Interpolation sort

Key takeaways

Interpolation sort belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Interpolation sort to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Interpolation sort from memory before moving on to harder problems.

Reference excerpt

Interpolation sort (or histogram sort) is a sorting algorithm that uses an interpolation formula to divide and conquer. It is a variant of bucket sort. Data is assigned to buckets using an interpolation function: Interpolation ( x ) = ⌊ x − min max − min × ( ArraySize − 1 ) ⌋ {\displaystyle {\text{Interpolation}}(x)=\lfloor {\frac {x-{\text{min}}}{{\text{max}}-{\text{min}}}}\times ({\text{ArraySize}}-1)\rfloor } where min {\displaystyle {\text{min}}} and max {\displaystyle {\text{max}}} are the minimum and maximum values within the array, and the floor function is used. This function returns an array index to where element x {\displaystyle x} can be repositioned.

Algorithm

Interpolation sort uses an array of record bucket lengths corresponding to the original number column. The array prevents the space complexity from becoming O ( n 2 ) {\displaystyle O(n^{2})} due to memory stacking. The segmentation record of the length array can using secondary function dynamically declare and delete the memory space of the array. The space complexity required to control the recursive program is O ( 3 n ) {\displaystyle O(3n)} . Contains a two-dimensional array of dynamically allocated memories and an array of record lengths. However the execution complexity can still be maintained as an efficient sorting method of O ( n + k ) {\displaystyle O(n+k)} . The array of dynamically allocated memory can be implemented using an array object (such as in JavaScript) or more basically via a linked list, stack, queue, associative array, or tree structure. The type of data structure affects the speed of data access and thus the sorting time. When the values in the ordered array are uniformly distributed in an arithmetic progression, the order of interpolation sort is linear time, O ( n ) {\displaystyle O(n)} .

Interpolation sort algorithm Set a bucket length array to record the length of the unsorted bucket. Initialize into the original array length. [Main Sort] If the bucket length array is cleared, the sort is completed. Otherwise execute Divide function. [Divide function] Pop the bucket at the end of the bucket length array. Find the maximum and minimum values in the bucket. If the maximum value is equal to the minimum value, the bucket is sorted, so stop Divide. Set up a two-dimensional array as all empty buckets. Divide into the bucket according to the interpolation number. After dividing into the buckets, push the length of the buckets into the array of bucket length. And put the items back into the original array one by one from all the buckets that are not empty. Return to [Main Sort].

Histogram sort algorithm NIST describes the histogram sort as an efficient 3-pass refinement of a bucket sort algorithm.

The first pass counts the number of items for each bucket in an auxiliary array, and then makes a running total so each auxiliary entry is the number of preceding items. The second pass puts each item in its proper bucket according to the auxiliary entry for the key of that item. The last pass sorts each bucket.

Practice

Interpolation sort implementation JavaScript code:

Interpolation sort recursive method Worst-case space complexity: O ( n 2 ) {\displaystyle O(n^{2})}

Histogram sort implementation

Variants

Interpolation tag sort

Interpolation tag sort is a recursive variant of interpolation sort. After the array data is distributed into buckets via an interpolation function, each bucket recursively runs the original algorithm until the sorting is completed. To avoid stack overflow caused by recursion, use a Boolean data type tag array to operate the recursive function to release the memory. The extra memory space required is close to 2 n + ( n ) {\displaystyle 2n+(n)} bits. Contains a two-dimensional array of dynamically allocated memory and a Boolean data type tag array. Buckets can be implemented using a stack, queue, associative array, or tree structure. Like interpolation sort, interpolation tag sort runs in linear time O ( n ) {\displaystyle O(n)} when the values in the array to be sorted are evenly distributed. The bucket sort algorithm does not limit the sorting to the lower limit of O ( n l o g n ) {\displaystyle O(n\ log\ n)} . Interpolation tag sort average performance complexity is O ( n + k ) {\displaystyle O(n+k)} .

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Interpolation sort

Start with the simplest possible case. Write down what Interpolation sort claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Interpolation sort before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Interpolation sort ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Interpolation sort

In research: Interpolation sort appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Interpolation sort in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Interpolation sort is common in secondary-school and first-year university syllabi. It links to neighbouring topics Sorting algorithms, Stable sorts, so understanding it makes those chapters shorter.
In everyday life: Look for Interpolation sort outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Interpolation sort in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Interpolation sort means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Interpolation sort out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Interpolation sort in simple terms?

Interpolation sort (or histogram sort) is a sorting algorithm that uses an interpolation formula to divide and conquer. It is a variant of bucket sort.

Why does Interpolation sort matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Interpolation sort?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Interpolation sort.