tsr = (path == "/" && n.handlers != nil) return } // handle wildcard child n = n.children[0] switch n.nType { case param: // find param end (either '/' or path end) end := 0 for end < len(path) && path[end] != '/' { end++ } // save param value if cap(p) < int(n.maxParams) { p = make(Params, 0, n.maxParams) } i := len(p) p = p[:i+1] // expand slice within preallocated capacity p[i].Key = n.path[1:] val := path[:end] if unescape { var err error if p[i].Value, err = url.QueryUnescape(val); err != nil { p[i].Value = val // fallback, in case of error } } else { p[i].Value = val } // we need to go deeper! if end < len(path) { if len(n.children) > 0 { path = path[end:] n = n.children[0] continue walk } // ... but we can't tsr = (len(path) == end+1) return } if handlers = n.handlers; handlers != nil { return } if len(n.children) == 1 { // No handle found. Check if a handle for this path + a // trailing slash exists for TSR recommendation n = n.children[0] tsr = (n.path == "/" && n.handlers != nil) } return case catchAll: // save param value if cap(p) < int(n.maxParams) { p = make(Params, 0, n.maxParams) } i := len(p) p = p[:i+1] // expand slice within preallocated capacity p[i].Key = n.path[2:] if unescape { var err error if p[i].Value, err = url.QueryUnescape(path); err != nil { p[i].Value = path // fallback, in case of error } } else { p[i].Value = path } handlers = n.handlers return default: panic("invalid node type") } } } else if path == n.path { // We should have reached the node containing the handle. // Check if this node has a handle registered. if handlers = n.handlers; handlers != nil { return } if path == "/" && n.wildChild && n.nType != root { tsr = true return } // No handle found. Check if a handle for this path + a // trailing slash exists for trailing slash recommendation for i := 0; i < len(n.indices); i++ { if n.indices[i] == '/' { n = n.children[i] tsr = (len(n.path) == 1 && n.handlers != nil) || (n.nType == catchAll && n.children[0].handlers != nil) return } } return } // Nothing found. We can recommend to redirect to the same URL with an // extra trailing slash if a leaf exists for that path tsr = (path == "/") || (len(n.path) == len(path)+1 && n.path[len(path)] == '/' && path == n.path[:len(n.path)-1] && n.handlers != nil) return } } ``` 之前总听大家说数据结构与算法有什么用,工作中又用不到,上面就是一个很好的示例。我们平时还是要多关注底层原理,做后端的同学多看看框架的代码,一定受益匪浅~ 本文转载自:https://michaelyou.github.io/2018/02/10/%E8%B7%AF%E7%94%B1%E6%9F%A5%E6%89%BE%E4%B9%8BRadix-Tree/ 作者:Youmai **感谢阅读,欢迎大家留言,分享,指正~** ![qrcode.png](https://static.studygolang.com/190508/d20b3d9f2790729effb6cbea985e443d.png)

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