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給定的測試數據如下，圖和起始點通過;號隔開，起始點通過 | 隔開：
處理函數如下：
func parseBody(body string) (string,string){
params := strings.Split(body, ";")
graphInfo := params[0]
evaluateInfo := params[1]
return graphInfo,evaluateInfo
}
處理函數如下將圖解析進入:
type Graphs map[string]map[string]map[string]float64
func (g *Graphs) getChildByKey(key string) map[string]float64 {
return (*g)["graph"][key]
}
func (g *Graphs) getLengthByKeys(key1, key2 string) float64 {
return (*g)["graph"][key1][key2]
}
//解析json
func parseGraph(graphStr string) (Graphs, error) {
graphMap := make(Graphs)
err := json.Unmarshal([]byte(graphStr), &graphMap)
if err != nil {
fmt.Println(err)
return graphMap, err
}
if _, ok := graphMap["graph"]; !ok {
return graphMap, errors.New("請傳入graph")
}
return graphMap, nil
}
將 map 轉換爲鄰接矩陣（此處處理的不是很好，暫時先用的）:
func mapToSlice(graphMap Graphs) ([][]float64, map[string]int, map[int]string, error) {
var vertex [][]float64
//頂點對應的下標
Key2Index := make(map[string]int)
//下標對應的頂點
Index2Key := make(map[int]string)
for k, v := range graphMap["graph"] {
Key2Index[k] = 0
for k1 := range v {
Key2Index[k1] = 0
}
}
i := 0
//每個節點映射一個下標，由於map的亂序性每次給同樣的key給的下標都不一樣
keys := make([]string, 0)
for k := range Key2Index {
keys = append(keys, k)
}
sort.Strings(keys)
for _, v := range keys {
Key2Index[v] = i
Index2Key[i] = v
i++
}
//初始化分配二維數組
for i := 0; i < len(Key2Index); i++ {
tmp := make([]float64, len(Key2Index))
vertex = append(vertex, tmp)
}
//給每個點賦值無窮大
for i := 0; i < len(Key2Index); i++ {
for j := 0; j < len(Key2Index); j++ {
vertex[i][j] = math.MaxFloat64
}
}
for k, v := range graphMap["graph"] {
for k1, v := range v {
vertex[Key2Index[k]][Key2Index[k1]] = v
vertex[Key2Index[k1]][Key2Index[k]] = v
}
}
return vertex, Key2Index, Index2Key, nil
}
狄傑斯特拉算法：
type Dis struct {
Path string
Length float64
Visited bool
}
var dis = []Dis{}
var datas = []string{} //此處由於需要併發處理聲明瞭全局變量並且加了鎖
//起點，終點，矩陣，矩陣中索引與json中key的對應
func getShortPathByDijkstra(startNode, endNode int,
vertex [][]float64, Index2Key map[int]string) {
var TablePathMin float64 //存放dis中,未遍歷的最小結點的值
defer wg.Done()
//記錄結點是否已經找到v0到vx的最小路徑
dis = make([]Dis, len(vertex))
//// 獲取v0這一行的權值數組
for i := 0; i < len(vertex); i++ {
dis[i].Length = vertex[startNode][i]
dis[i].Path = Index2Key[startNode] + "->" + Index2Key[i]
}
dis[startNode].Length = 0
dis[startNode].Visited = true
for v := 1; v < len(vertex); v++ {
TablePathMin = math.MaxFloat64
//找出dis中,未遍歷的最小結點的值
Vx := 0 //存放dis中,未遍歷的最小結點的下標
for w := 0; w < len(vertex); w++ {
if !dis[w].Visited && dis[w].Length < TablePathMin {
Vx = w
TablePathMin = dis[w].Length
}
}
dis[Vx].Visited = true
for j := 0; j < len(vertex); j++ {
if !dis[j].Visited && dis[Vx].Length+vertex[Vx][j] < dis[j].Length {
dis[j].Length = dis[Vx].Length + vertex[Vx][j
dis[j].Path = dis[Vx].Path + "->" + Index2Key[j]
}
}
}
path := c.getDijstraCadPath(dis[endNode], Index2Key[startNode], Index2Key[endNode])
datas = append(datas, path)
}
SPFA:
type Path struct {
StartNode string
EndNode string
Path string
Value float64
}
//s起點索引 e終點索引 n矩陣長度 vert矩陣 Index2Key矩陣中索引對應json中的key
func SPFA(s, e, n int, p *Path, Vert [][]float64, Index2Key map[int]string) []float64 {
dis := make([]float64, n) //
vis := make([]bool, n)
num := make([]int, n)
path := make([]int, n)
disMap := make(map[string]float64)
q := queue.New()
