HDU 4708 Rotation Lock Puzzle

最新推荐文章于 2025-08-17 21:38:20 发布

转载最新推荐文章于 2025-08-17 21:38:20 发布 · 114 阅读

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原文链接：http://www.cnblogs.com/james1207/p/3312920.html

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本文介绍了一种基于矩阵旋转的谜题锁解决方法，通过旋转矩阵以最大化主对角线和反对角线的数值总和，旨在寻找最优解。文章详细阐述了问题描述、输入输出格式、样例输入输出，并提供了完整的Java代码实现。

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Rotation Lock Puzzle

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 659 Accepted Submission(s): 193

Problem Description

Alice was felling into a cave. She found a strange door with a number square matrix. These numbers can be rotated around the center clockwise or counterclockwise. A fairy came and told her how to solve this puzzle lock: “When the sum of main diagonal and anti-diagonal is maximum, the door is open.”.
Here, main diagonal is the diagonal runs from the top left corner to the bottom right corner, and anti-diagonal runs from the top right to the bottom left corner. The size of square matrix is always odd.

This sample is a square matrix with 5*5. The numbers with vertical shadow can be rotated around center ‘3’, the numbers with horizontal shadow is another queue. Alice found that if she rotated vertical shadow number with one step, the sum of two diagonals is maximum value of 72 (the center number is counted only once).

Input

Multi cases is included in the input file. The first line of each case is the size of matrix n, n is a odd number and 3<=n<=9.There are n lines followed, each line contain n integers. It is end of input when n is 0 .

Output

For each test case, output the maximum sum of two diagonals and minimum steps to reach this target in one line.

Sample Input

    5 9 3 2 5 9 7 4 7 5 4 6 9 3 9 3 5 2 8 7 2 9 9 4 1 9 0 
  

Sample Output

    72 1 
  

Source

2013 ACM/ICPC Asia Regional Online —— Warmup

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
	BufferedReader bu;
	PrintWriter pw;
	int n;
	int[][] a;

	public static void main(String[] args) throws IOException {
		new Main().work();
	}

	void work() throws IOException {
		bu = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new OutputStreamWriter(System.out),true);
		n = Integer.parseInt(bu.readLine());
		while (n != 0) {
			a = new int[n][n];
			for (int i = 0; i < n; i++) {
				String str[] = bu.readLine().split(" ");
				for (int j = 0; j < n; j++) {
					a[i][j] = Integer.parseInt(str[j]);
				}
			}
			
			BigInteger result = BigInteger.ZERO;
			int step = 0;
			
			for (int i = 0; i < n / 2; i++) {//控制圈数
				BigInteger max = BigInteger.ZERO;
				int temp = 0;
				for (int j = i; j < n - 1 - i; j++) {
					
					BigInteger sum = BigInteger.ZERO;
					sum = sum.add(BigInteger.valueOf(a[i][j]));//第i圈的 第一行顺时针相加
					sum = sum.add(BigInteger.valueOf(a[n - 1 - i][n - 1 - j]));//第i圈的最后一行逆时针相加
					sum = sum.add(BigInteger.valueOf(a[j][n - 1 - i]));//第i圈的最后一列，顺时针相加
					sum = sum.add(BigInteger.valueOf(a[n - 1 - j][i]));//第i圈的第一列，逆时针相加
					int flag = Math.min(Math.abs(j - i),Math.abs(j - (n - 1 - i)));//每次转圈的最小步数
					 
					if (sum.compareTo(max) > 0) {
						max = sum;
						temp = flag;
					} else if (sum.compareTo(max) == 0 && temp > flag) {
						temp = flag;
					}

				}
				step += temp;
				result = result.add(max);
			}
			result = result.add(BigInteger.valueOf(a[n / 2][n / 2]));//最后再加上中心元素
			pw.println(result + " " + step);
			n = Integer.parseInt(bu.readLine());
		}
	}
}

转载于:https://www.cnblogs.com/james1207/p/3312920.html