牛客_魔法阵

魔法阵
https://www.nowcoder.com/practice/04c873db99a34a0c85d476be82533b98

import java.util.Arrays;
import java.util.Scanner;

/**
 * QQ9 魔法阵
 * @author d3y1
 */
public class Main {
    private static final int N = 4;

    public static void main(String[] args){
        Scanner in = new Scanner(System.in);

        while(in.hasNext()){
            solution1(in);
            // solution2(in);
        }
    }

    /**
     * 数学法: 向量
     * @param in
     */
    private static void solution1(Scanner in){
        int n = Integer.parseInt(in.nextLine());

        while(n-- > 0){
            String xStr = in.nextLine();
            String yStr = in.nextLine();

            int[] x = new int[N+1];
            int[] y = new int[N+1];

            for(int i=1; i<=N; i++){
                x[i] = Integer.parseInt(String.valueOf(xStr.charAt(i-1)));
                y[i] = Integer.parseInt(String.valueOf(yStr.charAt(i-1)));
            }

            // 1-A 2-B 3-C 4-D
            int[] vectorAD = new int[]{x[4]-x[1], y[4]-y[1]};
            int[] vectorBC = new int[]{x[3]-x[2], y[3]-y[2]};

            String result;
            if(isSquare(vectorAD, vectorBC)){
                result = "Yes";
            }else{
                result = "No";
            }

            System.out.println(result);
        }
    }

    /**
     * 是否正方形: 两条对角线向量的模相等且数量积为0
     * @param vectorAD
     * @param vectorBC
     * @return
     */
    private static boolean isSquare(int[] vectorAD, int[] vectorBC){
        // 向量模
        double lenAD = Math.pow(vectorAD[0],2)+Math.pow(vectorAD[1],2);
        double lenBC = Math.pow(vectorBC[0],2)+Math.pow(vectorBC[1],2);
        // 向量数量积(对角线)
        int dotProduct = vectorAD[0]*vectorBC[0]+vectorAD[1]*vectorBC[1];

        // 对角线向量 模相等且垂直(数量积为0)
        if(lenAD==lenBC && dotProduct==0){
            return true;
        }

        return false;
    }

    
    /**
     * 数学法
     * @param in
     */
    private static void solution2(Scanner in){
        int n = Integer.parseInt(in.nextLine());

        while(n-- > 0){
            char[] xChars = in.nextLine().toCharArray();
            char[] yChars = in.nextLine().toCharArray();

            int[] x = new int[N+1];
            int[] y = new int[N+1];

            for(int i=1; i<=N; i++){
                x[i] = xChars[i-1]-'0';
                y[i] = yChars[i-1]-'0';
            }
            
            // 1-A 2-B 3-C 4-D
            double[] edges = new double[N+2];
            double edgeAB = Math.pow(x[2]-x[1],2)+Math.pow(y[2]-y[1],2);
            double edgeAC = Math.pow(x[3]-x[1],2)+Math.pow(y[3]-y[1],2);
            double edgeAD = Math.pow(x[4]-x[1],2)+Math.pow(y[4]-y[1],2);
            double edgeBC = Math.pow(x[3]-x[2],2)+Math.pow(y[3]-y[2],2);
            double edgeBD = Math.pow(x[4]-x[2],2)+Math.pow(y[4]-y[2],2);
            double edgeCD = Math.pow(x[4]-x[3],2)+Math.pow(y[4]-y[3],2);
            edges[0] = edgeAB;
            edges[1] = edgeAC;
            edges[2] = edgeAD;
            edges[3] = edgeBC;
            edges[4] = edgeBD;
            edges[5] = edgeCD;

            Arrays.sort(edges);
            
            String result;
            if(checkSquare(edges)){
                result = "Yes";
            }else{
                result = "No";
            }

            System.out.println(result);
        }
    }

    /**
     * 是否正方形: 四条边相等 且 两条对角线相等 且 两边与对角线为直角三角形
     * @param edges
     * @return
     */
    private static boolean checkSquare(double[] edges){
        // 四条边相等 edges[0]==edges[3]
        // 两条对角线相等 edges[4]==edges[5]
        // 两边与对角线为直角三角形 edges[0]+edges[0]==edges[5]
        if(edges[0]==edges[3] && edges[4]==edges[5] && edges[0]+edges[0]==edges[5]){
            return true;
        }

        return false;
    }
}