分治算法（循环赛事问题，L型棋盘问题）

最新推荐文章于 2025-02-21 19:35:18 发布

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#分治算法

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本文探讨了两种算法实现：一是循环赛事的安排算法，通过递归方式生成比赛时间表；二是解决L型棋盘问题的算法，利用递归与条件判断填充棋盘上的数字，避免特定点。

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循环赛事

package com.ycit.sportsschedule;

public class SportsSchedule {
	public void sportsSchedule(int n,int[][] tables){
		if(n==1){
			tables[0][0]=1;
		}else{
			//填充左上角
			int m = n/2;
			sportsSchedule(m,tables);
			//填充右上角
			for(int i=0;i<m;i++){
				for(int j =m;j<n;j++){
					tables[i][j]=tables[i][j-m]+m;
				}
			}
			//填充左下方
			for(int i=m;i<n;i++){
				for(int j=0;j<m;j++){
					tables[i][j]=tables[i-m][j]+m;
				}
			}
			//填充右下方
			for(int i=m;i<n;i++){
				for(int j=m;j<n;j++){
					tables[i][j]=tables[i-m][j-m];
				}
			}
		}
	}
	public static void main(String[] args) {
		int	[][] tables =new int[8][8];
		int n=8;
		SportsSchedule schedule =new SportsSchedule();
		schedule.sportsSchedule(n, tables);
		int c = 0;
		for(int i=0;i<n;i++){
			for(int j=0;j<n;j++){
				System.out.print(tables[i][j]+" ");
				c++;
				if(c%8==0){
					System.out.println();
				}
			}
		}
	}
}

L型棋盘问题

package com.ycit.chessboradproblem;

public class ChessBoradProblem {
	private int[][] board;
	private int size;
	private int specialRow; //特殊点行下标
	private int specialCol; //特殊点列下标
	private int type=0;
	public ChessBoradProblem(int specialRow,int specialCol,int size){
		super();
		this.specialCol=specialCol;
		this.specialRow=specialRow;
		this.size = size;
		board = new int[size][size];
	}
	public void ChessBoary(int specialRow,int specialCol,int leftRow,int leftCol,int size){
		if(size==1){
			return;
		}
		int subsize = size/2;
		 type = type%4+1;
		 int n = type;
		 //假设特殊点在左上方
		 if(specialRow<leftRow+subsize&&specialCol<leftCol+subsize){
			 ChessBoary(specialCol,specialCol,leftRow,leftCol,subsize);
		 }else{
			 //不在左上方区域的右下方为特殊点
			 board[leftRow+subsize-1][leftCol+subsize-1]=n;
			 ChessBoary(leftRow+subsize-1,leftCol+subsize-1,leftRow,leftCol,subsize);
		 }
		 //特殊点在右上方
		 if(specialRow<leftRow+subsize&&specialCol>=leftCol+subsize){
			 ChessBoary(specialCol,specialCol,leftRow,leftCol+subsize,subsize);
		 }else{
			 board[leftRow+subsize-1][leftCol+subsize]=n;
			 ChessBoary(leftRow+subsize-1,leftCol+subsize,leftRow,leftCol+subsize,subsize);
		 }
		 //特殊点在左下方
		 if(specialRow>leftRow+subsize&&specialCol<specialCol-1){
			 ChessBoary(specialCol,specialCol,leftRow+subsize,leftCol,subsize);
		 }else{
			 board[leftRow+subsize][leftCol+subsize-1]=n;
			 ChessBoary(leftRow+subsize-1,leftCol+subsize,leftRow+subsize,leftCol,subsize);
		 }
		 //特殊点在右下方
		 if(specialRow>=leftRow+subsize&&specialCol>=specialCol+subsize){
			 ChessBoary(specialCol,specialCol,leftRow+subsize,leftRow+subsize,subsize);
		 }else{
			 board[leftRow+subsize][leftCol+subsize]=n;
			 ChessBoary(leftRow+subsize,leftCol+subsize,leftRow+subsize,leftRow+subsize,subsize);
		 }
	}
	public void printBoard(int specialRow,int specialCol,int size){
		ChessBoary(specialRow, specialCol, 0, 0, size);
		printResult();
	}
	
	private void printResult() {
		for(int i = 0;i<size;i++){
			for(int j = 0;j<size;j++){
				System.out.print(board[i][j]+" ");
			}
			System.out.println();
		}
	}
	public static void main(String[] args) {
		int N = 8;
		int specialRow = 0;
		int specialCol = 1;
		ChessBoradProblem boradProblem = new ChessBoradProblem(specialRow, specialCol, N);
		boradProblem.printBoard(specialRow, specialCol, N);
	}
}