POJ1001 Exponentiation

Description

Problems involving the computation of exact values of very large magnitude and precision are common. For example, the computation of the national debt is a taxing experience for many computer systems. 

This problem requires that you write a program to compute the exact value of Rⁿ where R is a real number ( 0.0 < R < 99.999 ) and n is an integer such that 0 < n <= 25.

Input

The input will consist of a set of pairs of values for R and n. The R value will occupy columns 1 through 6, and the n value will be in columns 8 and 9.

Output

The output will consist of one line for each line of input giving the exact value of R^n. Leading zeros should be suppressed in the output. Insignificant trailing zeros must not be printed. Don't print the decimal point if the result is an integer.

Sample Input

95.123 12
0.4321 20
5.1234 15
6.7592  9
98.999 10
1.0100 12

Sample Output

548815620517731830194541.899025343415715973535967221869852721
.00000005148554641076956121994511276767154838481760200726351203835429763013462401
43992025569.928573701266488041146654993318703707511666295476720493953024
29448126.764121021618164430206909037173276672
90429072743629540498.107596019456651774561044010001
1.126825030131969720661201

解决思路：由于是高精度数相乘，将被乘数和乘数的每一位分别存放在两个数组里面，以笔算的方式，用乘数的每一位分别去乘被乘数的所有位，将得到的结果累加即可。
步骤：1.将输入的小数以倒序的方式存放在数组R中，并去除小数点（采用倒序是因为方便根据数字所在的位置，在相乘后补零）
　　　2.被乘数Multiplied为上一次相乘的结果，乘数为R
　　  3.将R的每一位分别乘以Multiplied的所有位，将相乘的结果累加存放在数组Sum中
　　  4.由于是求幂，需要循环n-1次，得到最终的结果数组
　　  5.计算最终的小数点位置，并去除前置零和结尾无效零，输出最终结果
Code：https://github.com/felove2013/Algorithms/blob/master/Poj1001/Poj1001.cpp