Project Euler：Problem 56 Powerful digit sum

标签：c++   project euler   大数乘法   

A googol (10¹⁰⁰) is a massive number: one followed by one-hundred zeros; 100¹⁰⁰ is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.

Considering natural numbers of the form, a^b, where a, b < 100, what is the maximum digital sum?

大数乘法

基本上就是从前面做过的29题那里copy来的代码

#include <iostream>
#include <string>
using namespace std;

string num2str(int n)
{
	string ans = "";
	while (n)
	{
		int a = n % 10;
		char b = a + '0';
		ans = b + ans;
		n /= 10;
	}
	return ans;
}

void reverse_data(string &data)
{
	char temp = '0';
	int start = 0;
	int end = data.size() - 1;

	while (start < end)
	{
		temp = data[start];
		data[start++] = data[end];
		data[end--] = temp;
	}
}

void compute_value(string lhs, string rhs, string &result)
{
	reverse_data(lhs);
	reverse_data(rhs);
	int i = 0, j = 0, res_i = 0;
	int tmp_i = 0;
	int carry = 0;

	for (i = 0; i != lhs.size(); ++i, ++tmp_i)
	{
		res_i = tmp_i;  //在每次计算时，结果存储的位需要增加    
		for (j = 0; j != rhs.size(); ++j)
		{
			carry += (result[res_i] - '0') + (lhs[i] - '0') * (rhs[j] - '0');//此处注意，每次计算并不能保证以前计算结果的进位都消除， 并且以前的计算结果也需考虑。    
			result[res_i++] = (carry % 10 + '0');
			carry /= 10;
		}
		while (carry)//乘数的一次计算完成，可能存在有的进位没有处理    
		{
			result[res_i++] = (carry % 10 + '0');
			carry /= 10;
		}
	}
	for (int i = result.size() - 1; i >= 0; i--)
	{
		if (result[i] != '0')
			break;
		else
			result.pop_back();
	}
	
	reverse_data(result);
}

int count_num(string s)
{
	int count = 0;
	for (int i = 0; i < s.length(); i++)
	{
		count += s[i] - '0';
	}
	return count;
}

int powe(string a, int b)
{
	string res = a;
	for (int ii = 1; ii < b; ii++)
	{
		string tmp(res.length() + a.length(), '0');
		compute_value(res, a, tmp);
		res = tmp;
	}
	int count = count_num(res);
	return count;
}

int main()
{
	
	int maxc = 0;
	for (int a = 1; a < 100; a++)
	{
		for (int b = 1; b < 100; b++)
		{
			string s = num2str(a);
			int ans = powe(s, b);
			if (ans>maxc)
				maxc = ans;
		}
	}
	cout << maxc << endl;
	system("pause");
	return 0;
}

Project Euler：Problem 56 Powerful digit sum

标签：c++   project euler   大数乘法   

原文地址：http://blog.csdn.net/youb11/article/details/46795199