refers to the problem of finding a particular element from a list

Transcription

1 ORM 5 PASCAL PROGRAMMING Unit 11: Searching, Sorting and Merging March, SEARCHING refers to the problem of finding a particular element from a list Example: program SearchingProblem; const MAX = 10; (* Number of students *) var Name : array[1..max] of string; Score : array[1..max] of integer; arget : string; ound : boolean; Index : integer; procedure ReadData; var K : integer; Inile : text; assign( Inile, 'Students.dat' ); reset( Inile ); for K := 1 to MAX do readln( Inile, Name[K] ); readln( Inile, Score[K] ) close( Inile ) : : : (* Main program *) ReadData; (* Store data in arrays *) write( 'Enter name of student : ' ); readln( arget ); Search; (* Search for arget in array Name *) if ound then writeln( 'he score of ', arget, ' is ', Score[Index] ) writeln( 'Student not found!' ). pas11_98.doc 1 of 1

2 Linear (Sequential) Search and Ordered Linear Search examines the data items in order they appear in the list until the desired value is located or the of the list is reached; Comparison lowchart Program code L i n e a r S e a r c h ENER K <-- 1 ound <-- false Name[K] = arget? K <-- K + 1 K > MAX? REURN Index <-- K ound <-- true (*Linear search*) var K : integer; K := 1; ound := false; (*not yet found*) if Name[K] = arget then Index := K; ound := true K := K + 1 until ound or (K > MAX) O r d e r e d L i n e a r S e a r c h ENER K <-- 1 ound <-- false Name[K] = arget? Name[K] > arget? K <-- K + 1 K > MAX? REURN Index <-- K ound <-- true (*Ordered linear search*) var K : integer; K := 1; ound := false; (*not yet found*) if Name[K] = arget then Index := K; ound := true if Name[K] > arget then K := MAX + 1 (*force to exit the loop*) K := K + 1 until ound or (K > MAX) pas11_98.doc 2 of 2

3 Binary Search the list is cut in half edly until the target is found or the list is fully searched. program code: (* Binary search : Name[] must be already in alphabetical order. *) var op, Bottom, Middle : integer; op := 1; Bottom := MAX; Middle := (op + Bottom) div 2; if arget < Name[Middle] then Bottom := Middle - 1 if arget > Name[Middle] then op := Middle + 1 ound := true; Index := Middle until ound or (op > Bottom) (* arget is found or list is empty *) Comparison of searching algorithms: Sequential search Simple algorithm and easy to implement he list need not be sorted Requires many comparisons Slow in locating a target Binary search Algorithm rather complex he list must be sorted. Requires very few comparisons Very fast in locating a target 11.2 SORING refers to the problem of arranging a given list of elements in order Brute orce Sort Insertion Sort Selection Sort Bubble Sort *** 11.3 BUBBLE SOR starts at the top of the array and compares two adjacent elements. If they are not in the correct order, they are swapped. hen the next pair is compared until this is done for the entire array; pas11_98.doc 3 of 3

4 Example 1: Using bubble sort, the numbers 8, 6, 1, 9, 4 will be sorted in this way: irst pass he working list is: 8, 6, 1, 9, Swap 8 and 6 (because 8 > 6) Swap 8 and 1 (because 8 > 1) No swap is needed (because 8 < 9) Swap 9 and 4 (because 9 > 4) he largest element, 9, bubbles to the last position Second pass he working list is: 6, 1, 8, Swap 6 and 1 (because 6 > 1) No swap is needed (because 6 < 8) Swap 8 and 4 (because 8 > 4) wo elements are in proper positions hird pass he working list is: 1, 6, No swap is needed (because 1 < 6) Swap 6 and 4 (because 6 > 4) hree elements are in proper positions ourth pass he working list is: 1, No swap is needed (because 1 < 4) our elements are in proper positions Note that 4 passes are needed. After the fourth pass, the largest 4 elements are in their proper position. In general, to sort a list of N elements, at most N - 1 passes are needed. Program Codes: Normal Bubble Sort program Sorting; const Max = 100; type Elementype = integer; Arrayype = array[1..max] of Elementype; var i : integer; List : Arrayype; Enhanced Bubble Sort program ImprovedSorting; const Max = 100; type Elementype = integer; Arrayype = array[1..max] of Elementype; var i : integer; List : Arrayype; procedure BubbleSort( var List : Arrayype; N : integer ); var Pass, i : integer; emp : Elementype; for Pass := 1 to N - 1 do for i := 1 to N - Pass do if List[i] > List[i+1] then emp := List[i]; List[i] := List[i+1]; List[i+1] := emp for i := 1 to 10 do List[i] := random( 100 ); BubbleSort( List, 10 ); for i := 1 to 10 do writeln( List[i] ). procedure BubbleSort( var List : Arrayype; N : integer ); var Pass, i : integer; emp : Elementype; NoExchange : boolean; Pass := 1; NoExchange := true; for i := 1 to N - Pass do if List[i] > List[i+1] then emp := List[i]; List[i] := List[i+1]; List[i+1] := emp; NoExchange := false Pass := Pass + 1 until NoExchange = true for i:=1 to 10 do List[i] := random( 100 ); BubbleSort( List, 10 ); for i:=1 to 10 do writeln( List[i] ). pas11_98.doc 4 of 4

5 11.4 MERGING refers to the problem of combining two or more sorted lists into one single sorted list so that the elements in the new list are also in the correct order. List 1 Merging Merged list List 2 Example: o merge elements from A[ ] and B[ ] into a new array C[ ], the algorithm is as follows: ENER IA < 1 IB < 1 IC < 1 A[IA] = B[IB]? C[IC] < A[IA] C[IC+1] < B[IB] A[IA] = B[IB]? C[IC] < A[IA] C[IC] < B[IB] IA < IA + 1 IB < IB + 1 IC < IC + 1 IA < IA + 1 IC < IC + 1 IB < IB + 1 IC < IC + 1 IA < NA and IB < NB? IA > NA? IB > NB? S all remaining elements of array B[ ] to array C[ ] S all ramaining elements of array A[ ] to array C[ ] REURN ig pas11_98.doc 5 of 5

6 program Merging; const NA = 3; NB = 5; NC = 8; var I : integer; A : array [1..NA] of integer; B : array [1..NB] of integer; C : array [1..NC] of integer; procedure Merge; var IA, IB, IC, J : integer; IA := 1; IB := 1; IC := 1; if A[IA] = B[IB] then C[IC] := A[IA]; C[IC+1] := B[IB]; IA := IA + 1; IB := IB + 1; IC := IC + 2 if A[IA] < B[IB] then C[IC] := A[IA]; IA := IA + 1; IC := IC + 1 C[IC] := B[IB]; IB := IB + 1; IC := IC + 1 until (IA > NA) or (IB > NB); if IA > NA then (*S all remaining elements of B[] to C[]*) for J := IB to NC do C[IC+J-IB] := B[J] (*S all remaining elements of A[] to C[]*) for J := IA to NC do C[IC+J-IA] := A[J] (*End of procedure Merge*) (*Main program*) writeln( 'Enter the elements of array A' ); for I := 1 to NA do write( 'Data ', I, ' : ' ); readln( A[I] ) writeln; writeln( 'Enter the elements of array B' ); for I := 1 to NB do write( 'Data ', I, ' : ' ); readln( B[I] ) writeln; Merge; writeln( 'he numbers after merging are :' ); for I := 1 to NC do write( C[I]:4 ); writeln. of unit 11 pas11_98.doc 6 of 6