Motivation: Given an array of N numbers, you need to support two operations. Operation 1: find-min(i, j) = return the minimum value in array[i ... j]. Operation 2: update(i, v) = update the value at array[i] to v. Solve the problem for N <= 10^6, number of operations <= 10^6.

To solve the above problem, both the operations need to run in O(log N) time, but using an naive array gives O(N) run-time for operation 1 (and O(1) run-time for operation 2). So how do you solve the problem? Read on. :)

Video tutorial: This is a superb tutorial, giving the motivation, walking through example, and going step-by-step through the pseudocode.

In its simplest form, binary search is a method for quickly finding a specific target value in a sorted array. It begins by comparing the target value to the middle element of the array. Because the array is sorted, the comparison allows us to determine one-half of the array in which the target cannot lie. The search continues on the remaining half. By doing this repeatedly, we will eventually be left with a search space consisting of a single element, the target value.

Example

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Note: There is no official syllabus for ZCO vs INOI vs IOITC. Syllabus for ZCO, INOI has been determined by looking at all the concepts covered in all ZCO, INOI problems since last 5 years. All the topics covered by ZCO, INOI are also in the Basic topics section of ICO online study material. Syllabus for IOITC is same as syllabus for IOI, since the training camp is training you for IOI. There is a higher focus on the topics mentioned in the Advanced topics specifically covered in ICO online study material. :)

The below tutorials are the best tutorials on the internet for each topic. If you find better tutorials for a particular topic, please share them with everyone.

Zonal Computing Olympiad (ZCO):

• Episode 1: Why do we need (efficient) algorithms?
• Episode 2: Our first algorithm: Quick-sort
• Episode 3: Merge-sort
• Episode 4: Binary search

Here's the thing, I messed up my ZCO and is getting 0.

ZIO is my last shot as I am in 12th, and when I sat down to solve ZIO qpaper 2013, I was stumped by the very first question.

So, how do you come to an algorithm for problems in ZIO and what all can be done in 5 days.