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This function interleaves the first half of the array with the temporary array temp. Then copy temp back into a:
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half. It is easier to do this using a
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// The Perfect Shuffle for an even number of elements: void shuffle(float a[], int n) float temp[n]; for (int i = 0; i < n/2; i++) { I temp[2*i] = a[i]; temp[2*i + l] = n/2 + i; for (i = 0; i < n; i++) a[i] = temp[i];
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For the case n == 8, the first for loop copies a [ 0 ] into t emp [ 0 ] and a [ 4 ] into temp[l] when i == 0;thenitcopies a[l] into temp[2] and a[51 into temp[3] when i == 1;thenitcopies a[21 into temp[4] and a[6] into temp[5] when i == 2;thenit copies a[3] into temp[6] and a[71 into temp[7] when i == 3. 5.16 Write and test the function that rotates 90 clockwise a two-dimensional square array of
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ints. For example, it would transform the array 11 22 33 44 55 66 77 88 99 into the may 77 44 11 88 55 22 99 66 33
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This solution assumes that the type Matrix has been defined by a typede f .
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void rotate(Matrix m, const int n) Matrix temp; for (int i = 0; i < size; i++) for (int j = 0; j < size; j++) temp[i][j] = m[size-j-l][i]; for (i = 0; i c size; i++) for (j = 0; j c size; j++) m[il Cl = temp[i][j];
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We use a temporary array temp to hold the resulting rotated matrix, and then copy it back into m. For the case n = = 3,thefirst for loopcopies m[2] [0] into temp[O] [0], m[l] [0] into temp[O] [l],and m[O][O] into temp[0][2] when i == 0;thenitcopies m[2] [l] into temp[l][O], m[l][l] into temp[l] [l],and m[O][l] into temp[1][2] when i == 1;thenitcopies m[2] [2] into temp[2] [0], m[1][2] into temp[2] [l],and m[O][2] into temp[2][2] when i == 2.
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[CHAP. 5
Supplementary
Programming
Problems
5.17 Write and run a program like the one in Example 5.2, but fills the array in reverse and then
prints them in the order that they are stored. For example, the first number read is stored in the last position and is printed last .
5.18 Write and run a program like that in Problem 5.8 but computes and prints both the mean and the
standard deviation of the input data. The standard deviation of the n numbers ao, . . ., a,-, is defined by the formula
n- 1 Ji=O
C(ai-P)2
where p is the mean of the data. This means: square each deviation a [ i ] - mean; sum those squares; take the square root of that sum; divide that square root by n-l.
5.19 Extend the program from Problem 5.18 so that it also computes and prints the Z-scores of the
input data. The Z-scores of the n numbers ao, . . ., anml are defined by the formula zi = (ai - ~)/cT. They normalize the given data so ,that it is centered about 0 and has standard deviation 1.
5.20 In the good old days when a grade of C was considered average, teachers of large classes
would often curve their grades according to the following distribution: A .. 1.5 Iz B. 0.5 < z < 1.5 C .. -0.5 2 z < 0.5 D .. -1.5 I 2 < -0.5 F .. z < -1.5
If the grades were normally distributed (i.e., their density curve is bell-shaped), then this algorithm would produce about 7% A s, 24% B s, 38% C s, 24% D s, and 7% F s. Here the 2 values are the Z scores described in Problem 5.19. Extend the program from Problem 5.18 so that it prints the curved grade for each of the test scores read.
5.21 Write and test a function that replaces all the negative numbers in an array of integers with their
absolute values.
5.22 Write and test a function that returns the minimum value stored in an array. 5.23 Write and test a function that returns the index of the minimum value stored in an array. 5.24 Write and test the following function that returns through it reference parameters both the max-
imum and the minimum values stored in an array. void extremes(int& min, int& max, int a[], int n) 5.25 Write and test the following function that returns through it reference parameters both the largest and the second largest values (possibly equal) stored in an array. void largest(int& maxl, int& max2, int a[], int n)
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