深度优先搜索思想初体验

Posted 2020-08-12

1、求数字 1~n 的全排列

import java.util.Scanner ;

public class Permutation{                           //求数字 1~n 的全排列；
	int[] array ;
	int[] book ;
	int n ;
	public void permutation(int step){          // 深度优先搜索思想；
		if (step==n+1) {
			for (int i=1;i<=n;i++) {
				System.out.print(array[i] + " ") ;
			}
			System.out.println() ;
		}else{
			for (int i=1;i<=n;i++) {
				if (book[i]==0) {
					array[step] = i ;
					book[i] = 1 ;
					permutation(step+1) ;
					book[i] = 0 ;
				}
			}
		}
	}

	public static void main(String[] args){           //测试；
		Permutation p = new Permutation() ;
		Scanner sc = new Scanner(System.in) ;
		System.out.println("please input an integer:") ;
		p.n = sc.nextInt() ;
		p.array = new int[p.n+1] ;
		p.book = new int[p.n+1] ;
		p.permutation(1) ;
	}
}

 

2、若 abc + def = ghi，其中，a~i 为数字 1~9，请给出满足条件的全部组合；

public class DepthFirstSearch{                                 //饱含深度优先搜索思想；
	int[] array ;
	int[] book ;
	int n = 9 ;
	int total ;
	public void depthFirstSearch(int step){
		if (step==n+1) {
			if((array[1]+array[4]-array[7])*100+(array[2]+array[5]-array[8])*10+(array[3]+array[6]-array[9])==0){
				total++ ;
				for(int i=1;i<=n;i++){
					System.out.print(array[i]) ;
					if (i%3==0) {
						System.out.print(" ") ;
					}
				}
				System.out.println() ;
			}
		}else{
			for(int i=1;i<=n;i++){                           //深度优先搜索思想核心；
				if(book[i]==0){
					array[step] = i ;
					book[i] = 1 ; 
					depthFirstSearch(step+1) ;
					book[i] = 0 ;
				}
			}
		}
	}

	public static void main(String[] args) {　　　　　　　　　//测试；　　　　　　　　　　　　　　　
		DepthFirstSearch dfs = new DepthFirstSearch() ;
		dfs.array = new int[dfs.n+1] ;
		dfs.book = new int[dfs.n+1] ;
		dfs.depthFirstSearch(1) ;
		System.out.println(dfs.total/2) ;
	}
}

　　

3、最短路径

import java.util.Scanner ;

public class HelpHL{
	static int[][] map ;
	static int[][] book ;
	static int min = 99999999 ;
	static int p ;
	static int q ;
	static int m ;
	static int n ;
	
	public static void dfs(int x, int y, int step){
		
		if (x!=p || y!=q) {
			int[][] next = {{1,0},{-1,0},{0,1},{0,-1}} ;       //四个方向；
			for (int k=0;k<=3;k++) {
				int newX = x + next[k][0] ;
				int newY = y + next[k][1] ;
				if (newX>=0 && newX<m && newY>=0 && newY<n) {
					if (map[newX][newY]==0 && book[newX][newY]==0) {
						book[newX][newY] = 1 ;
						dfs(newX,newY,step+1) ;
						book[newX][newY] = 0 ;
					}
				}
			}
		}else{
			if(step<min){
				min = step ;
			}
		}
	}

	public static void main(String[] args){
		System.out.println("please input row(m) and column(n):") ;
		Scanner sc = new Scanner(System.in) ;
		m = sc.nextInt() ;
		n = sc.nextInt() ;
		map = new int[m][n] ;
		book = new int[m][n] ;
		System.out.println("please input destination (p,q):") ;
		p = sc.nextInt() ;
		q = sc.nextInt() ;
		System.out.println("please input map barrier:") ;
		for (int i=0;i<m;i++) {
			for (int j=0;j<n;j++) {
				map[i][j] = sc.nextInt() ;
			}
		}
		System.out.println("please input initial position (startX,startY):") ;
		int startX = sc.nextInt() ;
		int startY = sc.nextInt() ;
		dfs(startX,startY,0) ;
		System.out.println("The minimum " + min + " steps") ;

	}

}