What is the difference between Linear search and Binary search

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Try this   Pick a random name  Lastname  Firstname    and look it up in your phonebook   1st time   start at the beginning of the book  reading names until you find it  or else find the place where it would have occurred alphabetically and note that it isn t there   2nd time   Open the book at the half way point and look at the page  Ask yourself  should this person be to the left or to the right   Whichever one it is  take that 1 2 and find the middle of it   Repeat this procedure until you find the page where the entry should be and then either apply the same process to columns  or just search linearly along the names on the page as before   Time both methods and report back    also consider what approach is better if all you have is a list of names  not sorted

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For a clear understanding  please take a look at my codepen implementations https   codepen io serdarsenay pen XELWqN  Biggest difference is the need to sort your sample before applying binary search  therefore for most  normal sized   meaning to be argued  samples will be quicker to search with a linear search algorithm   Here is the javascript code  for html and css and full running example please refer to above codepen link   var unsortedhaystack       var haystack       function init       unsortedhaystack   document getElementById  haystack   value split         function sortHaystack       var t   timer  sort benchmark      haystack   unsortedhaystack sort      t stop       var timer   function name        var start   new Date        return           stop  function                 var end    new Date                var time   end getTime   - start getTime                console log  Timer    name   finished in   time   ms                        function lineerSearch       init      var t   timer  lineerSearch benchmark      var input   this event target value    for var i   0 i lt unsortedhaystack length - 1 i          if  unsortedhaystack i      input          document getElementById  result   innerHTML    result is         unsortedhaystack i        on index      i     of the unsorted array  Found      within     i     iterations         console log document getElementById  result   innerHTML         t stop           return unsortedhaystack i                 function binarySearch        init      sortHaystack      var t   timer  binarySearch benchmark      var firstIndex   0    var lastIndex   haystack length-1    var input   this event target value       currently point in the half of the array   var currentIndex    haystack length-1  2   0    var iterations   0     while  firstIndex  lt   lastIndex        currentIndex    firstIndex   lastIndex  2   0      iterations        if  haystack currentIndex    lt  input          firstIndex   currentIndex   1          console log currentIndex     added  fI   firstIndex    lI    lastIndex         else if  haystack currentIndex   gt  input          lastIndex   currentIndex - 1          console log currentIndex     substracted  fI   firstIndex    lI    lastIndex         else         document getElementById  result   innerHTML    result is         haystack currentIndex        on index      currentIndex     of the sorted array  Found      within     iterations     iterations         console log document getElementById  result   innerHTML         t stop           return true

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Linear search also referred to as sequential search looks at each element in sequence from the start to see if the desired element is present in the data structure  When the amount of data is small  this search is fast Its easy but work needed is in proportion to the amount of data to be searched Doubling the number of elements will double the time to search if the desired element is not present   Binary search is efficient for larger array  In this we check the middle element If the  value is bigger that what we are looking for  then look in the first half otherwise look in the second half  Repeat this until the desired item is found  The table must be sorted for binary search  It eliminates half the data at each iteration Its logarithmic   If we have 1000 elements to search   binary search takes about 10 steps  linear search 1000 steps

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A linear search starts at the beginning of a list of values  and checks 1 by 1 in order for the result you are looking for   A binary search starts in the middle of a sorted array  and determines which side  if any  the value you are looking for is on  That  half  of the array is then searched again in the same fashion  dividing the results in half by two each time

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binary search runs in O logn  time whereas linear search runs in O n  times thus binary search has better performance

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A linear search looks down a list  one item at a time  without jumping  In complexity terms this is an O n  search - the time taken to search the list gets bigger at the same rate as the list does   A binary search is when you start with the middle of a sorted list  and see whether that s greater than or less than the value you re looking for  which determines whether the value is in the first or second half of the list  Jump to the half way through the sublist  and compare again etc  This is pretty much how humans typically look up a word in a dictionary  although we use better heuristics  obviously - if you re looking for  cat  you don t start off at  M    In complexity terms this is an O log n  search - the number of search operations grows more slowly than the list does  because you re halving the  search space  with each operation

