This lecture is the first of two about succinct data structures-data structures using very close to the minimum amount of space ("just the data"). In particular, we'll see how to store an n-node binary trie in 2n + o(n) bits (which is optimal up to the little-oh term) and still be able to navigate to a node's left child / right child / parent in constant time per operation, as well as be able to compute the size of the subtree rooted at a node in constant time. Along the way, we'll see how to store an n-bit string in n + o(n) bits (which is again optimal up to little-oh) and be able to compute the number of 1 bits left of a given bit, and find the ith 1 bit, in constant time per operation. These data structures form the basis of many succinct data structures.
The Massachusetts Institute of Technology (MIT), founded in 1861, is located in Cambridge, Massachusetts, and is one of the foremost U.S. institutions in science and technology. It is comprised of five schools and one college, including the renowned School of Engineering and Sloan School of Management, offering Bachelor's, Master's, and Doctorate degrees. Notable alumni include Ben Bernanke, Chairman of the Federal Reserve, Benjamin Netanyahu, prime minister of Israel, and American astronaut "Buzz" Aldrin.