add marks

vbrazo · web-flow · commit 3587c859da10 · 2021-02-07T23:12:40.000-08:00
diff --git a/en/Sorting Algorithms/Radix Sort b/en/Sorting Algorithms/Radix Sort
@@ -1,4 +1,4 @@
-Radix Sort
+# Radix Sort
 
 The lower bound for Comparison based sorting algorithm (Merge Sort, Heap Sort, Quick-Sort .. etc) is `Ω(nLogn)`, i.e., they cannot do better than nLogn. 
 
@@ -9,10 +9,11 @@ We can’t use counting sort because counting sort will take `O(n2)` which is wo
 
 Radix Sort is the answer. The idea of Radix Sort is to do digit by digit sort starting from least significant digit to most significant digit. Radix sort uses counting sort as a subroutine to sort.
 
-The Radix Sort Algorithm 
+## The Radix Sort Algorithm 
 
 Do following for each digit i where i varies from least significant digit to the most significant digit. 
 Sort input array using counting sort (or any stable sort) according to the i’th digit.
+
 Example:
 
 Original, unsorted list:
@@ -31,13 +32,16 @@ Sorting by next digit (10s place) gives:
 
 Sorting by the most significant digit (100s place) gives:
 `2, 24, 45, 66, 75, 90, 170, 802`
-What is the running time of Radix Sort? 
+
+## What is the running time of Radix Sort? 
+
 Let there be d digits in input integers. Radix Sort takes `O(d*(n+b))` time where b is the base for representing numbers, for example, for the decimal system, b is 10.
 What is the value of d? If `k` is the maximum possible value, then d would be `O(logb(k))`. So overall time complexity is `O((n+b) * logb(k))`. Which looks more than the 
 time complexity of comparison-based sorting algorithms for a large k. Let us first limit k. Let k <= nc where c is a constant. In that case, the complexity becomes 
 `O(n logb(n))`. But it still doesn’t beat comparison-based sorting algorithms. 
 
-Is Radix Sort preferable to Comparison based sorting algorithms like Quick-Sort? 
+## Is Radix Sort preferable to Comparison based sorting algorithms like Quick-Sort? 
+
 If we have `log2n` bits for every digit, the running time of Radix appears to be better than Quick Sort for a wide range of input numbers. The constant factors hidden in 
 asymptotic notation are higher for Radix Sort and Quick-Sort uses hardware caches more effectively. Also, Radix sort uses counting sort as a subroutine and counting sort
 takes extra space to sort numbers.
