1. CSCI 130 Array Searching

2. 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

3. 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!!!’); } }

4. 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; } }

5. 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

6. Linear Search - Advantages Easier to write Easier to understand Set does not have to be ordered

7. 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

8. 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

9. 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!!!’); }

10. 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: 2 n < x <= 2 (n+1)

11. Binary Search How many ‘tries’ are needed to search for a value in an ordered set of 100000 elements? 2 16 = 65536 < 100000 < 2 17 = 131072 Hence 16 tries before the comparisons, or 18 tries after the comparisons

12. Binary Search - Advantages Efficiency for larger sets Lookup time is consistent –Lookup time for linear will vary