[原创]Light 1045 Digits of Factorial 【数论】

2016-06-30 15:54:37 Tabris_ 阅读数：241

https://blog.csdn.net/qq_33184171/article/details/51791054

Digits of Factorial
Time Limit:2000MS Memory Limit:32768KB 64bit IO Format:%lld & %llu
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Status
Description
Factorial of an integer is defined by the following function

f(0) = 1
f(n) = f(n - 1) * n, if(n > 0)

So, factorial of 5 is 120. But in different bases, the factorial may be different. For example, factorial of 5 in base 8 is 170.

In this problem, you have to find the number of digit(s) of the factorial of an integer in a certain base.

Input
Input starts with an integer T (≤ 50000), denoting the number of test cases.

Each case begins with two integers n (0 ≤ n ≤ 106) and base (2 ≤ base ≤ 1000). Both of these integers will be given in decimal.

Output
For each case of input you have to print the case number and the digit(s) of factorial n in the given base.

Sample Input
5
5 10
8 10
22 3
1000000 2
0 100
Sample Output
Case 1: 3
Case 2: 5
Case 3: 45
Case 4: 18488885
Case 5: 1

log(n!)=log(n)+log(n-1)+ … （以上底数为base）.

RE ： printf(“Case %d: %.0llf\n”,++p,f[n]/log(base)+0.5);

WA：printf(“Case %d: %d\n”,++p,(int)(f[n]/log(1.0*base)+0.5));