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HKOI 2005 Intermediate Training

This training module introduces essential searching algorithms vital for efficiently locating a key in a list or an array. We explore three primary searching methods: Linear Search, Binary Search, and Interpolation Search. Linear Search examines each element sequentially, while Binary Search, which requires a sorted list, eliminates impossible regions for faster identification. Interpolation Search enhances searching efficiency based on key distribution. We cover the complexities of each algorithm, offering foundational knowledge for handling data searches effectively.

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HKOI 2005 Intermediate Training

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  1. HKOI 2005Intermediate 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

  9. 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 begin 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) ***} end;

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