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mented, and true is returned to indicate a successful removal. If x is not found, the array is left unchanged and false is returned. (See Problem 6.12.) 6.14 Write and test the following function that removes items from an array:
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void removeAll(float a[], int& n, float x);
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The function removes all occurrences of x among the first n elements of the array a and decreases the value of n by the number removed. (See Problem 6.13.) 6.15 Write and test the following function:
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void rotate(int a[], int n, int k);
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The function rotates the first n elements of the array a, k positions to the right (or k positions to the left if k is negative). The last k elements are wrapped around to the beginning of the array. For example, the call rotate(a,8,3) would transform the array {22,33,44,55,66,77,88,99} into {77,88,99,22,33,44,55,66}. The call rotate(a,8,-5) would have the same effect. 6.16 Write and test the following function:
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void append(int a[], int m, int b[], int n);
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The function appends the first n elements of the array b onto the end of the first m elements of the array a. It assumes that a has room for at least m + n elements. For example, if a is {22,33,44,55,66,77,88,99} and b is {20,30,40,50,60,70,80,90} then the call append(a,5,b,3) would transform a into {22,33,44,55,66,20,30,40}. Note that b is left unchanged and only n elements of a are changed. 6.17 Write and test the function
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void insert(float a[], int& n, float x)
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6.20 6.21
This function inserts the item x into the sorted array a of n elements and increments n. The new item is inserted at the location that maintains the sorted order of the array. This requires shifting elements forward to make room for the new x. (Note that this requires the array to have at least n+1 elements allocated.) Implement the Insertion Sort algorithm for sorting an array of n elements. In this algorithm, the main loop index i runs from 1 to n 1. On the ith iteration, the element a[i] is inserted into its correct position among the subarray a[0..i]. This is done by shifting one position up all the elements in the subarray that are greater than a[i]. Then a[i] is copied into the gap between the elements that are less than or equal to a[i] and those that are greater. (Hint: use the insert() algorithm from Problem 6.17.) Implement the Selection Sort algorithm for sorting an array of n elements. This algorithm has n 1 iterations, each selecting the next largest element a[j] and swapping it with the element that is in the position where a[j] should be. So on the first iteration it selects the largest of all the elements and swaps it with a[n-1], and on the second iteration it selects the largest from the remaining unsorted elements a[0..n-2] and swaps it with a[n-2], etc. On its ith iteration it selects the largest from the remaining unsorted elements a[0..n-i] and swaps it with a[n-i]. (Hint: use the same loops as in Example 6.13 on page 134.) Rewrite and test the Bubble Sort function presented in Example 6.13 on page 134, as an indirect sort. Instead of moving the actual elements of the array, sort an index array instead. Write and test the function
int frequency(float a[], int n, int x);
This function counts the number of times the item x appears among the first n elements of the array a and returns that count as the frequency of x in a. 6.22 Implement the Sieve of Eratosthenes to find prime numbers. Define a boolean array named isPrime[SIZE], set its values isPrime[0] and isPrime[1] false (2 is the first
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