分治算法

算法思路:

实例: 乒乓球赛程安排:

实现:

(1) 分解: 首先把8人赛程安排划分为4人:

(2) 求解: 然后再把4人赛程划分为2人:

(3) 合并: 合并成4人赛程

import java.util.Scanner;

public class FenZhi {

    private static Scanner in;

    public static int[][] fenzhi(int[][] a, int k, int n) {

        
        //这里假设是从编号1开始处理的
        if (n == 2) {
            a[k][1] = k;
            a[k][2] = k + 1;
            a[k + 1][1] = k + 1;
            a[k + 1][2] = k;

            return a;
        }

        //分治算法,本质上是两次递归
        a = fenzhi(a, k, n / 2);
        a = fenzhi(a, k + n / 2, n / 2);

        // 填充右上角
        for (int i = k; i < k + n / 2; i++) {
            for (int j = 1 + n / 2; j <= n; j++) {
                a[i][j] = a[i + n / 2][j - n / 2];
            }
        }

        // 填充右下角
        for (int i = k + n / 2; i <= n; i++) {
            for (int j = 1 + n / 2; j <= n; j++) {
                a[i][j] = a[i - n / 2][j - n / 2];
            }
        }

        return a;
    }

    public static void main(String[] args) {

        in = new Scanner(System.in);
        System.out.print("请输入你想开始的编号: ");
        int k = in.nextInt();
        System.out.print("请输入您想要处理的数量: ");
        int n = in.nextInt();

        int[][] a = new int[n + 1][n + 1];
        a = fenzhi(a, k, n);

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                System.out.print(a[i][j] + "	");
            }
            System.out.println();
        }
    }

}