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locations from the given memory address and the array index. For example, in the input statement
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0x0064fdbb in Example 6.10, when n = 3 the system computes that the memory 0x0064fdbc 0x0064fdbd address of a[3] is 3 4 = 12 bytes past the memory address of a[0]. 0x0064fdbe 0x0064fdbf 0x0064fdc0 That address is passed (by value) to the function in the variable a, so the 0x0064fdc1 0x0064fdc2 explicit address of a[3] is obtained. For example, suppose that a[0] 0x0064fdc3 0x0064fdc4 is stored in the four contiguous bytes starting at location 0x0064fdbc 0x0064fdc5 0x0064fdc6 ( 0x0064fdbc is hexadecimal notation for 6,618,556). Then the 0x0064fdc7 0x0064fdc8 0x0064fdc9 calculated address for a[3] is 0x0064fdc8 (hexadecimal for 6,618,568 0x0064fdca 0x0064fdcb = 6,618,556 + 12). In this calculation, the number 12 is called the offset 0x0064fdcc 0x0064fdcd for the element a[3]. (See Problem 6.5 on page 143. Also see Appendix G for information on hexadecimal numerals.) Note that an array name (whose value is a memory address) itself is a constant, so it cannot be changed anywhere. This simply means that the array cannot be moved to another place in memory. 0x0064fdba
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EXAMPLE 6.11 Printing the Memory Location of an Array
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This program prints the value of the address stored in an array name. int main() { int a[] = { 22, 44, 66, 88 }; cout << "a = " << a; // the address of a[0] } a = 0x0064fdec
0 1 2 3
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The array name a has two interpretations. It is used with an index to name each element of the array, so it identifies the complete composite object. But as a variable, its value is the memory address of the first byte of the first element a[0] in the array. 6.6 THE LINEAR SEARCH ALGORITHM Computers are probably used more for the storage and retrieval of information than for any other purpose. Data is often stored in a sequential structure such as an array. The simplest way to find an object in an array is start at the beginning and inspect each element, one after the other, until the object is found. This method is called the Linear Search algorithm. EXAMPLE 6.12 The Linear Search
This program tests a function that implements the Linear Search algorithm: int index(int,int[],int); int main() { int a[] = { 22, 44, 66, 88, 44, 66, 55 }; cout << "index(44,a,7) = " << index(44,a,7) << endl; cout << "index(50,a,7) = " << index(50,a,7) << endl; }
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int index(int x, int a[], int n) { for (int i=0; i<n; i++) if (a[i] == x) return i; return n; // x not found } index(44,a,7) = 1 index(50,a,7) = 7
6.7 THE BUBBLE SORT ALGORITHM The Linear Search algorithm is not very efficient. It obviously would not be a good way to find a name in the telephone book. We can do this common task more efficiently because the names are sorted in alphabetical order. To use an efficient searching algorithm on a sequential data structure such as an array, we must first sort the structure to put its elements in order. There are many algorithms for sorting an array. Although not as efficient as most others, the Bubble Sort is one of the simplest sorting algorithms. It proceeds through a sequence of iterations, each time moving the next largest item into its correct position. On each iteration, it compares each pair of consecutive elements, moving the larger element up. EXAMPLE 6.13 The Bubble Sort
This program tests a function that implements the Bubble Sort algorithm. void print(float[],int); void sort(float[],int); int main() { float a[] = {55.5, 22.5, 99.9, 66.6, 44.4, 88.8, 33.3, 77.7}; print(a,8); sort(a,8); print(a,8); } void sort(float a[], int n) { // bubble sort: for (int i=1; i<n; i++) // bubble up max{a[0..n-i]}: for (int j=0; j<n-i; j++) if (a[j] > a[j+1]) swap(a[j],a[j+1]); // INVARIANT: a[n-1-i..n-1] is sorted }
55.5, 22.5, 99.9, 66.6, 44.4, 88.8, 33.3, 77.7 22.5, 33.3, 44.4, 55.5, 66.6, 77.7, 88.8, 99.9 The sort() function uses two nested loops. The inside for loop compares pairs of adjacent elements and swaps them whenever they are out of order. This way, each element bubbles up past all the elements that are less than it.
6.8 THE BINARY SEARCH ALGORITHM The binary search uses the divide and conquer strategy. It repeatedly divides the array into two pieces and then searches the piece that could contain the target value.
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