分治算法的应用

分治算法

分治算法的基本思想是将一个规模为N的问题分解为K个规模较小的子问题，这些子问题相互独立且与原问题性质相同。求出子问题的解，就可得到原问题的解。即一种分目标完成程序算法，简单问题可用二分法完成

回溯算法

回溯算法实际上一个类似枚举的搜索尝试过程，主要是在搜索尝试过程中寻找问题的解，当发现已不满足求解条件时，就“回溯”返回，尝试别的路径。回溯法是一种选优搜索法，按选优条件向前搜索，以达到目标。但当探索到某一步时，发现原先选择并不优或达不到目标，就退回一步重新选择，这种走不通就退回再走的技术为回溯法，而满足回溯条件的某个状态的点称为回溯点

public class FullPermutation {
    public static void main(String[] args) {
        String s ="ABC";
        char[] arr = s.toCharArray();
        HashSet set = new HashSet<>();
        permutation(set,arr,0,arr.length - 1);
        System.out.println(set);
    }

    private static void permutation(HashSet set, char[] arr, int from, int to) {
        if(from == to){
            set.add(String.valueOf(arr));
        }else{
            for(int i = from; i <= to; i++){
                swap(arr,i,from);
                permutation(set,arr,from + 1,to);
                swap(arr,i,from);
            }
        }

    }

    private static void swap(char[] arr, int i, int j) {
        char c = arr[i];
        arr[i] = arr[j];
        arr[j] = c;
    }
}

public class ChessBoardCoverage {
    private static int BOARD_SIZE = 8;
    private static int[][] board = new int[BOARD_SIZE][BOARD_SIZE];
    private static int title = 0;

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        System.out.println(">>>");
        int dr = input.nextInt();
        int dc = input.nextInt();
        chessBoard(0,0,dr,dc,BOARD_SIZE);
        printBoard();
    }
    private static void printBoard() {
        for (int i = 0; i < BOARD_SIZE; i++) {
            for (int j = 0; j < BOARD_SIZE; j++) {
                System.out.print(board[i][j] + "t");
            }
            System.out.println();
        }
    }

    private static void chessBoard(int tr, int tc, int dr, int dc, int size) {
        if(size == 1){
            return;
        }

        int num = ++title;
        int s = size / 2;
        if(dr < tr + s && dc < tc + s){
            chessBoard(tr,tc,dr,dc,s);
        }else{
            board[tr + s - 1][tc + s - 1] = num;
            chessBoard(tr,tc,tr + s - 1,tc + s - 1,s);
        }        
        if(dr < tr + s && dc >= tc + s){
            chessBoard(tr,tc + s,dr,dc,s);
        }else{
            board[tr + s - 1][tc + s] = num;
             chessBoard(tr,tc+s,tr + s - 1,tc + s,s);
        }     
        if(dr >= tr + s && dc < tc + s){
            chessBoard(tr+s,tc,dr,dc,s);
        }else{
            board[tr + s][tc + s - 1] = num;
            chessBoard(tr + s,tc,tr + s,tc + s - 1,s);
        }      
        if(dr >= tr + s && dc >= tc + s){
            chessBoard(tr + s,tc + s,dr,dc,s);
        }else{
            board[tr + s][tc + s] = num;
            chessBoard(tr + s,tc + s,tr + s,tc + s,s);
        }
    }
}

public class Hanoi {
    public static void main(String[] args) {
        String x = "X";
        String y = "Y";
        String z = "Z";
        hanoi(3,x,y,z);
    }
    private static void hanoi(int n, String begin, String mid, String end){
        if (n == 1) {
            System.out.println(begin + "->" + end);
        } else {
            hanoi(n - 1, begin, end, mid);
            System.out.println(begin + "->" + end);
            hanoi(n - 1, mid, begin, end);
        }
    }
}