for i := 0; i < n; i++ {
dis[i] = math.MaxFloat64
}
dis[s] = 0
vis[s] = true
num[s] = 1
q.Add(s)
p.StartNode = Index2Key[s]
p.EndNode = Index2Key[e]
for q.Length() != 0 {
a := q.Get(0)
u := a.(int)
q.Remove()
vis[u] = false
for v := 0; v < n; v++ {
if dis[v] > dis[u]+Vert[u][v] {
dis[v] = dis[u] + Vert[u][v]
disMap[Index2Key[v]] = dis[u] + Vert[u][v]
path[v] = u
if !vis[v] {
q.Add(v)
vis[v] = true
num[v]++
if num[v] >= n {
goto no
}
}
}
}
}
//以上是spfa的主要算法內容以下爲業務操作內容
fmt.Println("開始路徑封裝")
goto ok
no:
p.Path = "存在負權迴路"
p.Value = math.MaxFloat64
fmt.Println("結束路徑封裝", p.Path)
return dis
ok:
buf := bytes.Buffer{}
tmpE := e
buf.WriteString(Index2Key[tmpE])
for s != tmpE {
prv := path[tmpE]
buf.WriteString("<-" + Index2Key[prv])
if prv == tmpE {
break
}
tmpE = prv
}
p.Path = c.reversePath(buf.String())
p.Value = disMap[Index2Key[e]]
fmt.Println("結束路徑封裝", p.Path)
return dis
}
//起點，終點，路徑字符串(用來拼接路徑) ,傳入一個paths map用來記錄所有的路徑及其長度最終遞歸執行完，遍歷此map即可
func getAllPath(startNode, endNode, path string,
graph Graphs, paths map[string]float64, length float64) (string, float64) {
NextNodesMap := graph.getChildByKey(startNode)
if startNode == endNode || len(NextNodesMap) == 0 {
return path, length
}
curPath := path
curLength := length
for key := range NextNodesMap {
//判斷key在中間，在開頭，在結尾
if checkNodeIsPath(path, key) {
continue
}
//獲取到當前節點的路徑
addKey(&path, key)
//計算到當前節點的距離
calculatePath(≤ngth, startNode, key, graph)
lastPath, lastLength := getAllPath(key, endNode, path, graph, paths, length)
//當遍歷完當前節點的路徑後重置path,length爲當前path,length
path = curPath
length = curLength
if strings.Contains(lastPath, startNode) && strings.Contains(lastPath, endNode){
paths[lastPath] = lastLength
}
}
return curPath, curLength
}
func addKey(s *string, key string) {
var build strings.Builder
build.WriteString(*s)
build.WriteString("->")
build.WriteString(key)
*s = build.String()
}
func calculatePath(length *float64, preNode, curNode string, graph Graphs) {
*length += graph.getLengthByKeys(preNode, curNode)
}
遞歸全遍歷：
全部代碼：
/**
* @Author: xiaoxiao
* @Description:
* @File: CaclService
* @Version: 1.0.0
* @Date: 4/11/20 8:06 下午
*/
package service
import (
"bytes"
"encoding/json"
"errors"
"fmt"
"github.com/spf13/cast"
"github.com/xhaoxiong/util/cad"
"gopkg.in/eapache/queue.v1"
"math"
"sort"
"strings"
"sync"
)
type CacService struct{}
func NewCacService() *CacService {
return &CacService{}
}
/*Dijkstra使用*/
type Dis struct {
Path string
Length float64
Visited bool
}
var dis = []Dis{}
type Graphs map[string]map[string]map[string]float64
var datas = []string{}
var mutex sync.Mutex
/*SPFA使用*/
type Path struct {
StartNode string
EndNode string
Path string
Value float64
}
func (g *Graphs) getChildByKey(key string) map[string]float64 {
return (*g)["graph"][key]
}
func (g *Graphs) getLengthByKeys(key1, key2 string) float64 {
return (*g)["graph"][key1][key2]
}
/**
Dijkstra算法求解
*/
func (c *CacService) GetAllPathsByDijkstra(KVs string, graph string) string {
parseGraph, _ := c.parseGraph(graph)
vertex, m, m2, _ := c.mapToSlice(parseGraph)
kvs := strings.Split(KVs, "|")
wg := &sync.WaitGroup{}
datas = make([]string, len(kvs))
for _, KV := range kvs {
kv := strings.Split(KV, ":")
startNode, endNode := kv[0], kv[1]
wg.Add(1)
c.getShortPathByDijkstra(wg, m[startNode], m[endNode], vertex, m2)
}
wg.Wait()
return cad.GetCADSlice2Str(datas...)
