Data Structures and Algorithms      Processing      ArraysArrays   @     Often advantageous for a user to store several   ...
Data Structures and Algorithms        Processing        ArraysDynamic Arrays @     When using dynamic arrays, the programm...
Data Structures and Algorithms        Processing        ArraysBase-Zero Versus Base-One ArraysProcessing Arrays           ...
Data Structures and Algorithms        Processing        ArraysOne-Dimensional ArraysProcessing Arrays                     ...
Data Structures and Algorithms        Processing        ArraysParallel ArraysProcessing Arrays                   *Property...
Data Structures and Algorithms        Processing        ArraysEntering Data into an Array               Algorithm         ...
Data Structures and Algorithms        Processing        Arrays                    Algorithm         Flowchart             ...
Data Structures and Algorithms        Processing        Arrays                    Algorithm     Flowchart                 ...
Data Structures and Algorithms        Processing        ArraysPrinting an Array                    Algorithm   Flowchart  ...
Data Structures and Algorithms        Processing        ArraysAccumulating the Elements of an Array                    Alg...
Data Structures and Algorithms        Processing        ArraysTwo-Dimensional Arrays  @ A two-dimensional array is a block...
Data Structures and Algorithms        Processing        ArraysLoading a Two-Dimensional Array                             ...
Data Structures and Algorithms        Processing        Arrays Printing a Two-Dimensional Array                           ...
Data Structures and Algorithms        Processing        ArraysAccumulating the Rows and Columns of a Two-Dimensional Array...
Data Structures and Algorithms        Processing        Arrays                    Algorithm      Flowchart                ...
Data Structures and Algorithms        Processing        ArraysMultidimensional ArraysIn some cases there is a need for arr...
Data Structures and Algorithms        Processing        ArraysTable Look-up Technique @ A common application for arrays is...
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9 processing arrays

