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            Self Numbers

            Posted on 2006-06-16 23:32 mahudu@cppblog 閱讀(826) 評論(0)  編輯 收藏 引用 所屬分類: C/C++
            ???

            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 10000

            in increasing order, one per line.

            Output

            1
            3
            5
            7
            9
            20
            31
            42
            53
            64
            |
            | <-- a lot more numbers
            |
            9903
            9914
            9925
            9927
            9938
            9949
            9960
            9971
            9982
            9993

            Solution

            #include?<iostream>
            using?namespace?std;

            const?long?N?=?10000;?????//最大自然數
            char?Arr[N?+?9*4]={0};???//是否是被排除的數字??+9*4是為了要再多放4位數

            long?DealNum(long?n)
            {
            ??
            long?sum?=?n;
            ??
            while?(n?!=?0)
            ??
            {
            ????sum?
            +=?n%10;
            ????n?
            /=?10;
            ??}

            ??
            return?sum;
            }


            int?main()
            {
            ??
            int?i;
            ??
            for(i?=?1;?i?<?N;?i++)
            ??
            {
            ????Arr[DealNum(i)]?
            =?1;
            ??}

            ??
            for(i?=?1;?i?<?N;?i++)
            ??
            {
            ????
            if?(!Arr[i])
            ????????cout
            <<i<<endl;
            ??}

            ??
            return?0;
            }


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