Transcript of "Arraylineardatastructure21 110805065315-phpapp02"
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Array(ADT)Linear Data Structure www.eshikshak.co.in
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What are Arrays ? ● An Aay is collection of elements stored in adjacent memory locations. ● By ‘finite’ – specific number of elements in an Aay ● By ‘similar’ – all the elements in an Aay are of the same data type www.eshikshak.co.in
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What are Arrays ? (cont.) ● An Aay containing number of element is reference using an index values 0, 1, …n-1 ○ Lower bound–Lowest index value ○ Upper bound–Highest index value ● An Aay is set of pairs of an index and a value, for each index there is value associated with it. ● Various categories of Aay ○ 1D, 2D and Multi-D www.eshikshak.co.in
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What are Arrays ? (Cont.) ● The number of elements in the Aay is called its range. ● No matter how big an Aay is, its elements are always stored in contiguous memory locations. www.eshikshak.co.in
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Array OperationsOperation DescriptionTraversal Processing each element in the AaySearch Finding the location of an element with a given valueInsertion Adding new element to an AayDeletion Removing an element from an AaySorting Organizing the elements in some orderMerging Combining two Aays into a single AayReversing Reversing the elements of an Aay www.eshikshak.co.in
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Row-Major and Column-MajorArrangement ● All the elements of Aay are stored in adjacent memory. ● This leads to two possible Aangements of elements in memory ○ Row Major ○ ColumnMajor ● Base address , no. of rows ,& no. of columns helps to know any element in an Aay www.eshikshak.co.in
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Algorithm for Array Traversal ● Let A be a linear Aay with Lower Bound LB and Upper Bound UB. The following algorithm traverses A applying an operations PROCESS to each element of AStep 1. Initialize Counter Set Counter = LBStep 2. Repeat steps 3 and 4 while counter <= UB Else GoTo Step 5Step 3. Visit element Apply PROCESS to A[counter]Step 4. Increase Counter Set counter = counter + 1 GoTo 2Step 5. Exit www.eshikshak.co.in
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Algorithm for InsertionLet A be a Linear Array, N is number of elements, k is the positive integer suchthat k<=N, VAL to insert element at kth Position in an Array AStep 1. StartStep 2. Initialize Counter Set J = NStep 3. Repeat Steps 3 and 4 while J>=k otherwise GoTo StepStep 4. Move Jth element downward Set A[J+1] = A[J]Step 5. Decrease Counter Set J = J + 1 End of step 2 loopStep 6. Insert element Set A[k] = ITEMStep 7. Reset N Set N = N + 1Step 8. Exit www.eshikshak.co.in
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Algorithm for DeletionDELETE(A, N, K, VAL)Let A be an linear Aay. N is the number of elements, k is the positiveinteger such that k<=N. The algorithm deletes kth element from theAay.Step 1. StartStep 2. Set VAL = A[k]Step 3. Repeat for J = k to N-1[Move J+1 element Upward]Set A[J] = A[J+1)End of LoopStep 4. Reset the number N of elements in ASet N = N– 1Step 5. Exit www.eshikshak.co.in
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Algorithm for Linear SearchSuppose A is linear Array with N elements, and VAL is the given item ofinformation. This algorithm finds the location LOC of item in A or sets LOC=0 ifsearch is unsuccessfulStep 1. StartStep 2. [Insert VAL at the end of A] Set A[N+1] = VALStep 3. [Initialize counter] SET LOC = 1Step 4. [Search for VAL] Repeat while A[LOC] != VAL Set LOC = LOC + 1 [End of loop]Step 5. [Successful ?] if LOC = N+1 then set LOC = 0Step 6. Exit www.eshikshak.co.in
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Algorithm for sortingLet A be an Aay of N elements. The following algorithm sortsthe elements of A.Step 1. StartStep 2. Repeat Steps 2 and 3 for k=1 to N-1Step 3. Set PTR = 1 [Initialize pass pointer PTR]Step 4. Repeat while PTR<=N-K [Execute Pass]a. If A[PTR] > A[PTR+1], thenInterchange A[PTR] and A[PTR+1] [End of if structure]b. Set PTR = PTR + 1[End of inner loop][End of step1 outer loop]Step 5. Exit www.eshikshak.co.in
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