构建二叉树进行数值数组的去重及优化

构建二叉树进行数值数组的去重及优化

常见两层循环实现数组去重

let arr = [11, 12, 13, 9, 8, 7, 0, 1, 2, 2, 5, 7, 11, 11, 7, 6, 4, 5, 2, 2]
let newArr = []
for (let i = 0; i < arr.length; i++) {
    let unique = true
    for (let j = 0; j < newArr.length; j++) {
        if (newArr[j] === arr[i]) {
            unique = false
            break
        }
    }
    if (unique) {
        newArr.push(arr[i])
    }
}
console.log(newArr)

构建二叉树实现去重（仅适用于数值类型的数组）

将先前遍历过的元素，构建成二叉树，树中每个结点都满足：左子结点的值 < 当前结点的值 < 右子结点的值

这样优化了判断元素是否之前出现过的过程

若元素比当前结点大，只需要判断元素是否在结点的右子树中出现过即可

若元素比当前结点小，只需要判断元素是否在结点的左子树中出现过即可

let arr = [0, 1, 2, 2, 5, 7, 11, 7, 6, 4,5, 2, 2]
class Node {
    constructor(value) {
        this.value = value
        this.left = null
        this.right = null
    }
}
class BinaryTree {
    constructor() {
        this.root = null
        this.arr = []
    }

    insert(value) {
        let node = new Node(value)
        if (!this.root) {
            this.root = node
            this.arr.push(value)
            return this.arr
        }
        let current = this.root
        while (true) {
            if (value > current.value) {
                if (current.right) {
                    current = current.right
                } else {
                    current.right = node
                    this.arr.push(value)
                    break
                }
            }
            if (value < current.value) {
                if (current.left) {
                    current = current.left
                } else {
                    current.left = node
                    this.arr.push(value)
                    break
                }
            }
            if (value === current.value) {
                break
            }
        }
        return this.arr
    }
}

let binaryTree = new BinaryTree()
for (let i = 0; i < arr.length; i++) {
    binaryTree.insert(arr[i])
}
console.log(binaryTree.arr)

优化思路一，记录最大最小值

记录已经插入元素的最大最小值，若比最大元素大，或最小元素小，则直接插入

let arr = [11, 12, 13, 9, 8, 7, 0, 1, 2, 2, 5, 7, 11, 11, 7, 6, 4, 5, 2, 2]
class Node {
    constructor(value) {
        this.value = value
        this.left = null
        this.right = null
    }
}
class BinaryTree {
    constructor() {
        this.root = null
        this.arr = []
        this.max = null
        this.min = null
    }

    insert(value) {
        let node = new Node(value)
        if (!this.root) {
            this.root = node
            this.arr.push(value)
            this.max = value
            this.min = value
            return this.arr
        }
        if (value > this.max) {
            this.arr.push(value)
            this.max = value
            this.findMax().right = node
            return this.arr
        }
        if (value < this.min) {
            this.arr.push(value)
            this.min = value
            this.findMin().left = node
            return this.arr
        }
        let current = this.root
        while (true) {
            if (value > current.value) {
                if (current.right) {
                    current = current.right
                } else {
                    current.right = node
                    this.arr.push(value)
                    break
                }
            }
            if (value < current.value) {
                if (current.left) {
                    current = current.left
                } else {
                    current.left = node
                    this.arr.push(value)
                    break
                }
            }
            if (value === current.value) {
                break
            }
        }
        return this.arr
    }

    findMax() {
        let current = this.root
        while (current.right) {
            current = current.right
        }
        return current
    }

    findMin() {
        let current = this.root
        while (current.left) {
            current = current.left
        }
        return current
    }
}

let binaryTree = new BinaryTree()
for (let i = 0; i < arr.length; i++) {
    binaryTree.insert(arr[i])
}
console.log(binaryTree.arr)

