#摘要#

一转眼过去6年多了，没有更新过博客，由于近期遇到了用代码解决数学上的问题，比如今天说的排列组合。网上查了下，有好多人都实现了，方法各异，但都没有按照面向对象的方式求解。我承认我今天写的这些，可能小题大作，但我是按照最简单逻辑思维方式拓展开的，容易理解。

我们都知道排列和组合的区别，一个有顺序，一个没顺序。所以我用一个【全部的树】来表示排列结果，用一个【向后的树】来表示组合结果。看代码，您就知道了。

class PCNode {value = 0index = 0parent: PCNode | null = nullchildren: Array<PCNode>level = 1constructor() {this.children = new Array<PCNode>()}get pathIndexList(): Array<number> {const arr = new Array<number>()arr.push(this.index)if (this.parent) {let parent: PCNode | null = this.parentwhile (parent) {arr.push(parent.index)parent = parent.parent}}return arr}get pathValueList(): Array<number> {const arr = new Array<number>()arr.push(this.value)if (this.parent) {let parent: PCNode | null = this.parentwhile (parent) {arr.push(parent.value)parent = parent.parent}}return arr}
}

class PermutationCombination {nodeInfo: Array<PCNode>originArr: Array<number>constructor(isPermutation: boolean, originArray: Array<number>) {this.nodeInfo = new Array<PCNode>()this.originArr = originArrayisPermutation ? this.initPermutation() : this.initCombination()}private initPermutation() {const generateChildren = (parent: PCNode) => {for (let index = 0; index < this.originArr.length; index++) {if (parent.pathIndexList.indexOf(index) === -1) {const child = new PCNode()child.level = parent.level + 1child.index = indexchild.value = this.originArr[index]child.parent = parentparent.children.push(child)generateChildren(child)}}}for (let index = 0; index < this.originArr.length; index++) {const root = new PCNode()root.value = this.originArr[index]root.index = indexthis.nodeInfo.push(root)generateChildren(root)}}private initCombination() {const generateChildren = (parent: PCNode, startIndex: number) => {for (let index = startIndex; index < this.originArr.length; index++) {const child = new PCNode()child.level = parent.level + 1child.value = this.originArr[index]child.parent = parentparent.children.push(child)generateChildren(child, index + 1)}}for (let index = 0; index < this.originArr.length; index++) {const root = new PCNode()root.value = this.originArr[index]root.index = indexthis.nodeInfo.push(root)generateChildren(root, index + 1)}}getResultByDeep(deep: number) {const allConditions = new Array<Array<number>>()console.log(this.nodeInfo)const getChildByDeep = (parent: PCNode) => {if (parent.level === deep) {allConditions.push(parent.pathValueList)} else if (parent.level < deep) {parent.children.forEach(child => getChildByDeep(child))}}this.nodeInfo.forEach((value: PCNode) => getChildByDeep(value))return allConditions}
}

使用方法：
 

const pc = new PermutationCombination(false, [1,2,3,2,3])
console.log(pc.getResultByDeep(3))

解释下，这里传的参数3，也就是节点中的level值，就是我们说的C53中的C符号上的数字。找到这一层的节点后，按照自己的路径上找，即可形成一个解。我这里代码的逻辑完全来源于手动演算的结果。
 

经简单测试，没有发现问题。期待能有更多数学问题，能用这种方式解决，下次再见！