}
func (c *CacService) parseGraph(graphStr string) (Graphs, error) {
graphMap := make(Graphs)
err := json.Unmarshal([]byte(graphStr), &graphMap)
if err != nil {
fmt.Println(err)
return graphMap, err
}
if _, ok := graphMap["graph"]; !ok {
return graphMap, errors.New("請傳入graph")
}
return graphMap, nil
}
func (c *CacService) mapToSlice(graphMap Graphs) ([][]float64, map[string]int, map[int]string, error) {
var vertex [][]float64
//頂點對應的下標
Key2Index := make(map[string]int)
//下標對應的頂點
Index2Key := make(map[int]string)
for k, v := range graphMap["graph"] {
Key2Index[k] = 0
for k1 := range v {
Key2Index[k1] = 0
}
}
i := 0
//每個節點映射一個下標，由於map的亂序性每次給同樣的key給的下標都不一樣
keys := make([]string, 0)
for k := range Key2Index {
keys = append(keys, k)
}
sort.Strings(keys)
for _, v := range keys {
Key2Index[v] = i
Index2Key[i] = v
i++
}
//初始化分配二維數組
for i := 0; i < len(Key2Index); i++ {
tmp := make([]float64, len(Key2Index))
vertex = append(vertex, tmp)
}
//給每個點賦值無窮大
for i := 0; i < len(Key2Index); i++ {
for j := 0; j < len(Key2Index); j++ {
vertex[i][j] = math.MaxFloat64
}
}
for k, v := range graphMap["graph"] {
for k1, v := range v {
vertex[Key2Index[k]][Key2Index[k1]] = v
vertex[Key2Index[k1]][Key2Index[k]] = v
}
}
return vertex, Key2Index, Index2Key, nil
}
func (c *CacService) getShortPathByDijkstra(wg *sync.WaitGroup, startNode, endNode int,
vertex [][]float64, Index2Key map[int]string) {
var TablePathMin float64 //存放dis中,未遍歷的最小結點的值
defer wg.Done()
//記錄結點是否已經找到v0到vx的最小路徑
dis = make([]Dis, len(vertex))
//// 獲取v0這一行的權值數組
for i := 0; i < len(vertex); i++ {
dis[i].Length = vertex[startNode][i]
dis[i].Path = Index2Key[startNode] + "->" + Index2Key[i]
}
dis[startNode].Length = 0
dis[startNode].Visited = true
for v := 1; v < len(vertex); v++ {
TablePathMin = math.MaxFloat64
//找出dis中,未遍歷的最小結點的值
Vx := 0 //存放dis中,未遍歷的最小結點的下標
for w := 0; w < len(vertex); w++ {
if !dis[w].Visited && dis[w].Length < TablePathMin {
Vx = w
TablePathMin = dis[w].Length
}
}
dis[Vx].Visited = true
for j := 0; j < len(vertex); j++ {
if !dis[j].Visited && dis[Vx].Length+vertex[Vx][j] < dis[j].Length {
dis[j].Length = dis[Vx].Length + vertex[Vx][j]
//end := j + 1
//if j == len(vertex)-1 {
// end = j
//}
dis[j].Path = dis[Vx].Path + "->" + Index2Key[j]
}
}
}
path := c.getDijstraCadPath(dis[endNode], Index2Key[startNode], Index2Key[endNode])
datas = append(datas, path)
mutex.Unlock()
}
func (c *CacService) getDijstraCadPath(dis Dis,
startNode, endNode string) string {
if dis.Length == math.MaxFloat64 {
minPath := cad.GetCADObject(cad.GetCADString("起點", startNode),
cad.GetCADString("終點", endNode),
cad.GetCADSpaceString("路徑", getCADNoPath(startNode, endNode, "路徑不通")),
cad.GetCADString("長度", "0"))
return minPath
} else {
minPath := cad.GetCADObject(cad.GetCADString("起點", startNode),
cad.GetCADString("終點", endNode),
cad.GetCADSpaceString("路徑", getCADPath(dis.Path)),
cad.GetCADString("長度", cast.ToString(dis.Length)),
)
return minPath
}
}
/**
遞歸算法全路徑遍歷，然後找到最短的路徑
*/
func (c *CacService) GetAllPathsByRecursive(KVs string, graph string) string {
parseGraph, _ := c.parseGraph(graph)
kvs := strings.Split(KVs, "|")
wg := &sync.WaitGroup{}
datas = make([]string, len(kvs))
for _, KV := range kvs {
kv := strings.Split(KV, ":")
startNode, endNode := kv[0], kv[1]
wg.Add(1)
path, paths, length := startNode, make(map[string]float64), 0
go func(wg *sync.WaitGroup, startNode, endNode, path string,
graph Graphs, paths map[string]float64, length float64) {
c.getMinPath(wg, startNode, endNode, path, graph, paths, length)
}(wg, startNode, endNode, path, parseGraph, paths, float64(length))
}
wg.Wait()
return cad.GetCADObject(datas...)