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A linear search works by looking at each element in a list of data until it either finds the target or reaches the end  This results in O n  performance on a given list   A binary search comes with the prerequisite that the data must be sorted  We can leverage this information to decrease the number of items we need to look at to find our target  We know that if we look at a random item in the data  let s say the middle item  and that item is greater than our target  then all items to the right of that item will also be greater than our target  This means that we only need to look at the left part of the data  Basically  each time we search for the target and miss  we can eliminate half of the remaining items  This gives us a nice O log n  time complexity    Just remember that sorting data  even with the most efficient algorithm  will always be slower than a linear search  the fastest sorting algorithms are O n   log n    So you should never sort data just to perform a single binary search later on  But if you will be performing many searches  say at least O log n  searches   it may be worthwhile to sort the data so that you can perform binary searches  You might also consider other data structures such as a hash table in such situations

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Make sure to deliberate about whether the win of the quicker binary search is worth the cost of keeping the list sorted  to be able to use the binary search   I e  if you have lots of insert remove operations and only an occasional search the binary search could in total be slower than the linear search

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Linear Search looks through items until it finds the searched value    Efficiency  O n   Example Python Code   test list    1  3  9  11  15  19  29  test val1   25 test val2   15  def linear search input array  search value       index   0     while  index  lt  len input array   and  input array index   lt  search value           index    1     if index  gt   len input array  or input array index     search value          return -1      return index   print linear search test list  test val1  print linear search test list  test val2    Binary Search finds the middle element of the array  Checks that middle value is greater or lower than the search value  If it is smaller  it gets the left side of the array and finds the middle element of that part  If it is greater  gets the right part of the array  It loops the operation until it finds the searched value  Or if there is no value in the array finishes the search   Efficiency  O logn   Example Python Code   test list    1  3  9  11  15  19  29  test val1   25 test val2   15  def binary search input array  value       low   0     high   len input array  - 1     while low  lt   high          mid    low   high    2         if input array mid     value              return mid         elif input array mid   lt  value              low   mid   1         else              high   mid - 1      return -1   print binary search test list  test val1  print binary search test list  test val2    Also you can see visualized information about Linear and Binary Search here  https   www cs usfca edu  galles visualization Search html

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Think of it as two different ways of finding your way in a phonebook  A linear search is starting at the beginning  reading every name until you find what you re looking for  A binary search  on the other hand  is when you open the book  usually in the middle   look at the name on top of the page  and decide if the name you re looking for is bigger or smaller than the one you re looking for  If the name you re looking for is bigger  then you continue searching the upper part of the book in this very fashion

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A linear search looks down a list  one item at a time  without jumping  In complexity terms this is an O n  search - the time taken to search the list gets bigger at the same rate as the list does   A binary search is when you start with the middle of a sorted list  and see whether that s greater than or less than the value you re looking for  which determines whether the value is in the first or second half of the list  Jump to the half way through the sublist  and compare again etc  This is pretty much how humans typically look up a word in a dictionary  although we use better heuristics  obviously - if you re looking for  cat  you don t start off at  M    In complexity terms this is an O log n  search - the number of search operations grows more slowly than the list does  because you re halving the  search space  with each operation   As an example  suppose you were looking for U in an A-Z list of letters  index 0-25  we re looking for the value at index 20    A linear search would ask      list 0      U   No       list 1      U   No        list 2      U   No        list 3      U   No        list 4      U   No        list 5      U   No                 list 20      U   Yes  Finished    The binary search would ask      Compare list 12    M   with  U   Smaller  look further on   Range 13-25        Compare list 19    T   with  U   Smaller  look further on   Range 20-25        Compare list 22    W   with  U   Bigger  look earlier   Range 20-21        Compare list 20    U   with  U   Found it  Finished     Comparing the two    Binary search requires the input data to be sorted  linear search doesn t Binary search requires an ordering comparison  linear search only requires equality comparisons Binary search has complexity O log n   linear search has complexity O n  as discussed earlier Binary search requires random access to the data  linear search only requires sequential access  this can be very important - it means a linear search can stream data of arbitrary size

[algorithm] What is the difference between Linear search and Binary search?

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