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CS1001 Lecture 20

CS1001 Lecture 20. Quizzes 3 and 4 review Application of Arrays Stacks (continuation) Sorting. Quiz 3. Write a function that, given an integer N, calculate N! N! is N * ( N - 1 ) * ( N - 2 ) * ... * 1 INTEGER FUNCTION Factorial(N) INTEGER INTENT(IN) :: N INTEGER :: product product = 1

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CS1001 Lecture 20

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  1. CS1001 Lecture 20 • Quizzes 3 and 4 review • Application of Arrays • Stacks (continuation) • Sorting

  2. Quiz 3 Write a function that, given an integer N, calculate N! N! is N * ( N - 1 ) * ( N - 2 ) * ... * 1 INTEGER FUNCTION Factorial(N) INTEGER INTENT(IN) :: N INTEGER :: product product = 1 DO I= 2 , N product = product * I END DO factorial = product END FUNCTION Factorial C = M!/(R! * (M-R)!) ==> in Fortran: C = Factorial(M) / ( Factorial(R)*Factorial(M-R) ) product = 1 loop: I product 2 2 3 6 4 24 5 120 etc.

  3. QUIZ 4, #1 • 1.) What will be displayed when the following code segment executes? • INTEGER :: i, j • INTEGER, DIMENSION (10) :: Table • DO i = 1, 10 • Table(i) = i+1 • END DO • DO i = 1, 4 • j = i * 2 + 1 • print *, i, j, Table(j) • END DO First DO loop: i Table(i) 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 Second DO loop: i j Table(j) 1 3 4 2 5 6 3 7 8 4 9 10

  4. Quiz 4, #2 Assume that Nums is an array of 100 integers, and that a program has read in values for all 100 array elements. Write a fragment of Fortran code that will calculate and display the number of elements in the array Nums that contain the value -1. • Count = 0 • DO I = 1,100 • IF (Nums (I) .EQ. –1) Count = Count +1 • END DO • PRINT *, Count

  5. Stack • A data structure used to implement Last-in-first-out (LIFO) processes • e.g.: stack of trays in the cafeteria : • Two operations: • Push • Pop • Some design issues: • How long (or deep) should the stack be (i.e., the dimension of the stack)? • When push, is there room in array? • When pop, is the stack empty ? Top Stack(top) : Stack(4) Stack(3) Stack(2) Stack(1) Stack

  6. More practice with Arrays • Sorting - arranging the elements in a list so that they are in ascending or descending order • Consider simple selection sort: e.g., sort a list of integers in ascending • list represented in an one-dimensional array, say n integer numbers: x(1), x(2), ...,x(n). Modify this list so the numbers are in ascending order • find the smallest number and put it in the first position • find the second smallest number and put it in the second position • etc. • after n-1 times through, the list is in ascending order

  7. Selection Sort First time: x(1) 67 x(2) 33 x(3) 21 x(4) 84 x(5) 49 x(6) 50 x(7) 75 Third time: x(1) 21 x(2) 33 x(3) 67 x(4) 84 x(5) 49 x(6) 50 x(7) 75 Starting: x(1) 67 x(2) 33 x(3) 21 x(4) 84 x(5) 49 x(6) 50 x(7) 75 Second time: x(1) 21 x(2) 33 x(3) 67 x(4) 84 x(5) 49 x(6) 50 x(7) 75 Fourth time: x(1) 21 x(2) 33 x(3) 49 x(4) 84 x(5) 67 x(6) 50 x(7) 75 Fifth time: x(1) 21 x(2) 33 x(3) 49 x(4) 50 x(5) 67 x(6) 84 x(7) 75 Sixth time: x(1) 21 x(2) 33 x(3) 49 x(4) 50 x(5) 67 x(6) 84 x(7) 75 Finish: x(1) 21 x(2) 33 x(3) 49 x(4) 50 x(5) 67 x(6) 75 x(7) 84

  8. SUBROUTINE SelectionSort(Item) INTEGER, DIMENSION(:), INTENT(INOUT) :: Item INTEGER :: NumItems, SmallestItem, I INTEGER, DIMENSION(1) :: MINLOC_array NumItems = SIZE(Item) DO I = 1, NumItems - 1 ! Find smallest item in the sublist ! Item(I), ..., Item(NumItems) SmallestItem = MINVAL(Item(I:NumItems)) MINLOC_array = MINLOC(Item(I:NumItems)) LocationSmallest = (I - 1) + MINLOC_array(1) ! Interchange smallest item with Item(I) at ! beginning of sublist Item(LocationSmallest) = Item(I) Item(I) = SmallestItem END DO END SUBROUTINE SelectionSort

  9. Bubble Sort First time: 67 33 21 84 49 50 75 33 21 67 84 49 50 75 Starting: x(1) 67 x(2) 33 x(3) 21 x(4) 84 x(5) 49 x(6) 50 x(7) 75 33 67 21 84 49 50 75 33 21 67 84 49 50 75 33 21 67 49 84 50 75 33 21 67 49 50 84 75 33 21 67 49 50 75 84 21 33 49 50 67 75 84 Second time: 33 21 67 49 50 75 84 21 33 67 49 50 75 84 21 33 67 49 50 75 84 21 33 49 67 50 75 84 21 33 49 50 67 75 84 Finish: x(1) 21 x(2) 33 x(3) 49 x(4) 50 x(5) 67 x(6) 75 x(7) 84

  10. SUBROUTINE BubbleSort(Item) INTEGER, DIMENSION(:), INTENT(INOUT) :: Item INTEGER :: NumPairs, LastSwap, I, Temp NumPairs = SIZE(Item) - 1 DO IF (NumPairs == 0) EXIT ! If no more pairs to check, terminate repetition ! Otherwise scan the sublist of the first NumPairs pairs ! in the list, interchanging items that are out of order LastSwap = 1 DO I = 1, NumPairs IF (Item(I) > Item(I+1)) THEN ! Items out of order -- interchange them Temp = Item(I) Item(I) = Item(I+1) Item(I+1) = Temp ! Record position of last swap LastSwap = I END IF END DO NumPairs = LastSwap - 1 END DO END SUBROUTINE BubbleSort

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