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Projecteuler.net: Problem 4: Matlab: Largest Palindrome Product

Problem4 projecteuler.net

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. Solve using Matlab?

Solution

Here to find the solution we will generate number which are product of three digit number and will check if the number is palindrome or not. Finally we will find the largest number of the given set and that will be the solution.

If you don't know the ispalindrome function then go to our previous post on what is palindrome and the palindrome function to get a good idea to solve this problem. Click here to go to the post: 
Download the ispalindrome.m matlab file from here: ispalindrome.m
Note that the explanation for the program is below the program section, this program will take a minute or two to generate the answer, because we will have to loop through so many numbers.

Program

%This script will generate largest palindrome number which 
%is a multiple of three digit numbers

%An empty vector to store all the palindrome numbers
vec = [];


%Two for loops are created to loop through the multiplication
for i = 100:999
    for j = 100:999
        number = i*j;
        if ispalindrome(number)
            vec = [vec number];
        end
    end
end

vec = max(vec)

Explanation

In this script an empty vector is created to store the numbers generated which are palindrome.
Now two for loops are created to generate the value of multiples.
To make it simple we will go through the first two iterations and you will get a clear cut understanding.

First iteration

During the first iteration i = 100 now the computer will dig through the next line and again it will find another loop. In this iteration with the second loop the numbers generated are as follows:

i = 100, j = 100
i = 100, j= 101
i = 100, j = 102
.
.
.
i = 100, j = 999

Second iteration

During the second iteration the i value changes to 101 and the same process continues. The iterator values are as follows:

i = 101, j = 100
i = 101, j = 101
i = 101, j = 102
.
.
.
i = 101, j = 999

This iterations will continue till the i value 999 is reached.

In the next line there is a number variable which will find the product of i and j. So for every iteration of i 999 numbers are generated, and for every iteration of j 1 number is produced.

The ispalindrome function will check whether the number is palindrome or not and will store the number in the vec vector if the number is palindrome. 

Finally we will have a vector with all the palindrome numbers which are multiples of  two three digit numbers. We will use the max function in matlab to get the maximum valued number in the vector generated.

To download the this post and read online click here: problem4_projecteuler_matlab.pdf

The above code is formatted using hilite.me

This problem is from projecteuler.net and can be found here: problem4

Run the program and comment below the output you are getting for a given input.

 Keywords: projecteuler.net, problem 4, for loop, Largest Palindrome Product, Palindrome Numbers
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