LightOJ - 1282 - Leading and Trailing (math skills, quickly taking over power)

link:

https://vjudge.net/problem/LightOJ-1282

Meaning of the questions:

You are given two integers: n and k, your task is to find the most significant three digits, and least significant three digits of nk.

Ideas:

After three quick power to take over, consider the top three.
\ (n ^ k \) may be expressed as \ (a * 10 ^ m \ ) i.e. using scientific notation.
On both sides of the logarithm to give \ (k * log10 (n)
= log10 (a) + m \) then x = log10 (a) is k * log10 (n) of the fractional part.
a = pow (10, x) . is the front part of scientific notation.

Code:

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<math.h>
#include<vector>
#include<map>

using namespace std;
typedef long long LL;
const int INF = 1e9;

const int MAXN = 1e6+10;
const int MOD = 1e9+7;

LL n, k;

LL PowMod(LL a, LL b)
{
    LL res = 1;
    while(b)
    {
        if (b&1)
            res = res*a%1000;
        a = a*a%1000;
        b >>= 1;
    }
    return res;
}

int main()
{
    int t, cnt = 0;
    scanf("%d", &t);
    while(t--)
    {
        printf("Case %d:", ++cnt);
        scanf("%lld%lld", &n, &k);
        double v = 1.0*k*log10(n);
        v -= (LL)v;
        LL r1 = (LL)(pow(10, v)*100);
        LL r2 = PowMod(n, k);
        printf(" %lld %03lld\n", r1, r2);
    }
    
    return 0;
}