Arrays 1 Linear Arrays A linear array is

Arrays 1

Linear Arrays • A linear array is a list of a finite number n of homogeneous data elements (i. e. , data elements of the same type) such that: – The elements of the array are referenced respectively by an index set consisting of n consecutive numbers. – The elements of the array are stored respectively in successive memory locations. • The length or the number of data elements of the array can be obtained from the index set by the following formula: Length = UB - LB + 1

Representation of Linear Arrays in Memory • Let LA be a linear array in the memory of the computer. • The computer calculates the address of kth Element of the array by the following formula: LOC(LA[K]) = Base(LA) + w(K – LB) • Here, W is the number of words per memory cell for the array LA. 1000 LA[1] 1001 LA[2] 1002 LA[3] . . .

Traversing a linear array Algorithm 4. 1: 1. Set K : = LB 2. Repeat step 3 and 4 while K <= UB 3. Apply PROCESS to LA[K] 4. Set K : = K + 1 5. Exit

Inserting into a linear array Algorithm 4. 2: INSERT( LA, N, K, ITEM) 1. Set J : = N 2. Repeat Steps 3 and 4 while J >= K 3. Set LA[J+1] : = LA[J] 4. Set J : = J – 1 5. Set LA[K] : = ITEM 6. Set N : = N + 1 7. Exit

Deleting From a Linear Array Algorithm 4. 3: DELETE( LA, N, K, ITEM) 1. Set ITEM : = LA[K] 2. Repeat for J : = K to N – 1 Set LA[J] : = LA[J+1] 3. Set N : = N - 1 4. Exit

Searching refers to the operation of finding an item from a list of items based on some key value. Two Searching Methods (1) Linear Search (2) Binary Search

Linear Search • A linear search is a technique for finding a particular value in a unsorted or sorted list. • Search each item of list using key value, one at a time, until finding the item from the list. Algorithm: Linear-Search (LA, N, Key) 1. Set k : = 1 and Loc : = 0 2. Repeat Steps 3 and 4 while k <= N 3. If Key = LA[k], then Set Loc : = k, print: Loc and exit. 4. Set k : = k+1 5. If Loc = 0 then Write: Item is not in List 6. Exit Here L - The list of data items N – Total no. of items in L Key – Item to be searched.

Example of Linear Search List : 10, 6, 222, 44, 55, 77, 24 Key: 55 Steps: 1. 55 10 2. 55 10 3. 55 10 6 4. 55 10 6 222 5. 55 10 6 222 6 6 So, Item 55 is in position 5. 222 44 55 77 24 K=1 222 44 55 77 24 K=2 222 44 55 77 24 K=3 4455 77 24 K=4 5577 24 K=5 44

Complexity Analysis of Linear Search (1) Worst Case The worst case occurs when Item is the last element in the List or is not in the List. So, C(n) = n = O(n). (2) Average Case The average case occurs when the availability of the Item in the List is equally likely to occur at any position in the List. So, C(n) = = = 0(n)