CSCI 130

Array Searching

Methods of searching arrays

• Linear– sequential - one at the time– set does not have to be ordered

• Binary– continuously cutting the set in half– set must be ordered

Linear Search

• Checking each value in the array sequentially

• Ex: – assume x is a 10 element integer array and we are

searching for the number 16 for (y = 0; y < 10; y++) { if (x[y] == 16) { printf(‘16 found!!!’); } }

Linear Search

• Instead of searching all 10 elements everytime, we should end the loop if we find the search value

for (y = 0; y < 10; y++) { if (x[y] == 16) { printf(‘16 found!!!’); break; } }

Linear Search

• For a search set of 10 elements, the average number of ‘tries’ to find an element is 5– number of tries = 1/2 the number of elements

• For a set of n elements, n/2 ‘tries’ are needed

Linear Search - Advantages

• Easier to write

• Easier to understand

• Set does not have to be ordered

Binary Search

• Set must be ordered– Alphabetically or numerically

• Binary searches are more efficient for large sets of data– smaller sets are just as efficient with linear

searches

Binary search algorithm

• Find the midpoint of the set• Determine if the array element at the midpoint

subscript is greater than the search value– If so, cut the list in half and search only from the previous

start to the cut point– If not, cut the list in half and search only from the cut point

to the previous finish

• Continue doing this until the difference between the endpoints is 1

• Interrogate the array at both endpoints

Binary search algorithm while ((finish - start) > 1) { if (numArray[curValue] > 100) { finish = curValue; curValue = (finish - start) / 2; } else { start = curValue; curValue = start + (finish - start) /2; }

}

if ((numArray[start]==16)||(numArray[finish]==16)) {

printf(‘16 found!!!’); }

Binary Search

• For a search set of 2 elements, 0 tries are made before the comparisions

• For a search set of 4 elements, 1 try is made before the comparisons

• For a search set of 8 elements, 2 tries are made before the comparisons

• For a search set of x elements, n tries are made before the comparisons where:

2n < x <= 2(n+1)

Binary Search

• How many ‘tries’ are needed to search for a value in an ordered set of 100000 elements?

• 216 = 65536 < 100000 < 217 = 131072

• Hence 16 tries before the comparisons, or 18 tries after the comparisons

Binary Search - Advantages

• Efficiency for larger sets

• Lookup time is consistent– Lookup time for linear will vary