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 linear search


binary search

needs sorted value, 

time complexity = O(log(n))

The binary search tree and B-tree data structures are based on binary search. 


Given an array of elements with values or records sorted such that , and target value , the following subroutine uses binary search to find the index of in .[7]

  1. Set to and to .
  2. If , the search terminates as unsuccessful.
  3. Set (the position of the middle element) to the floor of , which is the greatest integer less than or equal to .
  4. If , set to and go to step 2.
  5. If , set to and go to step 2.
  6. Now , the search is done; return .


function binary_search(A, n, T) is
    L := 0
    R := n − 1
    while L ≤ R do
        m := floor((L + R) / 2)
        if A[m] < T then
            L := m + 1
        else if A[m] > T then
            R := m − 1
            return m
    return unsuccessful 

 Pseudocode ceil version:

function binary_search_alternative(A, n, T) is
    L := 0
    R := n − 1
    while L != R do
        m := ceil((L + R) / 2)
        if A[m] > T then
            R := m − 1
            L := m
    if A[L] = T then
        return L
    return unsuccessful

selection sort
for first step n-1 step 
2nd n-2 
n   2 
total step = n-1 + n-2 + ...1 = (n-1)/2 (n-1+1)/2=n(n-1)/2 

bubble sort 
push biggest element to right by comparing two adjacent 
on n-1 comparision we get first biggest select sorted

merge sort 

sort right half and left half 
merge two half by comparing smallest 



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