2006 - 整除问题

通过次数

0

提交次数

0

时间限制 : 1 秒 内存限制 : 128 MB

给出n个数a1,a2…an,求出一个数T,要求T能整除n个数中的其中n-1个,但不能整除所有的n个数,如果存在多个T,输出最小的。

例如2,3,5,则输出6,因为6是2和3的最小公倍数,但不是2,3,5的最小公倍数,T还可能是10,15,75等,但是由于6最小,所以输出6.

如果T不存在,则输出-1。

题目输入

第一行输入n,表示n个数,1<n<=6接下来一行输入n个数,0<a1…an,ai<=15

题目输出

一个数,T,其中每个测试数据占一行

输入/输出样例

输入格式

3
2 3 5
3
10 6 15

输出格式

6
-1

C++解答

#include<stdio.h>
#include<algorithm>
using namespace std;
int main()
{
    int a[6];
    int n;
    while(scanf("%d",&n)!=EOF)
    {  int co=1;
        for(int i=0;i<n;i++)
        {
             scanf("%d",&a[i]);
             co*=a[i];
        }
        sort(a,a+n);

        int z=0;
        for(int i=a[n-2];i<co;i++)
        { int t=0;
            for(int j=0;j<n;j++)
            {
                if(i%a[j]==0)t++;
            }

            if(t==n-1)
                {z=i;break;}

        }
        if(z==0) printf("-1\n");
        else printf("%d\n",z);
    }
}

Java解答

import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.List;
import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Laputa
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}
}

class Task {
	public void solve(int testNumber, InputReader cin, OutputWriter out) {
		while(cin.hasNext()){
			int n=cin.nextInt();
			int num[]=new int[n];
			for(int i=0;i<n;i++){				
				num[i]=cin.nextInt();				
			}
			long ans=Long.MAX_VALUE;
			for(int i=0;i<n;i++){
				long mul=1;
				for(int j=0;j<n;j++){
					if(i==j)
						continue;
					mul=IntegerUtils.lcm(mul,num[j]);
				}
				if(mul%num[i]!=0)
					ans=Math.min(ans,mul);				
			}
			if(ans!=Long.MAX_VALUE)
				out.println(ans);
			else
				out.println(-1);
		}
	}
}

class InputReader {

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	public int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int peek() {
		if (numChars == -1)
			return -1;
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				return -1;
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar];
	}

	public int nextInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	public static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	public boolean isExhausted() {
		int value;
		while (isSpaceChar(value = peek()) && value != -1)
			read();
		return value == -1;
	}

	public boolean hasNext() {
		return !isExhausted();
	}

	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}

	public void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void println(Object... objects) {
		print(objects);
		writer.println();
	}

	public void close() {
		writer.close();
	}

	}

class IntegerUtils {
	public static long gcd(long a, long b) {
		a = Math.abs(a);
		b = Math.abs(b);
		while (b != 0) {
			long temp = a % b;
			a = b;
			b = temp;
		}
		return a;
	}

	public static long lcm(long a, long b) {
		return a / gcd(a, b) * b;
	}

	}