Searching & Sorting Computational Complexity (JS)
Sorting Algorithms
Time Complexity: Quadratic O(n^2)
The inner for-loop contributes to O(n), however in a worst case scenario the while loop will need to run n times before bringing all n elements to their final resting spot.
Space Complexity: O(1)
Bubble Sort will always use the same amount of memory regardless of n.
The first major sorting algorithm one learns in introductory programming courses.
Gives an intro on how to convert unsorted data into sorted data.
It’s almost never used in production code because:
There is stigma attached to it
Worst Case & Best Case are always the same because it makes nested loops.
Double for loops are polynomial time complexity or more specifically in this case Quadratic (Big O) of: O(n²)
Time Complexity: Quadratic O(n^2)
Our outer loop will contribute O(n) while the inner loop will contribute O(n / 2) on average. Because our loops are nested we will get O(n²);
Space Complexity: O(1)
Selection Sort will always use the same amount of memory regardless of n.
Selection sort organizes the smallest elements to the start of the array.
Summary of how Selection Sort should work:
Search the minimum element in the list.
Swap with value at location Min
Time Complexity: Quadratic O(n^2)
Our outer loop will contribute O(n) while the inner loop will contribute O(n / 2) on average. Because our loops are nested we will get O(n²);
Space Complexity: O(n)
Because we are creating a subArray for each element in the original input, our Space Comlexity becomes linear.
Time Complexity: Log Linear O(nlog(n))
Since our array gets split in half every single time we contribute O(log(n)). The while loop contained in our helper merge function contributes O(n) therefore our time complexity is O(nlog(n)); Space Complexity: O(n)
We are linear O(n) time because we are creating subArrays.
Example of Merge Sort
Merge sort is O(nlog(n)) time.
We need a function for merging and a function for sorting.
Steps:
If there is only one element in the list, it is already sorted; return the array.
Otherwise, divide the list recursively into two halves until it can no longer be divided.
Merge the smallest lists into new list in a sorted order.
Time Complexity: Quadratic O(n^2)
Even though the average time complexity O(nLog(n)), the worst case scenario is always quadratic.
Space Complexity: O(n)
Our space complexity is linear O(n) because of the partition arrays we create.
QS is another Divide and Conquer strategy.
Some key ideas to keep in mind:
Time Complexity: Log Time O(log(n))
Space Complexity: O(1)
Recursive Solution
Min Max Solution
Must be conducted on a sorted array.
Binary search is logarithmic time, not exponential b/c n is cut down by two, not growing.
Binary Search is part of Divide and Conquer.
Works by building a larger and larger sorted region at the left-most end of the array.
Steps:
If it is the first element, and it is already sorted; return 1.
Compare with all elements in the sorted sub list