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9 processing arrays

  1. 1. Data Structures and Algorithms Processing ArraysArrays @ Often advantageous for a user to store several values for the same variable in the internal memory of the computer because it decreases processing time. @ This multiple storage means there has to be more than one memory location in the computer for each variable name. @ When more than one memory location is designated for a single variable, it is called an array.Static Arrays @ This means that once the computer is told how many locations to save, that number cannot be changed unless the instruction is changed.Processing Arrays *Property of STI Page 1 of 17
  2. 2. Data Structures and Algorithms Processing ArraysDynamic Arrays @ When using dynamic arrays, the programmer designates the number of array locations as a variable, which can be expanded or contracted during the execution of the solution.Base-Zero System @ Because computers are zero-based, for counting purposes, many programming languages are also zero-based. @ This means that the first array element is numbered zero and not one.Base-One System @ Base one is easier for the programmer to understand since the first element will have an index of 1.Processing Arrays *Property of STI Page 2 of 17
  3. 3. Data Structures and Algorithms Processing ArraysBase-Zero Versus Base-One ArraysProcessing Arrays *Property of STI Page 3 of 17
  4. 4. Data Structures and Algorithms Processing ArraysOne-Dimensional ArraysProcessing Arrays *Property of STI Page 4 of 17
  5. 5. Data Structures and Algorithms Processing ArraysParallel ArraysProcessing Arrays *Property of STI Page 5 of 17
  6. 6. Data Structures and Algorithms Processing ArraysEntering Data into an Array Algorithm Flowchart A LOOP:R = 1 TO N STEP 1 R 1 N ENTER A(R) 1 LOOP-END:R ENTER A(R) R = Counter R N = Number of elements in the array A(R) = Element R B in the A arrayProcessing Arrays *Property of STI Page 6 of 17
  7. 7. Data Structures and Algorithms Processing Arrays Algorithm Flowchart A R=0 1. R = 0 2. REPEAT REPEAT R = R+1 R=R+1 ENTER A(R) UNTIL A(R) = -1 ENTER A(R) *3. N = R-1 F UNTIL A(R) = -1 T * N=R-1 BProcessing Arrays *Property of STI Page 7 of 17
  8. 8. Data Structures and Algorithms Processing Arrays Algorithm Flowchart A 1. R = 1 R=1 2. ENTER A(R) 3. WHILE A(R) <> -1 ENTER A(R) R = R+1 ENTER A(R) WHILE F A(R) <> -1 WHILE - END *4. N = R-1 R=R+1 ENTER A(R) * N=R+1 BProcessing Arrays *Property of STI Page 8 of 17
  9. 9. Data Structures and Algorithms Processing ArraysPrinting an Array Algorithm Flowchart A LOOP: R=1 TO N STEP 1 PRINT A(R) R 1 N 1 LOOP-END: R PRINT R = Element number A(R) N = Total number of elements R A(R) = Rth element of the A array BProcessing Arrays *Property of STI Page 9 of 17
  10. 10. Data Structures and Algorithms Processing ArraysAccumulating the Elements of an Array Algorithm Flowchart A LOOP:R = 1 TO N STEP 1 SUM = SUM + A(R) R 1 N LOOP-END: R 1 N = Number of elements SUM = SUM + A(R) R = Element number SUM = Sum of the R elements of A A(R) = Rth element of the array B TEST: R SUM A 1 2 1 2 3 2 6 12 4 5 6 7 20 30 42 2 4 3 6 4 8 N 5 10 6 6 12Processing Arrays *Property of STI Page 10 of 17
  11. 11. Data Structures and Algorithms Processing ArraysTwo-Dimensional Arrays @ A two-dimensional array is a block of memory locations associated with a single memory variable name and designated by row and column numbers.Processing Arrays *Property of STI Page 11 of 17
  12. 12. Data Structures and Algorithms Processing ArraysLoading a Two-Dimensional Array Row by Row@ You load a two- Data Block A dimensional array 1 Array with nested loops. 2 R A 3 1 3 The data are C 1 2 3 4 4 1 R normally loaded 5 1 1 2 3 4 6 2 5 6 7 8 row by row. When 7 C 3 9 10 11 12 you load the data 8 9 1 1 4 The row remains row by row, the 10 constant as the column varies. 11 outer loop 12 ENTER represents the row, A(R, C) and the inner loop represents the C column. C = Column R R = Row BProcessing Arrays *Property of STI Page 12 of 17
  13. 13. Data Structures and Algorithms Processing Arrays Printing a Two-Dimensional Array A PRINT COLUMN HEADINGS R 1 NR 1 PRINT ROW HEADING (R) C 1 NC 1 PRINT A(R,C) W/O CURSOR R = Row RETURN NR = Number of rows C C = Column RETURN CURSOR NC = Number of columns R BProcessing Arrays *Property of STI Page 13 of 17
  14. 14. Data Structures and Algorithms Processing ArraysAccumulating the Rows and Columns of a Two-Dimensional Array @ Column 5 holds the sum of each of the rows @ Row 4 holds the sum of each of the columns @ A (4,5) holds the grand totalProcessing Arrays *Property of STI Page 14 of 17
  15. 15. Data Structures and Algorithms Processing Arrays Algorithm Flowchart A LOOP:R = 1 TO NR STEP 1 R 1 NR 1 LOOP: C = 1 TO NC STEP 1 A(R,NC + 1) = A(R,NC + 1) C 1 NC + A(R,C) 1 A(NR + 1,C) = A(NR + 1,C) + A(R,C) A(R, NC + 1) = A(R, NC + 1) + A(R,C) LOOP-END: C A(NR + 1,C)= A(NR + 1,NC + 1) = A(NR + 1,C) + A(R,C) A(NR + 1, NC + 1) +A(R, NC + 1) C LOOP-END: R A(NR + 1,NC + 1) =A(NR + 1, NC + 1) +A(R, NC + 1) R BProcessing Arrays *Property of STI Page 15 of 17
  16. 16. Data Structures and Algorithms Processing ArraysMultidimensional ArraysIn some cases there is a need for arrays with a third oreven a fourth dimension. These arrays are calledmultidimensional arrays.Advantages : @ Facilitate an understanding of the data @ Improve the readability of algorithms @ Facilitate processingProcessing Arrays *Property of STI Page 16 of 17
  17. 17. Data Structures and Algorithms Processing ArraysTable Look-up Technique @ A common application for arrays is using a value to look up another value in a table. A one-dimensional array would be used if the element number can be utilized as the given value. A two- dimensional array with two columns would be used if the element number cannot be utilized. element DAYS Algorithm FLOWCHART: 1 31 1. ENTER MONTH 2. DAYS_OF_THE_MONTH = START DAYS(MONTH) 2 28 3. PRINT DAYS_OF_MONTH 4. END 3 31 ENTER 4 30 MONTH 5 31 6 30 DAYS_OF_THE_ MONTH = DAYS(MONTH) 7 31 8 31 PRINT DAYS_OF_ 9 30 MONTH 10 31 11 30 END 12 31Processing Arrays *Property of STI Page 17 of 17

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