Improved Markdown in README

README.md

@@ -74,8 +74,8 @@ From [Wikipedia][quick-wiki]: **Quicksort** (sometimes called *partition-exchang
 
 __Properties__
 * Worst case performance	O(n<sup>2</sup>)
-* Best case performance	O(n log n) or O(n) with three-way partition
-* Average case performance	O(n log n)
+* Best case performance	O(*n* log *n*) or O(n) with three-way partition
+* Average case performance	O(*n* log *n*)
 
 ###### View the algorithm in [action][quick-toptal]
 
@@ -85,9 +85,9 @@ __Properties__
 From [Wikipedia][heap-wiki]: Heapsort is a comparison-based sorting algorithm. It can be thought of as an improved selection sort. It divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element and moving that to the sorted region
 
 __Properties__
-* Worst case performance	O(n log n)
-* Best case performance	O(n log n)
-* Average case performance	O(n log n)
+* Worst case performance	O(*n* log *n*)
+* Best case performance	O(*n* log *n*)
+* Average case performance	O(*n* log *n*)
 
 
 
@@ -120,8 +120,8 @@ __Properties__
 From [Wikipedia][shell-wiki]: **Shellsort** is a generalization of *insertion sort* that allows the exchange of items that are far apart.  The idea is to arrange the list of elements so that, starting anywhere, considering every nth element gives a sorted list.  Such a list is said to be h-sorted.  Equivalently, it can be thought of as h interleaved lists, each individually sorted.
 
 __Properties__
-* Worst case performance O(nlog2 2n)
-* Best case performance O(n log n)
+* Worst case performance O(*n*log<sup>2</sup>*n*)
+* Best case performance O(*n* log *n*)
 * Average case performance depends on gap sequence
 
 ###### View the algorithm in [action][shell-toptal]
@@ -136,7 +136,7 @@ Comparing the complexity of sorting algorithms (*Bubble Sort*, *Insertion Sort*,
 
 ![Complexity Graphs](https://github.com/prateekiiest/Python/blob/master/sorts/sortinggraphs.png)
 
-Choosing of a sort technique-Quicksort is a very fast algorithm but can be pretty tricky to implement ,Bubble sort is a slow algorithm but is very easy to implement. To sort small sets of data, bubble sort may be a better option since it can be implemented quickly, but for larger datasets, the speedup from quicksort might be worth the trouble implementing the algorithm.
+Selecting a sort technique: Quicksort is a very fast algorithm but can be pretty tricky to implement while bubble sort is a slow algorithm which is very easy to implement. For a small value of n, bubble sort may be a better option since it can be implemented quickly, but for larger datasets, the speedup from quicksort might be worth the trouble implementing the algorithm.
 
 
 
@@ -167,7 +167,7 @@ __Properties__
 * Worst case space complexity	O(1)
 
 ## Interpolation
-Interpolation search is an algorithm for searching for a key in an array that has been ordered by numerical values assigned to the keys (key values). It was first described by W. W. Peterson in 1957.[1] Interpolation search resembles the method by which people search a telephone directory for a name (the key value by which the book's entries are ordered): in each step the algorithm calculates where in the remaining search space the sought item might be, based on the key values at the bounds of the search space and the value of the sought key, usually via a linear interpolation. The key value actually found at this estimated position is then compared to the key value being sought. If it is not equal, then depending on the comparison, the remaining search space is reduced to the part before or after the estimated position. This method will only work if calculations on the size of differences between key values are sensible.
+Interpolation search is an algorithm for searching for a key in an array that has been ordered by numerical values assigned to the keys (key values). It was first described by W. W. Peterson in 1957. Interpolation search resembles the method by which people search a telephone directory for a name (the key value by which the book's entries are ordered): in each step the algorithm calculates where in the remaining search space the sought item might be, based on the key values at the bounds of the search space and the value of the sought key, usually via a linear interpolation. The key value actually found at this estimated position is then compared to the key value being sought. If it is not equal, then depending on the comparison, the remaining search space is reduced to the part before or after the estimated position. This method will only work if calculations on the size of differences between key values are sensible.
 
 By comparison, binary search always chooses the middle of the remaining search space, discarding one half or the other, depending on the comparison between the key found at the estimated position and the key sought — it does not require numerical values for the keys, just a total order on them. The remaining search space is reduced to the part before or after the estimated position. The linear search uses equality only as it compares elements one-by-one from the start, ignoring any sorting.
 
@@ -178,26 +178,26 @@ In interpolation-sequential search, interpolation is used to find an item near t
 
 ## Jump Search
 ![alt text][JumpSearch-image]
-In computer science, a jump search or block search refers to a search algorithm for ordered lists. It works by first checking all items Lkm, where {\displaystyle k\in \mathbb {N} } k\in \mathbb {N}  and m is the block size, until an item is found that is larger than the search key. To find the exact position of the search key in the list a linear search is performed on the sublist L[(k-1)m, km].
+In computer science, a jump search or block search refers to a search algorithm for ordered lists. It works by first checking all items L<sub>km</sub>, where ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a5bc4b7383031ba693b7433198ead7170954c1d)  and *m* is the block size, until an item is found that is larger than the search key. To find the exact position of the search key in the list a linear search is performed on the sublist L<sub>[(k-1)m, km]</sub>.
 
 The optimal value of m is √n, where n is the length of the list L. Because both steps of the algorithm look at, at most, √n items the algorithm runs in O(√n) time. This is better than a linear search, but worse than a binary search. The advantage over the latter is that a jump search only needs to jump backwards once, while a binary can jump backwards up to log n times. This can be important if a jumping backwards takes significantly more time than jumping forward.
 
