Project Euler: 04 Largest Palindrome Product
Per the problem description, a palindromic number reads the same both ways. The largest palindrome made from the product of two \(2\)-digit numbers is \(9009 = 91 \times 99\). The goal of this problem is to find the largest palindrome made from the product of two \(3\)-digit numbers.
Solution
To check that a given number \(n\) is a palindrome, we will reverse the number and check if the \(n\) is equal to its reverse.
int isPalindrome(int n) {
int reminder, reverse = 0, number = n;
while (n > 0) {
reminder = n % 10;
reverse = reverse * 10 + reminder;
n = n / 10;
}
return (reverse == number);
}
To find the largest product of \(3\) digit numbers, we will use a double loop starting from \(999\) and going down. At any point, if we find a palindrome that is smaller than the current largest one, we will exit.
int largestPalindrome(int n) {
int palindrome, largestPalindrome = 0;
for (int i = 999; i >= 0; i--) {
for (int j = i; j >= 0; j--) {
if (i * j < largestPalindrome) { break; }
palindrome = isPalindrome(i * j);
if (palindrome && i * j > largestPalindrome && i * j <= n) {
largestPalindrome = i * j;
}
}
}
return largestPalindrome;
}Calling this to find the largest palindrome is then trivial.
printf("%d\n", largestPalindrome(999999));
The entire code is here.