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004.cpp
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004.cpp
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/*
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers.
*/
/*
The product of two 3-digit numbers is a number of 6 or less digits, 999x999 = 998001
1st approach) Create all 6-digit palindromes (abccba) and 5 digit palindromes (0abcba) and decompose in 3-digit products.
2nd approach) Generate all 3-digit numbers, multiply them and check for palindromes within.
*/
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
class Palindrome
{
private:
int palindrome[6];
public:
Palindrome(int a, int b, int c, int d, int e, int f)
{
palindrome[0] = a;
palindrome[1] = b;
palindrome[2] = c;
palindrome[3] = d;
palindrome[4] = e;
palindrome[5] = f;
}
int toInt()
{
int intPal = 0;
for(int i = 0; i < 6; ++i)
{
intPal += this->palindrome[i] * std::pow(10, i);
}
return intPal;
}
};
std::vector<Palindrome*> Collection;
void registerPalindrome(int a, int b, int c, int d, int e, int f)
{
Palindrome* mPalindrome = new Palindrome(a, b, c, d, e, f);
Collection.push_back( mPalindrome );
}
void generatePalindromes()
{
int a, b, c, d;
for(int i = 0; i < 10; ++i)
{
a = i;
for(int ii = 0; ii < 10; ++ii)
{
b = ii;
for(int iii = 0; iii < 10; ++iii)
{
c = iii;
if(a == 0)
{
for(int iv = 0; iv < 10; ++iv)
{
d = iv;
registerPalindrome(a, b, c, d, c, b);
}
}
else
{
registerPalindrome(a, b, c, c, b, a);
}
}
}
}
}
void factorize(Palindrome* mPal)
{
int intPal = mPal->toInt();
for(int i = 100; i < 1000; ++i)
{
if(intPal % i == 0)
{
int possible_factor = intPal / i;
if(possible_factor > 99 && possible_factor < 1000)
{
std::cout << intPal << " = " << i << " x " << possible_factor << std::endl;
}
}
}
}
int main()
{
generatePalindromes();
std::for_each(Collection.begin(), Collection.end(), factorize);
return 0;
}