第九届蓝桥杯大赛省赛C语言B组-填空题-乘积尾零（Java实现）

乘积尾零

如下的10行数据，每行有10个整数，请你求出它们的乘积的末尾有多少个零？

5650 4542 3554 473 946 4114 3871 9073 90 4329 
2758 7949 6113 5659 5245 7432 3051 4434 6704 3594 
9937 1173 6866 3397 4759 7557 3070 2287 1453 9899 
1486 5722 3135 1170 4014 5510 5120 729 2880 9019 
2049 698 4582 4346 4427 646 9742 7340 1230 7683 
5693 7015 6887 7381 4172 4341 2909 2027 7355 5649 
6701 6645 1671 5978 2704 9926 295 3125 3878 6785 
2066 4247 4800 1578 6652 4616 1113 6205 3264 2915 
3966 5291 2904 1285 2193 1428 2265 8730 9436 7074 
689 5510 8243 6114 337 4096 8199 7313 3685 211 

注意：需要提交的是一个整数，表示末尾零的个数。不要填写任何多余内容。

【题解】

第一种，因为2*5=10，所以只需把全部的数分解为2和5的质因数，看有多少个2和5相乘即可。

第二种，使用大数类累乘计算出完整结果，数一下尾数几个零

第三种（代码略）直接算出2个数的乘积，统计末尾有多少个0，去零后保留后四位再与下一个数相乘，直至全部数都乘完，统计0的个数

方法一：分解为2和5的质因数

package 省赛._09第九届;

public class C3乘积尾零2 {
	public static void main(String[] args) {
		int[] a={5650,4542,3554,473,946,4114,3871,9073,90,4329,
				2758,7949,6113,5659,5245,7432,3051,4434,6704,3594,
				9937,1173,6866,3397,4759,7557,3070,2287,1453,9899,
				1486,5722,3135,1170,4014,5510,5120,729,2880,9019,
				2049,698,4582,4346,4427,646,9742,7340,1230,7683,
				5693,7015,6887,7381,4172,4341,2909,2027,7355,5649,
				6701,6645,1671,5978,2704,9926,295,3125,3878,6785,
				2066,4247,4800,1578,6652,4616,1113,6205,3264,2915,
				3966,5291,2904,1285,2193,1428,2265,8730,9436,7074,
				689,5510,8243,6114,337,4096,8199,7313,3685,211};
		int a2=0, a5=0;
		for(int i=0; i<100; i++) {
			while(a[i]>0) {
				if(a[i]%2==0) {
					a2++;
					a[i]=a[i]/2;
				}else if(a[i]%5==0) {
					a5++;
					a[i]=a[i]/5;
				}else {
					a[i]=0;
				}
			}
		}
		//因为2*5=10，所以只需把全部的数分解为2和5的质因数，看有多少个2和5相乘即可。
		System.out.println(Math.min(a2, a5));
	}
}

方法二：使用大数类累乘 

package 省赛._09第九届;

import java.math.BigInteger;

public class C3乘积尾零 {
	public static void main(String[] args) {
		//ctrl+f 查找替换
		int[] a={5650,4542,3554,473,946,4114,3871,9073,90,4329,
				2758,7949,6113,5659,5245,7432,3051,4434,6704,3594,
				9937,1173,6866,3397,4759,7557,3070,2287,1453,9899,
				1486,5722,3135,1170,4014,5510,5120,729,2880,9019,
				2049,698,4582,4346,4427,646,9742,7340,1230,7683,
				5693,7015,6887,7381,4172,4341,2909,2027,7355,5649,
				6701,6645,1671,5978,2704,9926,295,3125,3878,6785,
				2066,4247,4800,1578,6652,4616,1113,6205,3264,2915,
				3966,5291,2904,1285,2193,1428,2265,8730,9436,7074,
				689,5510,8243,6114,337,4096,8199,7313,3685,211};
		//用大数类累乘，数一下尾数几个零
		BigInteger sum = BigInteger.ONE;
		for(int i=0; i<a.length; i++) 
			sum = sum.multiply(BigInteger.valueOf(a[i]));
		System.out.println(sum);
	}
}

结果

112142221918653666702449201125076321480831896827506427440731023870278025729017605653056978504625081950967446934475613782859722081655293509714201067451491601144000940085173776751705443818861349991600968912829674368417898694508188364854988187881792613763161458365648071883922054736261940944120399031297726871056069331318210560000000000000000000000000000000

答案：31