算法最短路徑-Dijkstra(Golang)

//假設有9個節點,圖在代碼下方,可以參考

shortTablePath存放着V0到Vx某節點的最短路徑

該算法,第一次先將V0的節點連接的權值存入shortTablePath,沒連接的,用MAXWEIGHT表示.

package main

import (
	"fmt"
)

const MAXVEX int = 9
const MAXWEIGHT int = 1000

var shortTablePath = [MAXVEX]int{MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT}

func main() {
	graph := NewGraph()

	var TablePathMin int       //存放shortTablePath中,未遍歷的最小結點的值
	var Vx int                 //存放shortTablePath中,未遍歷的最小結點的下標
	var isgetPath [MAXVEX]bool //記錄結點是否已經找到v0到vx的最小路徑

	// 獲取v0這一行的權值數組
	for v := 0; v < len(graph); v++ {
		shortTablePath[v] = graph[0][v]
	}
	shortTablePath[0] = 0
	isgetPath[0] = true

	//遍歷v1 ~ v8
	for v := 1; v < len(graph); v++ {
		TablePathMin = MAXWEIGHT

		//找出shortTablePath中,未遍歷的最小結點的值
		for w := 0; w < len(graph); w++ {
			if !isgetPath[w] && shortTablePath[w] < TablePathMin {
				Vx = w
				TablePathMin = shortTablePath[w]
			}
		}
		isgetPath[Vx] = true
		for j := 0; j < len(graph); j++ {
			if !isgetPath[j] && TablePathMin+graph[Vx][j] < shortTablePath[j] {
				shortTablePath[j] = TablePathMin + graph[Vx][j]
			}
		}

		fmt.Println("遍歷完V", v, "后:", shortTablePath)

	}

	//輸出
	for i := 0; i < len(shortTablePath); i++ {
		fmt.Println("V0到V", i, "最小路徑:", shortTablePath[i])
	}

}

func NewGraph() [MAXVEX][MAXVEX]int {
	var graph [MAXVEX][MAXVEX]int
	var v0 = [MAXVEX]int{0, 1, 5, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT}
	var v1 = [MAXVEX]int{1, 0, 3, 7, 5, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT}
	var v2 = [MAXVEX]int{5, 3, 0, MAXWEIGHT, 1, 7, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT}
	var v3 = [MAXVEX]int{MAXWEIGHT, 7, MAXWEIGHT, 0, 2, MAXWEIGHT, 3, MAXWEIGHT, MAXWEIGHT}
	var v4 = [MAXVEX]int{MAXWEIGHT, 5, 1, 2, 0, 3, 6, 9, MAXWEIGHT}
	var v5 = [MAXVEX]int{MAXWEIGHT, MAXWEIGHT, 7, MAXWEIGHT, 3, 0, MAXWEIGHT, 5, MAXWEIGHT}
	var v6 = [MAXVEX]int{MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, 3, 6, MAXWEIGHT, 0, 2, 7}
	var v7 = [MAXVEX]int{MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, 9, 5, 2, 0, 4}
	var v8 = [MAXVEX]int{MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, MAXWEIGHT, 7, 4, 0}
	graph[0] = v0
	graph[1] = v1
	graph[2] = v2
	graph[3] = v3
	graph[4] = v4
	graph[5] = v5
	graph[6] = v6
	graph[7] = v7
	graph[8] = v8
	return graph
}

 

graph 圖:

 

遍歷完V 1 后: [0 1 4 8 6 1000 1000 1000 1000]
遍歷完V 2 后: [0 1 4 8 5 11 1000 1000 1000]
遍歷完V 3 后: [0 1 4 7 5 8 11 14 1000]
遍歷完V 4 后: [0 1 4 7 5 8 10 14 1000]
遍歷完V 5 后: [0 1 4 7 5 8 10 13 1000]
遍歷完V 6 后: [0 1 4 7 5 8 10 12 17]
遍歷完V 7 后: [0 1 4 7 5 8 10 12 16]
遍歷完V 8 后: [0 1 4 7 5 8 10 12 16]
V0到V 0 最小路徑: 0
V0到V 1 最小路徑: 1
V0到V 2 最小路徑: 4
V0到V 3 最小路徑: 7
V0到V 4 最小路徑: 5
V0到V 5 最小路徑: 8
V0到V 6 最小路徑: 10
V0到V 7 最小路徑: 12
V0到V 8 最小路徑: 16