优化思路二，构建红黑树

构建红黑树，平衡树的高度

有关红黑树的部分，请见红黑树的插入

let arr = [11, 12, 13, 9, 8, 7, 0, 1, 2, 2, 5, 7, 11, 11, 7, 6, 4, 5, 2, 2]
console.log(Array.from(new Set(arr)))

class Node {
    constructor(value) {
        this.value = value
        this.left = null
        this.right = null
        this.parent = null
        this.color = 'red'
    }
}

class RedBlackTree {
    constructor() {
        this.root = null
        this.arr = []
    }

    insert(value) {
        let node = new Node(value)
        if (!this.root) {
            node.color = 'black'
            this.root = node
            this.arr.push(value)
            return this
        }
        let cur = this.root
        let inserted = false
        while (true) {
            if (value > cur.value) {
                if (cur.right) {
                    cur = cur.right
                } else {
                    cur.right = node
                    this.arr.push(value)
                    node.parent = cur
                    inserted = true
                    break
                }
            }

            if (value < cur.value) {
                if (cur.left) {
                    cur = cur.left
                } else {
                    cur.left = node
                    this.arr.push(value)
                    node.parent = cur
                    inserted = true
                    break
                }
            }

            if (value === cur.value) {
                break
            }
        }
        // 调整树的结构
        if(inserted){
            this.fixTree(node)
        }
        return this
    }

    fixTree(node) {
        if (!node.parent) {
            node.color = 'black'
            this.root = node
            return
        }
        if (node.parent.color === 'black') {
            return
        }
        let son = node
        let father = node.parent
        let grandFather = father.parent
        let directionFtoG = father === grandFather.left ? 'left' : 'right'
        let uncle = grandFather[directionFtoG === 'left' ? 'right' : 'left']
        let directionStoF = son === father.left ? 'left' : 'right'
        if (!uncle || uncle.color === 'black') {
            if (directionFtoG === directionStoF) {
                if (grandFather.parent) {
                    grandFather.parent[grandFather.parent.left === grandFather ? 'left' : 'right'] = father
                    father.parent = grandFather.parent
                } else {
                    this.root = father
                    father.parent = null
                }
                father.color = 'black'
                grandFather.color = 'red'

                father[father.left === son ? 'right' : 'left'] && (father[father.left === son ? 'right' : 'left'].parent = grandFather)
                grandFather[grandFather.left === father ? 'left' : 'right'] = father[father.left === son ? 'right' : 'left']

                father[father.left === son ? 'right' : 'left'] = grandFather
                grandFather.parent = father
                return
            } else {
                grandFather[directionFtoG] = son
                son.parent = grandFather

                son[directionFtoG] && (son[directionFtoG].parent = father)
                father[directionStoF] = son[directionFtoG]

                father.parent = son
                son[directionFtoG] = father
                this.fixTree(father)
            }
        } else {
            father.color = 'black'
            uncle.color = 'black'
            grandFather.color = 'red'
            this.fixTree(grandFather)
        }
    }
}

let redBlackTree = new RedBlackTree()
for (let i = 0; i < arr.length; i++) {
    redBlackTree.insert(arr[i])
}
console.log(redBlackTree.arr)

其他去重方法

通过 Set 对象去重

[...new Set(arr)]

通过 sort() + reduce() 方法去重

排序后比较相邻元素是否相同，若不同则添加至返回的数组中

值得注意的是，排序的时候，默认 compare(2, '2') 返回 0；而 reduce() 时，进行全等比较

let arr = [0, 1, 2, '2', 2, 5, 7, 11, 7, 5, 2, '2', 2]
let newArr = []
arr.sort((a, b) => {
    let res = a - b
    if (res !== 0) {
        return res
    } else {
        if (a === b) {
            return 0
        } else {
            if (typeof a === 'number') {
                return -1
            } else {
                return 1
            }
        }
    }
}).reduce((pre, cur) => {
    if (pre !== cur) {
        newArr.push(cur)
        return cur
    }
    return pre
}, null)

通过 includes() + map() 方法去重

let arr = [0, 1, 2, '2', 2, 5, 7, 11, 7, 5, 2, '2', 2]
let newArr = []
arr.map(a => !newArr.includes(a) && newArr.push(a))

通过 includes() + reduce() 方法去重

let arr = [0, 1, 2, '2', 2, 5, 7, 11, 7, 5, 2, '2', 2]
let newArr = arr.reduce((pre, cur) => {
    !pre.includes(cur) && pre.push(cur)
    return pre
}, [])

通过对象的键值对 + JSON 对象方法去重

let arr = [0, 1, 2, '2', 2, 5, 7, 11, 7, 5, 2, '2', 2]
let obj = {}
arr.map(a => {
    if(!obj[JSON.stringify(a)]){
        obj[JSON.stringify(a)] = 1
    }
})

console.log(Object.keys(obj).map(a => JSON.parse(a)))