A Party to the World » proof http://dan.lecocq.us/wordpress Life, love, and computer science Sun, 25 Jul 2010 16:20:14 +0000 en hourly 1 http://wordpress.org/?v=3.0 Sum of Combinatoric Terms http://dan.lecocq.us/wordpress/2008/10/03/sum-of-combinatoric-terms/ http://dan.lecocq.us/wordpress/2008/10/03/sum-of-combinatoric-terms/#comments Fri, 03 Oct 2008 17:42:14 +0000 Dan http://dan.lecocq.us/wordpress/2008/10/03/sum-of-combinatoric-terms/ Matt Matteson had a homework problem dealing with (n+a)^b, and finding a bound for it. Expanding this and evaluating it at n=a piqued my curiosity about the sum of each of the binomial expansion terms. That is to say, the sum of bC0 + bC1 + … + bCb. Well, I explored it a little bit, and did a quick-and-dirty writeup of my findings:

Sum of Combinatoric Terms

]]> http://dan.lecocq.us/wordpress/2008/10/03/sum-of-combinatoric-terms/feed/ 0 Heapsort http://dan.lecocq.us/wordpress/2008/06/24/heapsort/ http://dan.lecocq.us/wordpress/2008/06/24/heapsort/#comments Wed, 25 Jun 2008 00:05:43 +0000 Dan http://dan.lecocq.us/wordpress/2008/06/24/heapsort/ I was reading about Algorithm Geeks, a Google Group dedicated to algorithm-related questions apparently. I looked at one of the topics, Unique Elements in an Array, wondering what the chatter looked like.

To remove duplicate elements of an array, the best way I know is to sort your array, and then do a linear traversal, comparing each to its successor, and when they match, deleting the one of them. Quicksort is generally the algorithm-of-choice in large part because of its simplicity, but someone on this thread suggested heapsort – an algorithm of which I had never heard. I looked it over, and was drawn to the article on heaps. On that page, I was looking at an analysis of the time complexity for building the heap, and I got curious about the summation they present (h/2^h). So, I took some time and proved its convergence:

Convergence of Infinite Sum

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