}
func (c *CacService) getAllPath(startNode, endNode, path string,
graph Graphs, paths map[string]float64, length float64) (string, float64) {
NextNodesMap := graph.getChildByKey(startNode)
if startNode == endNode || len(NextNodesMap) == 0 {
return path, length
}
curPath := path
curLength := length
for key := range NextNodesMap {
//判斷key在中間，在開頭，在結尾
if c.checkNodeIsPath(path, key) {
continue
}
//獲取到當前節點的路徑
c.addKey(&path, key)
//計算到當前節點的距離
c.calculatePath(≤ngth, startNode, key, graph)
lastPath, lastLength := c.getAllPath(key, endNode, path, graph, paths, length)
//當遍歷完當前節點的路徑後重置path,length爲當前path,length
path = curPath
length = curLength
if strings.Contains(lastPath, startNode) && strings.Contains(lastPath, endNode) {
paths[lastPath] = lastLength
}
}
return curPath, curLength
}
func (c *CacService) checkNodeIsPath(path, node string) bool {
ps := strings.Split(path, "->")
m := make(map[string]bool)
for i := range ps {
m[ps[i]] = true
}
return m[node]
}
func (c *CacService) addKey(s *string, key string) {
var build strings.Builder
build.WriteString(*s)
build.WriteString("->")
build.WriteString(key)
*s = build.String()
}
func (c *CacService) calculatePath(length *float64, preNode, curNode string, graph Graphs) {
*length += graph.getLengthByKeys(preNode, curNode)
}
func (c *CacService) getMinPath(wg *sync.WaitGroup, startNode, endNode, path string,
graph Graphs, paths map[string]float64, length float64) {
defer wg.Done()
c.getAllPath(startNode, endNode, path, graph, paths, length)
//正常應該有多條最短路徑，需求僅僅只需要返回一條
minPaths := c.getShortPaths(paths, startNode, endNode)
mutex.Lock()
datas = append(datas, minPaths)
mutex.Unlock()
}
func (c *CacService) getShortPaths(paths map[string]float64, startNode, endNode string) string {
minLen := float64(0)
minK := ""
for k, v := range paths {
if minLen == 0 {
minLen = v
minK = k
}
if minLen != 0 && v < minLen {
minLen = v
minK = k
}
}
//這是存在最短路徑
if len(paths) > 0 {
minPath := cad.GetCADObject(cad.GetCADString("起點", startNode),
cad.GetCADString("終點", endNode),
cad.GetCADSpaceString("路徑", getCADPath(minK)),
cad.GetCADString("長度", cast.ToString(minLen)),
)
return minPath
} else {
minPath := cad.GetCADObject(cad.GetCADString("起點", startNode),
cad.GetCADString("終點", endNode),
cad.GetCADSpaceString("路徑", getCADNoPath(startNode, endNode, "路徑不通")),
cad.GetCADString("長度", cast.ToString(minLen)), )
return minPath
}
}
/**
SPFA算法
*/
func (c *CacService) GetAllPathBySPFA(KVs string, graph string) string {
splits := strings.Split(KVs, "|")
parseGraph, _ := c.parseGraph(graph)
vert, Key2Index, Index2Key, _ := c.mapToSlice(parseGraph)
Paths := make([]*Path, 0)
for v := range splits {
k := strings.Split(splits[v], ":")
startNode := Key2Index[k[0]]
endNode := Key2Index[k[1]]
path := &Path{}
c.SPFA(startNode, endNode, len(vert), path, vert, Index2Key)
Paths = append(Paths, path)
}
datas := make([]string, 0)
for _, p := range Paths {
datas = append(datas, c.getSPFACADPath(p))
}
return cad.GetCADSlice2Str(datas...)
