9 processing arrays
- 1. Data Structures and Algorithms Processing Arrays Arrays @ 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. Data Structures and Algorithms Processing Arrays Dynamic 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. Data Structures and Algorithms Processing Arrays Base-Zero Versus Base-One Arrays Processing Arrays *Property of STI Page 3 of 17
- 4. Data Structures and Algorithms Processing Arrays One-Dimensional Arrays Processing Arrays *Property of STI Page 4 of 17
- 5. Data Structures and Algorithms Processing Arrays Parallel Arrays Processing Arrays *Property of STI Page 5 of 17
- 6. Data Structures and Algorithms Processing Arrays Entering 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 array Processing Arrays *Property of STI Page 6 of 17
- 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 B Processing Arrays *Property of STI Page 7 of 17
- 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 B Processing Arrays *Property of STI Page 8 of 17
- 9. Data Structures and Algorithms Processing Arrays Printing 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 B Processing Arrays *Property of STI Page 9 of 17
- 10. Data Structures and Algorithms Processing Arrays Accumulating 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 12 Processing Arrays *Property of STI Page 10 of 17
- 11. Data Structures and Algorithms Processing Arrays Two-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. Data Structures and Algorithms Processing Arrays Loading 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 B Processing Arrays *Property of STI Page 12 of 17
- 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 B Processing Arrays *Property of STI Page 13 of 17
- 14. Data Structures and Algorithms Processing Arrays Accumulating 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 total Processing Arrays *Property of STI Page 14 of 17
- 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 B Processing Arrays *Property of STI Page 15 of 17
- 16. Data Structures and Algorithms Processing Arrays Multidimensional Arrays In some cases there is a need for arrays with a third or even a fourth dimension. These arrays are called multidimensional arrays. Advantages : @ Facilitate an understanding of the data @ Improve the readability of algorithms @ Facilitate processing Processing Arrays *Property of STI Page 16 of 17
- 17. Data Structures and Algorithms Processing Arrays Table 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 31 Processing Arrays *Property of STI Page 17 of 17