九宫格问题（回溯法，Go语言实现）

九宫格问题（回溯法，Go语言实现）

问题重现：

有1~10十个数，填入9个数到九宫格，现要求相邻（上下、左右）的两数之和为质数，问有多少种填法？

此题比较简单，所以直接给代码了。

解法一

package main

import (
	"fmt"
)

var pos [9]int
var sub []int = []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
var num []int = []int{1, 2, 3, 5, 7, 11, 13, 17, 19}

/*从质数中查找，找到返回true*/
func searchFromNum(n int) bool {
	for i := 0; i < 9; i++ {
		if n == num[i] {
			return true
		}
	}
	return false
}

/*检验结果是否正确*/
func check(i, n int) bool {
	//纵向
	if i-3 >= 0 {
		if searchFromNum(pos[i]+pos[i-3]) == false {
			return false
		}
	}
	//横向
	if i%3 != 0 {
		if searchFromNum(pos[i]+pos[i-1]) == false {
			return false
		}
	}
	return true
}

var down, up int = 0, 9

/*填入1~10到九宫格的解，回溯法*/
func fillBox(i, n, r int, count *int) {
	if i == n {
		(*count)++
		for i := 0; i < r; i++ {
			for j := 0; j < r; j++ {
				fmt.Printf("%3d", pos[i*r+j])
			}
			fmt.Println()
		}
		fmt.Println("============")
		return
	}
	for j := down; j <= up; j++ {
		//先放入
		pos[i] = sub[j]
		if sub[j] != -1 && check(i, n) {
			sub[j] = -1
			fillBox(i+1, n, r, count)
			sub[j] = pos[i]
		}

	}
}

func main() {
	count := 0
	fillBox(0, 9, 3, &count)
	fmt.Println(count)
}

解法二

package main

import (
	"fmt"
)

var pos [9]int
var sub []int = []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
var num []int = []int{1, 2, 3, 5, 7, 11, 13, 17, 19}

/*从质数中查找，找到返回true*/
func searchFromNum(n int) bool {
	for i := 0; i < 9; i++ {
		if n == num[i] {
			return true
		}
	}
	return false
}

/*检验结果是否正确*/
func check(n int) bool {
	//行相邻
	for i := 0; i < n; i++ {
		for j := 0; j < n-1; j++ {
			if searchFromNum(pos[i*n+j]+pos[i*n+j+1]) == false {
				return false
			}
		}
	}
	//列相邻
	for j := 0; j < n; j++ {
		for i := 0; i < n-1; i++ {
			if searchFromNum(pos[i*n+j]+pos[(i+1)*n+j]) == false {
				return false
			}
		}
	}
	return true
}

var down, up int = 0, 9

/*填入0~8到九宫格的解，全排列（枚举）*/
func fillBox(i, n, r int, count *int) {
	if i == n {
		if check(r) {
			(*count)++
			for i := 0; i < r; i++ {
				for j := 0; j < r; j++ {
					fmt.Printf("%3d", pos[i*r+j])
				}
				fmt.Println()
			}
			fmt.Println("============")
		}
		return
	}
	for j := down; j <= up; j++ {
		if sub[j] != -1 {
			pos[i] = sub[j]
			sub[j] = -1
			fillBox(i+1, n, r, count)
			sub[j] = pos[i]
		}

	}
}

func main() {
	count := 0
	fillBox(0, 9, 3, &count)
	fmt.Println(count)
}