-The algorithm can be modified by performing multiple levels of jump search on the sublists, before finally performing the linear search. For an k-level jump search the optimum block size ml for the lth level (counting from 1) is n(k-l)/k. The modified algorithm will perform k backward jumps and runs in O(kn1/(k+1)) time.
+The algorithm can be modified by performing multiple levels of jump search on the sublists, before finally performing the linear search. For an k-level jump search the optimum block size m<sub>l</sub> for the l<sup>th</sup> level (counting from 1) is n<sup>(k-l)/k</sup>. The modified algorithm will perform *k* backward jumps and runs in O(kn<sup>1/(k+1)</sup>) time.
 ###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Jump_search)
 
 ## Quick Select
 ![alt text][QuickSelect-image]
-In computer science, quickselect is a selection algorithm to find the kth smallest element in an unordered list. It is related to the quicksort sorting algorithm. Like quicksort, it was developed by Tony Hoare, and thus is also known as Hoare's selection algorithm.[1] Like quicksort, it is efficient in practice and has good average-case performance, but has poor worst-case performance. Quickselect and its variants are the selection algorithms most often used in efficient real-world implementations.
+In computer science, quickselect is a selection algorithm to find the kth smallest element in an unordered list. It is related to the quicksort sorting algorithm. Like quicksort, it was developed by Tony Hoare, and thus is also known as Hoare's selection algorithm. Like quicksort, it is efficient in practice and has good average-case performance, but has poor worst-case performance. Quickselect and its variants are the selection algorithms most often used in efficient real-world implementations.
 
-Quickselect uses the same overall approach as quicksort, choosing one element as a pivot and partitioning the data in two based on the pivot, accordingly as less than or greater than the pivot. However, instead of recursing into both sides, as in quicksort, quickselect only recurses into one side – the side with the element it is searching for. This reduces the average complexity from O(n log n) to O(n), with a worst case of O(n2).
+Quickselect uses the same overall approach as quicksort, choosing one element as a pivot and partitioning the data in two based on the pivot, accordingly as less than or greater than the pivot. However, instead of recursing into both sides, as in quicksort, quickselect only recurses into one side – the side with the element it is searching for. This reduces the average complexity from O(n log n) to O(n), with a worst case of O(n<sup>2</sup>).
 
 As with quicksort, quickselect is generally implemented as an in-place algorithm, and beyond selecting the k'th element, it also partially sorts the data. See selection algorithm for further discussion of the connection with sorting.
 ###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Quickselect)
 
 ## Tabu
-Tabu search uses a local or neighborhood search procedure to iteratively move from one potential solution {\displaystyle x} x to an improved solution {\displaystyle x'} x' in the neighborhood of {\displaystyle x} x, until some stopping criterion has been satisfied (generally, an attempt limit or a score threshold). Local search procedures often become stuck in poor-scoring areas or areas where scores plateau. In order to avoid these pitfalls and explore regions of the search space that would be left unexplored by other local search procedures, tabu search carefully explores the neighborhood of each solution as the search progresses. The solutions admitted to the new neighborhood, {\displaystyle N^{*}(x)} N^*(x), are determined through the use of memory structures. Using these memory structures, the search progresses by iteratively moving from the current solution {\displaystyle x} x to an improved solution {\displaystyle x'} x' in {\displaystyle N^{*}(x)} N^*(x).
+Tabu search uses a local or neighborhood search procedure to iteratively move from one potential solution ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4) to an improved solution ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac74959896052e160a5953102e4bc3850fe93b2) in the neighborhood of ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4), until some stopping criterion has been satisfied (generally, an attempt limit or a score threshold). Local search procedures often become stuck in poor-scoring areas or areas where scores plateau. In order to avoid these pitfalls and explore regions of the search space that would be left unexplored by other local search procedures, tabu search carefully explores the neighborhood of each solution as the search progresses. The solutions admitted to the new neighborhood, ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/4db1b4a2cfa6f356afe0738e999f0af2bed27f45), are determined through the use of memory structures. Using these memory structures, the search progresses by iteratively moving from the current solution ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4) to an improved solution ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac74959896052e160a5953102e4bc3850fe93b2) in ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/4db1b4a2cfa6f356afe0738e999f0af2bed27f45).
 
-These memory structures form what is known as the tabu list, a set of rules and banned solutions used to filter which solutions will be admitted to the neighborhood {\displaystyle N^{*}(x)} N^*(x) to be explored by the search. In its simplest form, a tabu list is a short-term set of the solutions that have been visited in the recent past (less than {\displaystyle n} n iterations ago, where {\displaystyle n} n is the number of previous solutions to be stored — is also called the tabu tenure). More commonly, a tabu list consists of solutions that have changed by the process of moving from one solution to another. It is convenient, for ease of description, to understand a “solution” to be coded and represented by such attributes.
+These memory structures form what is known as the tabu list, a set of rules and banned solutions used to filter which solutions will be admitted to the neighborhood ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/4db1b4a2cfa6f356afe0738e999f0af2bed27f45) to be explored by the search. In its simplest form, a tabu list is a short-term set of the solutions that have been visited in the recent past (less than ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b) iterations ago, where ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b) is the number of previous solutions to be stored — is also called the tabu tenure). More commonly, a tabu list consists of solutions that have changed by the process of moving from one solution to another. It is convenient, for ease of description, to understand a “solution” to be coded and represented by such attributes.
 ###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Tabu_search)
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