1. HKOI 2005 Intermediate Training
Searching and Sorting
9/4/2005

2. Introduction Task of searching for a key in a list or in an array
Searching algorithms will be discussed:
Linear Search
Binary Search
Interpolation Search

3. Linear Search Or called Sequential Search
checking every element of a list sequentially until a match is found
Complexity: O(N)
On average, N/2 comparisons is needed
Best case: the first element searched is the value we want
Worst case: the last element searched is the value we want

4. Binary Search Requirement: the list of data is sorted
The idea is based on the elimination of impossible region

5. Binary Search Algorithm:
Let the current region is from A[low] to A[high]
Compare key with A[midpoint]
If key<A[midpoint], then A[midpoint] to A[high] does not contain the key
If key>A[midpoint], then A[low] to A[midpoint] does not contain the key
Repeat the above process until the key is found

6. Binary Search int search( key, r ) typekey key; dataarray r;
{ int high, i, low;
for ( low=(-1), high=n; high-low > 1; ) {
i = (high+low) / 2;
if ( key <= r[i].k ) high = i;
else low = i; }
if ( key==r[high].k ) return( high );
else return( -1 );

7. Binary Search
Complexity: O(log N)

8. Interpolation Search
Requirement: the list of data is sorted

10. Interpolation Search
function search( key : typekey; var r : dataarray ) : integer;
var high, j, low : integer;
begin
low := 1;
high := n;
while (r[high].k >= key) and (key > r[low].k) do
j := trunc( (key-r[low].k) / (r[high].k-r[low].k) *
(high-low) ) + low;
if key > r[j].k then low := j+1
else if key < r[j].k then high := j-1
else low := j
end;
if r[low].k = key then search := low {*** found(r[low]) ***}
else search := -1; {*** notfound(key) ***}