}
func (c *CacService) SPFA(s, e, n int, p *Path, Vert [][]float64, Index2Key map[int]string) []float64 {
dis := make([]float64, n) //
vis := make([]bool, n)
num := make([]int, n)
path := make([]int, n)
disMap := make(map[string]float64)
q := queue.New()
for i := 0; i < n; i++ {
dis[i] = math.MaxFloat64
}
dis[s] = 0
vis[s] = true
num[s] = 1
q.Add(s)
p.StartNode = Index2Key[s]
p.EndNode = Index2Key[e]
for q.Length() != 0 {
a := q.Get(0)
u := a.(int)
q.Remove()
vis[u] = false
for v := 0; v < n; v++ {
if dis[v] > dis[u]+Vert[u][v] {
dis[v] = dis[u] + Vert[u][v]
disMap[Index2Key[v]] = dis[u] + Vert[u][v]
path[v] = u
if !vis[v] {
q.Add(v)
vis[v] = true
num[v]++
if num[v] >= n {
goto no
}
}
}
}
}
//以上是spfa的主要算法內容以下爲業務操作內容
fmt.Println("開始路徑封裝")
goto ok
no:
p.Path = "存在負權迴路"
p.Value = math.MaxFloat64
fmt.Println("結束路徑封裝", p.Path)
return dis
ok:
buf := bytes.Buffer{}
tmpE := e
buf.WriteString(Index2Key[tmpE])
for s != tmpE {
prv := path[tmpE]
buf.WriteString("<-" + Index2Key[prv])
if prv == tmpE {
break
}
tmpE = prv
}
p.Path = c.reversePath(buf.String())
p.Value = disMap[Index2Key[e]]
fmt.Println("結束路徑封裝", p.Path)
return dis
}
func (c *CacService) reversePath(path string) string {
buf := bytes.Buffer{}
pathSlice := strings.Split(path, "<-")
for i, j := 0, len(pathSlice)-1; i < j; i, j = i+1, j-1 {
pathSlice[i], pathSlice[j] = pathSlice[j], pathSlice[i]
}
node := ""
for i := 0; i < len(pathSlice); i++ {
if i != len(pathSlice)-1 {
node = pathSlice[i] + "->"
} else {
node = pathSlice[i]
}
buf.WriteString(node)
}
return buf.String()
}
func (c *CacService) getSPFACADPath(p *Path) string {
if p.Value == math.MaxFloat64 {
minPath := cad.GetCADObject(cad.GetCADString("起點", p.StartNode),
cad.GetCADString("終點", p.EndNode),
cad.GetCADSpaceString("路徑", getCADNoPath(p.StartNode, p.EndNode, p.Path)),
cad.GetCADString("長度", "0"))
return minPath
} else {
minPath := cad.GetCADObject(cad.GetCADString("起點", p.StartNode),
cad.GetCADString("終點", p.EndNode),
cad.GetCADSpaceString("路徑", getCADPath(p.Path)),
cad.GetCADString("長度", cast.ToString(p.Value)),
)
return minPath
}
}
func getCADPath(path string) string {
var build strings.Builder
nodes := strings.Split(path, "->")
for index, v := range nodes {
build.WriteString(`"`)
build.WriteString(v)
if index == len(nodes)-1 {
build.WriteString(`"`)
} else {
build.WriteString(`" `)
}
}
return build.String()
}
func getCADNoPath(startNode, endNode, path string) string {
var build strings.Builder
build.WriteString(` "`)
build.WriteString(startNode)
build.WriteString(`"`)
build.WriteString(` "`)
build.WriteString(path)
build.WriteString(`"`)
build.WriteString(` "`)
build.WriteString(endNode)
build.WriteString(`"`)
return build.String()
}