【Codeforces 582A】GCD Table

【链接】 我是链接,点我呀:)

【题意】

给你一个数组A[]经过a[i][j] = gcd(A[i],A[j])的规则生成的二维数组
让你求出原数组A

【题解】

我们假设原数组是A
然后让A数组满足A[i](感性认知一下)

每次都把A[i+1..n]这些数字产生的gcd都删掉

那么剩余的a[][]里面只有A[1..i]产生的gcd

那么因为A[i]是最大值,所以gcd(A[i],A[i])肯定也是a[][]里面的最大值,也即A[i]=剩余的a[][]里面的最大值

【代码】

import java.io.*;
import java.util.*;

public class Main {

    static InputReader in;
    static PrintWriter out;

    public static void main(String[] args) throws IOException{
        //InputStream ins = new FileInputStream("E:\\rush.txt");
        InputStream ins = System.in;
        in = new InputReader(ins);
        out = new PrintWriter(System.out);
        //code start from here
        new Task().solve(in, out);
        out.close();
    }

    static int N = 500;
    static class Task{

        int n;
        int ans[] = new int[N+10];
        TreeMap<Integer, Integer> dic = new TreeMap<Integer,Integer>();

        int _findmax() {
        	int x = dic.lastKey();
        	return x;
        }

        int gcd(int x,int y) {
        	if (y==0) return x;
        	else return gcd(y,x%y);
        }

        void _delete(int x) {
        	int y = dic.get(x);
        	y--;
        	if (y==0) dic.remove(x);else dic.put(x, y);
        }

        public void solve(InputReader in,PrintWriter out) {
        	n = in.nextInt();
        	for (int i = 1;i <= n*n;i++) {
        		int x = in.nextInt();
        		if (dic.containsKey(x)) {
        			int y = dic.get(x);
        			y++;
        			dic.put(x, y);
        		}else dic.put(x, 1);
        	}
        	for (int i = n;i >= 1;i--) {
        		ans[i] = _findmax();
        		_delete(gcd(ans[i],ans[i]));
        		for (int j = i+1;j<= n;j++) {
        			_delete(gcd(ans[i],ans[j]));
        			_delete(gcd(ans[i],ans[j]));
        		}
        	}
        	for (int i = 1;i <= n;i++)
        		out.print(ans[i]+" ");
        	out.println();
        }
    }

    static class InputReader{
        public BufferedReader br;
        public StringTokenizer tokenizer;

        public InputReader(InputStream ins) {
            br = new BufferedReader(new InputStreamReader(ins));
            tokenizer = null;
        }

        public String next(){
            while (tokenizer==null || !tokenizer.hasMoreTokens()) {
                try {
                tokenizer = new StringTokenizer(br.readLine());
                }catch(IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}