HDU1128--Self Numbers
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Self Numbers
Time Limit: 20000/10000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 6156 Accepted Submission(s): 2688
Problem Description
In 1949 the Indian mathematician D.R. Kaprekar discovered a class of numbers called self-numbers. For any positive integer n, define d(n) to be n plus the sum of the digits of n. (The d stands for digitadition, a term coined by Kaprekar.) For example, d(75) = 75 + 7 + 5 = 87. Given any positive integer n as a starting point, you can construct the infinite increasing sequence of integers n, d(n), d(d(n)), d(d(d(n))), .... For example, if you start with 33, the next number is 33 + 3 + 3 = 39, the next is 39 + 3 + 9 = 51, the next is 51 + 5 + 1 = 57, and so you generate the sequence
33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, ...
The number n is called a generator of d(n). In the sequence above, 33 is a generator of 39, 39 is a generator of 51, 51 is a generator of 57, and so on. Some numbers have more than one generator: for example, 101 has two generators, 91 and 100. A number with no generators is a self-number. There are thirteen self-numbers less than 100: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, and 97.
Write a program to output all positive self-numbers less than or equal 1000000 in increasing order, one per line.
33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, ...
The number n is called a generator of d(n). In the sequence above, 33 is a generator of 39, 39 is a generator of 51, 51 is a generator of 57, and so on. Some numbers have more than one generator: for example, 101 has two generators, 91 and 100. A number with no generators is a self-number. There are thirteen self-numbers less than 100: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, and 97.
Write a program to output all positive self-numbers less than or equal 1000000 in increasing order, one per line.
Sample Output
135792031425364|| <-- a lot more numbers|9903991499259927993899499960997199829993|||
Source
Mid-Central USA 1998
题意:如题目所举的例子,就拿75来说,因为75+7+5=87,所以75是87的祖先,同理,33是39的祖先。
但是有的数祖先不一定只有一个数,比如100,91都是101的祖先。
因此,推导出自身数的定义:没有一个祖先的数为自身数,设计程序,打印1到100^3的自身数。
思路:自己首先想到筛法求素数的方法,利用数组下标标记。
题意:如题目所举的例子,就拿75来说,因为75+7+5=87,所以75是87的祖先,同理,33是39的祖先。
但是有的数祖先不一定只有一个数,比如100,91都是101的祖先。
因此,推导出自身数的定义:没有一个祖先的数为自身数,设计程序,打印1到100^3的自身数。
思路:自己首先想到筛法求素数的方法,利用数组下标标记。
/***************Author:jiabeimuweiSources:HDU1128Times:203ms***************/#include<cstring>#include<cstdlib>#include<cstdio>using namespace std;const long long int n=1000000;bool a[n]={0};long long f(long long n){ long long s=n; while(n) { long long int c=n%10; n/=10; s+=c; } return s;}int main(){ long long int i,j; for(i=1; i<=n; i++) { a[f(i)]=1; } for(i=1; i<=n; i++) if(!a[i]) printf("%d\n",i); }
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