Hello, everyone! Today we will solve the problem of implementing a Absolute Value Heap<\/strong>. We will tackle an algorithm problem and utilize C# features in the process. The ‘Absolute Value Heap’ mentioned earlier is a special heap that is sorted based on the absolute values using a heap structure. This topic often appears in algorithm problems.<\/p>\n The Absolute Value Heap supports the following functionalities:<\/p>\n For example, we can perform the following operations:<\/p>\n As a result of the above operations, the value that will be removed is -1. Therefore, the problem we need to solve is as follows:<\/p>\n Implement the functionalities of the Absolute Value Heap. Given N operations, provide the appropriate outputs for each operation.<\/p>\n The input comprises several integers, each representing one of the following three operations:<\/p>\n The first line contains the number of operations Subsequent lines will contain the operations, where each operation is Print each removed number on a new line. If there are no numbers to remove, print Now, let’s write the C# code to solve the problem. In this problem, we can implement the Absolute Value Heap using a Priority Queue<\/strong>.<\/p>\n A priority queue has each element associated with a priority, and in this case, a heap structure is used. In C#, it can be easily implemented using Below is the C# code that implements the Absolute Value Heap:<\/p>\n The above code demonstrates a simple way to implement an Absolute Value Heap. The main steps are as follows:<\/p>\n This algorithm stores and removes input values based on absolute values with a logarithmic complexity. Therefore, the complexity is O(N log N). In most cases, this level of time complexity will meet the input constraints.<\/p>\n In this post, we learned how to implement an Absolute Value Heap. We can efficiently solve algorithm problems by utilizing the SortedSet feature of C#. When tackling algorithm problems, it is important to carefully read the problem requirements and choose the appropriate data structure. We will return next time with another interesting algorithm problem!<\/p>\n <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"Problem Description<\/h2>\n
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\n1. Insert: 3\n2. Insert: -1\n3. Insert: -2\n4. Remove\n<\/pre>\n
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Problem<\/h3>\n
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0<\/code>: Remove and print the number with the smallest absolute value from the Absolute Value Heap.<\/li>\nX<\/code>: Insert the integer X<\/code> into the Absolute Value Heap.<\/li>\n<\/ul>\n<\/blockquote>\nInput and Output<\/h2>\n
Input<\/h3>\n
N<\/code>. (1 \u2264 N \u2264 100,000)<\/p>\nX<\/code> (-1,000,000 \u2264 X<\/code> \u2264 1,000,000) or 0<\/code>.<\/p>\nOutput<\/h3>\n
0<\/code>.<\/p>\nSolution<\/h2>\n
Priority Queue (Heap) Explanation<\/h3>\n
SortedSet<\/code> or PriorityQueue<\/code>.<\/p>\nC# Code Implementation<\/h3>\n
\nusing System;\nusing System.Collections.Generic;\nusing System.Linq;\n\nclass AbsoluteHeap\n{\n static void Main()\n {\n int n = int.Parse(Console.ReadLine());\n var pq = new SortedSet<(int absolute, int value)>();\n\n for (int i = 0; i < n; i++)\n {\n int x = int.Parse(Console.ReadLine());\n if (x == 0)\n {\n if (pq.Count == 0)\n {\n Console.WriteLine(0);\n }\n else\n {\n var min = pq.First();\n pq.Remove(min);\n Console.WriteLine(min.value);\n }\n }\n else\n {\n pq.Add((Math.Abs(x), x));\n }\n }\n }\n}\n<\/code><\/pre>\nCode Explanation<\/h2>\n
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SortedSet<\/code> to store tuples in the form (absolute value, actual value). Here, it is sorted based on the absolute value, and in case of ties, it is sorted by the actual value.<\/li>\nSortedSet<\/code>. If no value exists, print 0. If x is not 0, add the absolute value and actual value as a tuple.<\/li>\n<\/ol>\nEfficiency<\/h3>\n
Conclusion<\/h2>\n