## Problem:

NOTE: This problem is a more challenging version of Problem 81.

The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, and right, is indicated in red and bold; the sum is equal to 994.

131 673 234 103 18
201 96 342 965 150
630 803 746 422 111
537 699 497 121 956
805 732 524 37 331

Find the minimal path sum, in matrix.txt (right click and 'Save Link/Target As...'), a 31K text file containing a 80 by 80 matrix, from the left column to the right column.

45228

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 32 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */import java.util.Arrays;public final class p032 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p032().run());	}			public String run() {		// A candidate product has at most 4 digits. This is because if it has 5 digits,		// then the two multiplicands must have at least 5 digits put together.		int sum = 0;		for (int i = 1; i < 10000; i++) {			if (hasPandigitalProduct(i))				sum += i;		}		return Integer.toString(sum);	}			private static boolean hasPandigitalProduct(int n) {		// Find and examine all factors of n		for (int i = 1; i <= n; i++) {			if (n % i == 0 && isPandigital("" + n + i + n/i))				return true;		}		return false;	}			private static boolean isPandigital(String s) {		if (s.length() != 9)			return false;		char[] temp = s.toCharArray();		Arrays.sort(temp);		return new String(temp).equals("123456789");	}	}

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