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。

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Happy Numbers

Background

Let the sum of the squares of the digits of a positive integer s₀ be represented by s₁. In a similar way, let the sum of the squares of the digits of s₁ be represented by s₂, and so on. If s_i=1 for some i>=1, then the original integer s₀ is said to be happy. For example, starting with 7 gives the sequence

7, 49 (=7^2), 97 (=4^2+9^2), 130 (=9^2+7^2), 10 (=1^2+3^2), 1 (=1^2),

so 7 is a happy number.

The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, .... The number of iterations i required for these to reach 1 are, respectively, 1, 6, 2, 3, 5, 4, 4, 3, 4, 5, 5, 3, ....

A number that is not happy is called unhappy. Once it is known whether a number is happy (unhappy), then any number in the sequence s₁, s₂, s₃, ... will also be happy (unhappy). Unhappy numbers have eventually periodic sequences of s_i which do not reach 1 (e.g., 4, 16, 37, 58, 89, 145, 42, 20, 4, ...).

Any permutation of the digits of a happy (unhappy) number must also be happy (unhappy). This follows from the fact that addition is commutative. Moreover, the product of a happy (unhappy) number by any power of ten is a happy (unhappy) number. Example: 58 is an unhappy number; then, so are 85, 580, 850, 508, 805, 5800, 5080, 5008, 8050, 8500, and so on.

Problem

Decide which numbers, in a given closed interval, are happy numbers.

Input

The input has n lines each of them corresponding to a test case. Every line contains two positive integers between 1 and 99999 (inclusive) each; the first integer, L, is the low limit of the closed interval; the second one, H, is the high limit (L ≤ H).

Output

The output is composed of the happy numbers that lie in the interval [L,H], together with the number of iterations required for the corresponding sequences of squares to reach 1.

There must be a line for each happy number containing the happy number followed by a space and the number of iterations required for the sequence of squares to reach 1.

Print a blank line between two consecutive test cases.

Sample Input

5 28
233 250

Sample Output

7 6
10 2
13 3
19 5
23 4
28 4

236 6
239 6

---

#include <stdio.h>
#include <set>
using namespace std;
int happy[100000] = {};
void solve() {
    int i;
    for(i = 1; i < 100000; i++) {
        int l = 0, n = i, tmp;
        set<int> s;
        while(n != 1) {
            l++;
            tmp = 0;
            while(n) {
                tmp += (n%10)*(n%10);
                n /= 10;
            }
            n = tmp;
            if(s.find(n) != s.end())
                break;
            s.insert(n);
        }
        if(n == 1)
            happy[i] = l+1;
    }
}
int main() {
    solve();
    int flag = 0, L, H;
    while(scanf("%d %d", &L, &H) == 2) {
        if(flag)
            puts("");
        flag = 1;
        for(int i = L; i <= H; i++) {
            if(happy[i])
                printf("%d %d\n", i, happy[i]);
        }
    }
    return 0;
}