Linear and binary search

Linear and binary search

• 1.
  DATA STRUCTURE
• 2.
  SEARCHING • SEARCHING MEANSTOFINDWHETHER A PARTICULARVALUE IS PRESENT INTHE ARRAY OR NOT. SEARCHING LINEAR SEARCH BINARY SEARCH
• 3.
  LINEAR SEARCH • LINEARSEARCH IS AVERY SIMPLE SEARCH ALGORITHM. INTHISTYPE OF SEARCH, A SEQUENTIAL SEARCH IS MADE OVER ALL ITEMS ONE BY ONE. EVERY ITEM IS CHECKED AND IF A MATCH IS FOUNDTHENTHAT PARTICULAR ITEM IS RETURNED, OTHERWISETHE SEARCH CONTINUES TILLTHE END OFTHE DATA COLLECTION.
• 4.
  • THIS ISKNOWNAS SEQUENTIAL SEARCH. ALGORITHM FOR LINEAR SEARCH LINEAR SEARCH(A, N,VAL, POS) STEP 1 : [INITIALIZE] SET POS = -1 STEP 2 : [INITIALIZE] SET I = 0 STEP 3 : REPEAT STEP 4WHILE I<N STEP 4 : IF A[I] =VAL,THEN SET POS = I PRINT POS GOTO STEP 6 [END OF IF] [END OF LOOP] STEP 5 : PRINT “VALUE NOT PRESENT IN ARRAY” STEP 6 : EXIT
• 5.
  BINARY SEARCH • BINARYSEARCH IS A FAST SEARCH ALGORITHM.THIS SEARCH ALGORITHM WORKS ONTHE PRINCIPLE OF DIVIDE AND CONQUER. FORTHIS ALGORITHMTOWORK PROPERLY,THE DATA COLLECTION SHOULD BE IN THE SORTED FORM. • BINARY SEARCH LOOKS FOR A PARTICULAR ITEM BY COMPARINGTHE MIDDLE MOST ITEM OFTHE COLLECTION. IF A MATCH OCCURS,THENTHE INDEX OF ITEM IS RETURNED. IFTHE MIDDLE ITEM IS GREATERTHANTHE ITEM,THENTHE ITEM IS SEARCHED INTHE SUB-ARRAYTOTHE RIGHT OF THE MIDDLE ITEM. OTHERWISE,THE ITEM IS SEARCHED FOR INTHE SUB- ARRAYTOTHE LEFT OFTHE MIDDLE ITEM.THIS PROCESS CONTINUES ON THE SUB-ARRAY ASWELL UNTILTHE SIZE OFTHE SUBARRAY REDUCESTO ZERO.
• 6.
  • WORKS EFFICIENTLYWITH SORTED LIST. • ALGORITHM FINDSTHE POSITION OF A PARTICULAR ELEMENT INTHE ARRAY. ALGORITHM FOR BINARY SEARCH BINARY SEARCH(A, LOWER_BOUND, UPPER_BOUND,VAL, POS) STEP 1 : [INITIALIZE] SET BEG= LOWER_BOUND, END = UPPER_BOUND, POS = -1 STEP 2 : REPEAT STEP 3 AND STEP 4WHILE BEG<=END STEP 3 : SET MID = (BEG+END)/2 STEP 4 :IF A[MID] =VAL,THEN POS = MID PRINT POS GOTO STEP 6 IF A[MID] >VALTHEN ;
• 7.
  SET END =MID -1 ELSE SET BEG = MID + 1 [END OF IF] [END OF LOOP] STEP 5 : PRINT “VALUE NOT PRESENT IN ARRAY” STEP 6 : EXIT
• 8.
  If we aresearching for 31(VAL) then answer is 5(POS)
• 9.
  THANK YOU