By Alexander Shen
That ebook does not include natural algorithms idea (like Kormen's or Skiena's book), yet difficulties (and such a lot of them are with solutions). each bankruptcy begins with the straightforward challenge, through a few discussions of attainable strategies, and after progressively more hard projects ends with lovely tough problems.
The publication (in my opinion) is actually very sensible (well, it comprises a few concept, yet no longer very formal) and is beneficial if you are getting ready to the programming contests or Google/Microsoft-like interviews.
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Additional info for Algorithms and Programming: Problems and Solutions (Modern Birkhäuser Classics)
Our trees have root at the bottom. Please note that in most computer science books trees are drawn with the root at the top. While it seems to be nonintuitive, it is the de facto standard. The proof of the program below uses the following conventions. Assume that the position of the robot is fixed. Then all the leaves of the tree are divided into three categories: (1) leaves above the robot; (2) leaves on the left of the robot and (3) leaves on the right of the robot. Indeed, the (unique) path from the root to a given leaf (a) may go through the robot's position; (b) may turn to the left before the robot's position, or (c) may go to the right before it.
X [ n ] in r e v e r s e d order Remark. This program suffers from the usual problem: x [t+l] is undefined when t = n. 1. Generate all subsets of the set 1 . n having k elements. Solution. Each subset may be represented by a bit string of length n that contains exactly k ls. ) We generate these bit strings in alphabetic order. There is a natural way to do this: Generate all bit strings and select those that contain exactly k ls. However, this solution is considered as inefficient, because bit strings with k ls form a tiny fraction of all bit strings of length n.
We move pieces according to the following rule: Find the rightmost piece that can be moved in the direction of the arrow on it, and move it. At the same time all the pieces on the right (they cannot move in the direction of their arrows) are turned over. It is evident that at each step only one piece is moving, therefore only one term in the corresponding sequence is changed by I. Let us prove by induction on n that all sequences of length n composed of the numbers 1 . k will appear. The case n = l is evident, so assume that n > 1.
Algorithms and Programming: Problems and Solutions (Modern Birkhäuser Classics) by Alexander Shen