Searching linear & binary search

Searching linear & binary search

• 1.
  LINEAR SEARCH Presented By NikunjPatel Parth Patel DATA STRUCTURE
• 2.
  Searching: Finding thelocation of item or printing some message when item is not found. SEARC H LINEAR BINARY
• 3.
   Linear search:Traversing data sequentially to locate item is called linear search.  Ex: Searching an item for operation in array.  Binary search: Data in array which is sorted in increasing numerical order or alphabetically.  Ex: Searching name in telephone directory, searching words in dictionary.
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  LINEAR SEARCH  Ittest whether the ITEM in DATA is present or not.  It test the data in sequential manner.  It searches the data one by one fully and returns the ITEM as the result.  Otherwise, it returns the value 0.  We see this by ALGORITHM.
• 5.
  Alg:LINEAR(DATA,N,ITEM,LOC)  Items explanation: 1.DATA --Linear array 2. N --Number of elements 3. ITEM --Elements to find 4. LOC --Location of the item
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  STEPS: 1. [Insert ITEMat the end] Set DATA[N+1]:=ITEM. 2. [Initialize counter] Set LOC:=1. 3. [Search for ITEM] Repeat while DATA[LOC]= ITEM: Set LOC:=LOC+1. [End if loop] 4. [Successful?]If LOC:=N+1, then ; Set LOC:=0 5. Exit
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  EXECUTION WITH EXAMPLE PARTICULARS: 1.DATA [6] = 2. ITEM=G Cell name A B C D E F Loc 1 2 3 4 5 6
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   To findthe item we are first inserting the item to the end of the list.  Step 1: DATA[N+1]=ITEM. Exp: N=6 DATA[6]=F DATA[6+1]=G  So the item is added at LOC[7] A B C D E F G 1 2 3 4 5 6 7
• 9.
   Step 2: Initializingthe counter to start the search. Therefore, LOC=1. It starts the search from LOC=1{i.e. from DATA[1]=A}  Step 3: WHILE loop is executed till DATA[LOC]=ITEM From the step 2, LOC=1
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  A B CD E F G A B C D E F G A B C D E F G A B C D E F G S E A R C H I N G
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  A B CD E F G S E A R C H I N G A B C D E F G A B C D E F G
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  Here the itemis found  The item ‘G’ is located  So the loop executes until this condition A B C D E F G
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   STEP 4: Originallythe location is 6. We added the item at the end. So the item is located in 7. LOC=N+1 We reached the condition then LOC=0  STEP 5: Searching is finished and the algorithm exits.
• 14.
  Binary Search • Ifthe array is sorted, then we can apply the binary search technique. number • The basic idea is straightforward. First search the value in the middle position. If X is less than this value, then search the middle of the left half next. If X is greater than this value, then search the middle of the right half next. Continue in this manner. 5 12 17 23 38 44 77 0 1 2 3 4 5 6 7 8 84 90
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  Sequence of SuccessfulSearch - 1 5 12 17 23 38 44 77 0 1 2 3 4 5 6 7 8 84 90 search( 44 )low high mid 0 8#1 highlow       2 highlow mid 38 < 44 low = mid+1 = 5 mid 4
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  Sequence of SuccessfulSearch - 2 5 12 17 23 38 44 77 0 1 2 3 4 5 6 7 8 84 90 search( 44 )low high mid 0 8#1       2 highlow mid 44 < 77high = mid-1=5 4 mid 6 highlow 5 8#2
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  Sequence of SuccessfulSearch - 3 5 12 17 23 38 44 77 0 1 2 3 4 5 6 7 8 84 90 search( 44 )low high mid 0 8#1       2 highlow mid 44 == 44 4 5 8#2 6 highlow 5 5#3 mid 5 Successful Search!!
• 18.
  Sequence of UnsuccessfulSearch - 4 5 12 17 23 38 44 77 0 1 2 3 4 5 6 7 8 84 90 search( 45 )low high mid 0 8#1       2 highlow mid 4 5 8#2 6 5 5#3 5 high low 6 5#4 Unsuccessful Search low > highno more elements to search
• 19.
  Binary Search Routine publicint binarySearch (int[] number, int searchValue) { int low = 0, high = number.length - 1, mid = (low + high) / 2; while (low <= high && number[mid] != searchValue) { if (number[mid] < searchValue) { low = mid + 1; } else { //number[mid] > searchValue high = mid - 1; } mid = (low + high) / 2; //integer division will truncate } if (low > high) { mid = NOT_FOUND; } return mid; }