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    <p>Sorry but you're using an incorrect algorithm.<br> What you're using is called a <a href="http://en.wikipedia.org/wiki/Greedy_algorithm" rel="noreferrer">Greedy Algorithm</a>, but the correct algorithm to use is <a href="http://en.wikipedia.org/wiki/Dynamic_programming" rel="noreferrer">Dynamic Programming</a>. The major difference is that greedy choose a best current option as a choice, while dynamic programming enumerates EVERY possible option and generate a series of choices. </p> <p>There is a simple case on which your solution(greedy) would fail:</p> <pre><code>0, 1, 0, 0, 0, 10 </code></pre> <p>The best result is 10, but your algorithm would give 1 instead.</p> <p>Think about it yourself for a moment, and then try seeking for information on Dynamic Programming. Project Euler is a great place and it's feels utterly great when you come up with a solution. So I won't say many on it for now. :)</p> <p><strong>UPDATED:</strong> </p> <blockquote> <p>But Ques: By starting at the top of the triangle below and moving to "adjacent numbers" on the row below. I have made my code according to this Word. Sorry for interrupting but can you make me more clear with this word ? </p> </blockquote> <p>Notice there would be actually <code>2^(n-1)</code> possible routes on a given <code>n</code> level triangle. And in the original problem <code>maximum total</code> means the maximum total among all these routes.<br> There's no grantee that your code would find the maximum among <code>ALL</code> routes since you only choose a better one in <code>TWO</code> choices at any step.</p> <p><strong>AGAIN UPDATED:</strong></p> <p>Actually in this problem since <code>n=15</code> is small enough, you can also enumerate all <code>2^(n-1)=16384</code> possible routes, summarize the total value of each route, and finally get a maximum total among all you get. However in <a href="https://projecteuler.net/index.php?section=problems&amp;id=67" rel="noreferrer">Problem 67 of Project Euler</a> the problem size <code>n</code> is increased to 100 and it would be not possible to enumerate all <code>2^(n-1)=633825300114114700748351602688</code> routes. </p> <p>By the way, I've posted a link to wiki page of Dynamic Programming, but I'm afraid it's to complex to read as a starter. Sorry for that.<br> But don't worry, just Google <a href="https://www.google.com/search?q=dynamic+programming+tutorial" rel="noreferrer">dynamic programming tutorial</a> and you'll got many useful resources to see :)</p>
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    1. POCorrect code but Wrong ans :(
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    1. COThanks for the reply :) I appreciate you ans. But Ques: By starting at the top of the triangle below and moving to "adjacent numbers" on the row below. I have made my code according to this Word. Sorry for interrupting but can you make me more clear with this word ? and its use!
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      1. USMohit Aphale
    2. CO@MohitAphale well I apologize for my poor English writing as a non-native speaker.. I'll try to edit the original answer to add some updates.
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    3. COAh! its fine! thanks a lot. I would be glad :D
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