Insertion sort vs Bubble Sort Algorithms

Question

I m trying to understand a few sorting algorithms  but I m struggling to see the difference in the bubble sort and insertion sort algorithm   I know both are O n2   but it seems to me that bubble sort just bubbles the maximum value of the array to the top for each pass  while insertion sort just sinks the lowest value to the bottom each pass  Aren t they doing the exact same thing but in different directions   For insertion sort  the number of comparisons potential swaps starts at zero and increases each time  ie 0  1  2  3  4       n  but for bubble sort this same behaviour happens  but at the end of the sorting  ie n  n-1  n-2      0  because bubble sort no longer needs to compare with the last elements as they are sorted   For all this though  it seems a consensus that insertion sort is better in general  Can anyone tell me why   Edit  I m primarily interested in the differences in how the algorithms work  not so much their efficiency or asymptotic complexity

User · Accepted Answer

In bubble sort in ith iteration you have n-i-1 inner iterations (n^2)/2 total, but in insertion sort you have maximum i iterations on i'th step, but i/2 on average, as you can stop inner loop earlier, after you found correct position for the current element. So you have (sum from 0 to n) / 2 which is (n^2) / 4 total;

That's why insertion sort is faster than bubble sort.

User · Answer

Another difference  I didn t see here   Bubble sort has 3 value assignments per swap  you have to build a temporary variable first to save the value you want to push forward no 1   than you have to write the other swap-variable into the spot you just saved the value of no 2  and then you have to write your temporary variable in the spot other spot no 3   You have to do that for each spot - you want to go forward - to sort your variable to the correct spot   With insertion sort you put your variable to sort in a temporary variable and then put all variables in front of that spot 1 spot backwards  as long as you reach the correct spot for your variable  That makes 1 value assignement per spot  In the end you write your temp-variable into the the spot    That makes far less value assignements  too   This isn t the strongest speed-benefit  but i think it can be mentioned   I hope  I expressed myself understandable  if not  sorry  I m not a nativ Britain

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Insertion Sort  After i iterations the first i elements are ordered   In each iteration the next element is bubbled through the sorted section until it reaches the right spot   sorted    unsorted 1 3 5 8   4 6 7 9 2 1 3 4 5 8   6 7 9 2   The 4 is bubbled into the sorted section  Pseudocode   for i in 1 to n     for j in i downto 2         if array j - 1   gt  array j              swap array j - 1   array j           else             break   Bubble Sort  After i iterations the last i elements are the biggest  and ordered   In each iteration  sift through the unsorted section to find the maximum   unsorted    biggest 3 1 5 4 2   6 7 8 9 1 3 4 2   5 6 7 8 9   The 5 is bubbled out of the unsorted section  Pseudocode   for i in 1 to n     for j in 1 to n - i          if array j   gt  array j   1               swap array j   array j   1     Note that typical implementations terminate early if no swaps are made during one of the iterations of the outer loop  since that means the array is sorted    Difference  In insertion sort elements are bubbled into the sorted section  while in bubble sort the maximums are bubbled out of the unsorted section

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Insertion sort  can be resumed as  Look for the element which should be at first position the minimum   make some space by shifting next elements  and put it at first position  Good  Now look at the element which should be at 2nd      and so on     Bubble sort operate differently which can be resumed as   As long as I find two adjacent elements which are in the wrong order  I swap them

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Though both the sorts are O N 2  The hidden constants are much smaller in Insertion sort Hidden constants refer to the actual number of primitive operations carried out   When insertion sort has better running time    Array is nearly sorted-notice that insertion sort does fewer operations in this case  than bubble sort  Array is of relatively small size  insertion sort you move elements around  to put the current element This is only better than bubble sort if the number of elements is few    Notice that insertion sort is not always better than bubble sort To get the best of both worlds  you can use insertion sort if array is of small size  and probably merge sort or quicksort  for larger arrays

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well bubble sort is better than insertion sort only when someone is looking for top k elements from a large list of number i e  in bubble sort after k iterations you ll get top k elements  However after k iterations in insertion sort  it only assures that those k elements are sorted

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Bubble sort is almost useless under all circumstances  In use cases when insertion sort may have too many swaps  selection sort can be used because it guarantees less than N times of swap  Because selection sort is better than bubble sort  bubble sort has no use cases

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Bubble Sort is not online  it cannot sort a stream of inputs without knowing how many items there will be  because it does not really keep track of a global maximum of the sorted elements  When an item is inserted you will need to start the bubbling from the very beginning

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Number of swap in each iteration   Insertion-sort does at most 1 swap in each iteration  Bubble-sort does 0 to n swaps in each iteration    Accessing and changing sorted part   Insertion-sort accesses and changes when needed  the sorted part to find the correct position of a number in consideration  When optimized  Bubble-sort does not access what is already sorted    Online or not   Insertion-sort is online  That means Insertion-sort takes one input at a time before it puts in appropriate position  It does not have to compare only adjacent-inputs   Bubble-sort is not-online  It does not operate one input at a time  It handles a group of inputs if not all  in each iteration  Bubble-sort only compare and swap adjacent-inputs in each iteration

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insertion sort   1 In the insertion sort swapping is not required   2 the time complexity of insertion sort is O n for best case and O n 2  worst case   3 less complex as compared to bubble sort   4 example  insert books in library  arrange cards   bubble sort  1 Swapping required in bubble sort   2 the time complexity of bubble sort is O n for best case and O n 2  worst case   3 more complex as compared to insertion sort

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The main advantage of insert sort is that it s online algorithm  You don t have to have all the values at start  This could be useful  when dealing with data coming from network  or some sensor   I have a feeling  that this would be faster than other conventional n log n  algorithms  Because the complexity would be n  n log n   e g  reading storing each value from stream  O n   and then sorting all the values  O n log n    resulting in O n 2 log n    On the contrary using Insert Sort needs O n  for reading values from the stream and O n  to put the value to the correct place  thus it s O n 2  only  Other advantage is  that you don t need buffers for storing values  you sort them in the final destination

[algorithm] Insertion sort vs Bubble Sort Algorithms

Examples related to algorithm

Examples related to sorting