MEX Subarray Count in C++

In this article, we will discuss the MEX Subarray Count in C++ with its example and benefits.

When given an array of size N, every element falls inside the range [0, N-1], meaning that the array is a permutation. Finding the number of subarrays whose MEX is more than the median is the current task.

The smallest whole number that is absent from the array is MEX, it should be noted.

Examples:

Input: N=4, arr=[0, 2, 1, 3]

Output: 4

Explanation: The subarrays whose MEX is greater than the Median are [0], [0, 2], [0, 2, 1], and [0, 2, 1, 3].

Input: N=4, arr=[1, 0]

Output: 2

Explanation: The subarrays with MEX greater than Median are [0], [1, 0].

MEX Subarray Count using Two Pointers:

First, we can observe that the MEX of each subarray will be between 0 and N. to calculate the answer for a MEX fixed value. For a fixed value of MEX, let l be the index of the number that is farthest to the left, 0, 1, 2,... mex-1, and let r be the index of the number that is farthest to the right, 0, 1, 2,... mex-1. Let curr, or curr=(r-l)+1, be the current length of the subarray. The number of subarrays can be found using a variety of techniques if the curr is less than or equal to 2*MEX. The MED of the subarray in this instance will be arr[l..r] and fall between [0..MEX-1. Curr's greater than 2*MEX indicates a higher MED for the subarray.

Follow the steps to solve the problem:

• Create an index and frequency array to hold the index and frequency of elements. The number of subarrays with MEX higher than the median should be stored in the ans
• Preserve the two pointers, l and r, which hold the index of the first, second, third, and so forth. The r and mex-1 represent the right-most numbers 0, 1, 2,... mex-1.
• While mex is less than or equal to N, perform a loop:
• Determine the current subarray's size using curr=(r-l)+1 and set len=2*mex.
• The answer is updated using certain formulas if curr<=len, which indicates that the subarray's median is less than mex.
• The response won't be updated if not.
• Update mex, l, and r.
• Answer back.

Example:

Below is the implementation of the above approach:

Output:

Complexity Analysis:

Time Complexity: O(N)

Auxiliary Space: O(N)

Benefits of MEX Subarray Count in C++

The Minimum Excluded Element is commonly called "MEX" in a set or array. When we discuss the "MEX Subarray Count", we may be referring to determining how many subarrays in a particular array have a minimum excluded element. But in the absence of further information or a particular problem statement, allow us to list some possible advantages of handling MEX subarray count-related issues:

1. Algorithmic Difficulties: MEX subarray count problems frequently pose intriguing algorithmic puzzles that call for effective solutions. Working on such difficulties improves our ability to solve problems and think algorithmically.
2. Knowing How to Manipulate Arrays: A solid grasp of array manipulation techniques is necessary when working with MEX subarray count problems. We might need to track specific properties, iterate over the array, and dynamically update values.
3. Application of Prefix Sum Techniques: Using prefix sum or other array transformation techniques may be necessary to solve some MEX subarray count difficulties. It offers a chance to use and comprehend these methods in a real-world setting.
4. Effective Time and Space Complexity: Resolving MEX subarray count issues frequently calls for the efficient use of time and space complexity. It tests our ability to create effective algorithms that can process big datasets in a reasonable amount of time and memory.
5. Knowing the concept of MEX (Minimum Excluded Element): We can better understand the idea of the minimum excluded element in a set or array by solving MEX-related tasks. This idea appears frequently in a variety of mathematical and computer science issues.
6. Use of Data Structures: We may need to employ other data structures, including arrays, sets, or other complex data structures, depending on the particular problem. It lets us experiment and use different data structures according to the situation's needs.
7. Coding Exercise: Solving MEX subarray count issues is a great way to gain experience with coding. It strengthens our comprehension of basic C++ programming constructs and helps us become a better implementer.
8. Programming in competition: Many MEX-related issues come up in programming competitions. Knowledge of these kinds of challenges can help us to tackle them in coding competitions.

Recall that the advantages vary depending on the situation and issue. Practicing MEX subarray count problems is one technique to develop your comprehension of algorithmic principles in the context of arrays and sets. Each problem advances our general programming and problem-solving abilities.