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  • cf468C Hack it!

    Little X has met the following problem recently.

    Let's define f(x) as the sum of digits in decimal representation of number x (for example, f(1234) = 1 + 2 + 3 + 4). You are to calculate

    Of course Little X has solved this problem quickly, has locked it, and then has tried to hack others. He has seen the following C++ code:


    ans = solve(l, r) % a;
    if (ans <= 0)
    ans += a;

    This code will fail only on the test with . You are given number a, help Little X to find a proper test for hack.
    Input

    The first line contains a single integer a (1 ≤ a ≤ 1018).

    Output

    Print two integers: l, r (1 ≤ l ≤ r < 10200) — the required test data. Leading zeros aren't allowed. It's guaranteed that the solution exists.

    Examples
    Input
    46
    Output
    1 10
    Input
    126444381000032
    Output
    2333333 2333333333333

    这题贼鸡儿恶心

    令f(x)表示x各个位上数字之和,给个p,要求构造一组[l,r],使得{f(l)+f(l+1)+...+f(r)} % p = 0

    注意到p<=10^18,当x<=10^18时,又有这样的式子成立:f(10^18+x)=f(x)+1   (这很显然,因为就在最前面加了个1)

    所以,如果[l,r]表示{f(l)+f(l+1)+...+f(r)} % p

    假设[0,10^18] -> a

    [1,10^18+1]->a+1

    ...

    [p-a,10^18+p-a]->p (其实这里模p应该是0了)

    这个区间就可以了

    然后a不会算……就算了个[0,10^18-1]=8.1*10^19,所以右区间还要减一

    这个数字好像还是爆long long的,需要81拆成9*9来搞

    1 #include<cstdio>
    2 int main()
    3 {
    4     long long p,t,e=1e18;scanf("%lld",&p);
    5     t=9*e%p*9%p;
    6     printf("%lld %lld
    ",p-t,e-1+p-t);
    7 }
    cf 468C
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  • 原文地址:https://www.cnblogs.com/zhber/p/7163864.html
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