@ChaoXu, I didn't understand your construction, where did you put that 1? Increment operation cannot be removed simply because we have to progress through the array, as well as the unconditional jump at the end of the loop block. It only takes a minute to sign up. However, we can fix that condition: just put the requested value at the end of the array and we have eliminated the need to test whether we have iterated outside bounds of the array. Here is the pseudocode of the function: function Search (a, v) begin a - array containing n elements v - value to be found in the array for i = 0 to n - 1 if a [i] = v then … Conditional jump which tests array elements is also mandatory because we do not know which element equals the requested value, if any. MathJax reference. That statement is present because we do not know whether we are still within bounds of the array or not. Example 1: Suppose that array is: 7, 2, 6, 1, 8, 4, 5. What would be a proper way to retract emails sent to professors asking for help? Binary Search ¶ Sequential search is the best that we can do when trying to find a value in an unsorted array. (I would also like to know if this sort of problem is well known and has a name and there are additional pointers I can read read. Do I have to say Yes to "have you ever used any other name?" Searching through an unsorted array looks like a simple task - we just iterate through the array and return an element index as soon as the match is found. What does “blaring YMCA — the song” mean? Most efficient algorithm to search an unsorted array with a very precise data structure, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, “Question closed” notifications experiment results and graduation, Offline multidimensional RMQ/RSQ in query model. But Pam, I think the problem as the way I understand it, is solvable in O(log n) by modifying binary search such that in each comparison compares given number with middle one and 4 number in the right and 4 number in the left of that middle number. For v=3, function returns negative value (e.g. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Merge Sort – This sorting algorithm is based on Divide and Conquer algorithm. (in other words a sort of "fractal" arrangement, we might perhaps say (?)). To subscribe to this RSS feed, copy and paste this URL into your RSS reader. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Theoretical Computer Science Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Problem Analysis. Which one can be removed? (I apologize in advance if this question sounds a bit practical, but I suspect it might have an interesting theoretical aspect.). There are a lot of sorting algorithms out there, but since we're only looking at this for the sake of an interview question, we'll go over four good ones. How many pawns make up for a missing queen in the endgame? if we take any one of these parts and, within it, we repeat the subdivision in 4 equal parts, the above fact holds always again for each of the new parts, all the way down, until we arrive at the smallest part, of size 4 elements. And, not to forget, the model you develop in this way will be correct and free of bugs. The array has a length that is a (very large) power of 4. if the array is split in 4 parts - all of the same number of elements - then in each part the first element is the Minimum of this part, and the last element is the Maximum of this part (minimum < maximum). Theoretical Computer Science Stack Exchange is a question and answer site for theoretical computer scientists and researchers in related fields. In four and a half hours of this course, you will learn how to control design of classes, design of complex algorithms, and how to recognize and implement data structures.