go拓扑排序

拓扑排序常用来确定一个依赖关系集中，事物发生的顺序。例如，在日常工作中，可能会将项目拆分成A、B、C、D四个子部分来完成，但A依赖于B和D，C依赖于D。为了计算这个项目进行的顺序，可对这个关系集进行拓扑排序，得出一个线性的序列，则排在前面的任务就是需要先完成的任务。

注意：这里得到的排序并不是唯一的！就好像你早上穿衣服可以先穿上衣也可以先穿裤子，只要里面的衣服在外面的衣服之前穿就行。

考虑这样一个问题： 给定一些计算机课程，每个课程都有前 置课程，只有完成了前置课程才可以开始当前课程的学习；我们的目标是选择出一组课程，这组课程必 须确保按顺序学习时，能全部被完成。每个课程的前置课程如下：

var prereqs = map[string][]string{
	"algorithms": {"data structures"},
	"calculus": {"linear algebra"},
	"compilers": { "data structures", "formal languages", "computer organization", },
	"data structures": {"discrete math"},
	"databases": {"data structures"},
	"discrete math": {"intro to programming"},
	"formal languages": {"discrete math"},
	"networks": {"operating systems"},
	"operating systems": {"data structures", "computer organization"},
	"programming languages": {"data structures", "computer organization"},
}

必须先学完右边的课程才能学习左边的课程，如果右边有多门课程的话学习顺序不固定只要都学完就可以。现在我们用拓扑排序算出学习课程的顺序。

package main

import (
	"fmt"
	"sort"
)

var prereqs = map[string][]string{
	"algorithms": {"data structures"},
	"calculus": {"linear algebra"},
	"compilers": { "data structures", "formal languages", "computer organization", },
	"data structures": {"discrete math"},
	"databases": {"data structures"},
	"discrete math": {"intro to programming"},
	"formal languages": {"discrete math"},
	"networks": {"operating systems"},
	"operating systems": {"data structures", "computer organization"},
	"programming languages": {"data structures", "computer organization"},
}

func topoSort(m map[string][]string)[]string {
	order := []string{}
	seen := make(map[string]bool)
	var visitAll func(items []string)
	visitAll = func(items []string) {
		for _, item := range items {
			if !seen[item] {
				seen[item] = true
				visitAll(m[item])
				order = append(order, item)
			}
		}
	}
	keys := []string{}
	for key := range m {
		keys = append(keys, key)
	}
	sort.Strings(keys)
	visitAll(keys)
	return order
}

func main() {
	order := topoSort(prereqs)
	for i, v := range order {
		fmt.Printf("%d: %s\n", i, v)
	}
}

输出如下：

0: intro to programming
1: discrete math
2: data structures
3: algorithms
4: linear algebra
5: calculus
6: formal languages
7: computer organization
8: compilers
9: databases
10: operating systems
11: networks
12: programming languages