Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

49愛的鼓勵 6訂閱站台

The Problem

Recreational mathematics is mathematics that is fun and used as either as a diversion from serious mathematics or as a way of making serious mathematics understandable or palatable.  These are the pedagogic uses of recreational mathematics.  They are already present in the oldest known mathematics and continue to the present day. One of the topic of the recreational mathematics is the Automorphic numbers  which have many use in different  fields.

Automorphic numbers are those numbers whose square ends with the number itself:

52	=	25,
252	=	625,
762	=	5776.

The first automorphic numbers are 1, 5, 6, 25, 76,  ... By definition 0 is not an Automorphic Number and for this particular problem we will not consider 1 as an Automorphic Number.

Automorphic numbers have enormous application in mathematics. In this problem you are to determine whether a given number is Automorphic or not.

The Input

Each line containing a arbitrarily big integer. Some Automorphic number have leading zeros. So leading zeros must be considered as significant. Input is terminated by end of file.

The Output

If the input is an Automorphic number print ``Automorphic number of n-digit.'', where n is the number of digit of the integer which will not be greater then 2000. Otherwise print ``Not an Automorphic number.''.

Sample Input

5
76
34

Sample Output

Automorphic number of 1-digit.
Automorphic number of 2-digit.
Not an Automorphic number.

---

Suman Mahbub
Created: 01-09-2002
Updated: 14-12-2002

做法：
這題有幾個要點要處理，特別是 0 與 1 不算是 Automaorphic Numbers
同時， 0001, 000001 .... 也都不是，就因為這樣錯了好多次。

有很多加速的地方，就如只有一些特別的尾數是可行解，特別判斷一下，
就可以在運算上比較好處理。


#include <stdio.h>
#include <string.h>
char in[5000];
int main() {
    int i, j, k;
    while(scanf("%s", in) == 1) {
        if(!strcmp(in, "0") || !strcmp(in, "1")) {
            puts("Not an Automorphic number.");
            continue;
        }
        int x[3005] = {}, y[3005] = {};
        int len = strlen(in);
        for(i = 0, j = len-1; i < len; i++, j--)
            x[j] = in[i]-'0';
        int top = len-1;
        while(top >= 0 && x[top] == 0)
            top--;
        if(top < 0 || (top == 0 && x[top] == 1)) {
            puts("Not an Automorphic number.");
            continue;
        }
        int error = 0;
        for(i = 0; i < len && !error; i++) {
            if(x[i])
                for(j = 0; i+j < len; j++)
                    y[i+j] += x[i]*x[j];
            y[i+1] += y[i]/10;
            y[i] %= 10;
            if(y[i] != x[i])
                error = 1;
        }
        if(error)
            puts("Not an Automorphic number.");
        else
            printf("Automorphic number of %d-digit.\n", len);
    }
    return 0;
}