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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 AZgorithm.
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EXAMPLE 5.11 The Linear Search
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This program tests a function that implements the Linear Search Algorithm:
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void se rch(int& found, int& location, int a[], int n, int target);
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main0 1 int &I = (55, 22, 99, 66, 44, 88, 33, 77}, target, found, lot; do tout C-C "Target: "; tin >> target; search(found,loc,a,8,target); if (found) tout CC target CC ' is at a[' CC lot CC "].\n"; else tout -CC target << ' was not found.\n"; } while (target != 0);
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// Linear Search: void search(int& found, int& location, int a[], int n, int target) -l found = location = 0; while (!found &SC location c n) found = (a[location++] == target); --location; : , .. : I. i. ;. _. :
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.33 i s at a[6J1 Target: 44 44 is ax q[43. Targeg: 50 50 wEG3 lx3e fuund. Target: 0 0 w&s nut found.
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In each iteration of the search loop, the current element a [ location] is compared with target. The loop continues until a match is found or all the elements have been checked. Each iteration increments the index location, after it is accessed. So if the loop terminates because a match was found, locator must be decremented to the index where target was found. Note that the search ( > function has three input parameters (a, n, and target) and two output parameters ( found and location). We follow the conventional practice of listing the output parameters in front of the input parameters.
5.7 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
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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 element 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 5.12 The Bubble Sort
swap
This program tests a function that implements the Bubble Sort Algorithm. It is compiled with the function shown in Example 4.15:
void print(float [I, const int); void sort(float [I, const int); main0 t float a[81 = (55.5, print(a, 8); sort(a, 8); print(a, 8); 1 void { print(float a[],
22.5,
99.9,
66.6,
44.4,
88.8,
33.3,
77.7);
const
for (int i = 0; i < n-l; i++) { tout +c a[i] << '1, '1; if ((i+1)%16 == 0) tout CC endl; 1 tout << a[n-l] -CC endl;
1 void swap(float& x, float& y)
// Bubble Sort: void sort(float a[], 1 for (int i = n-l; for (int j = i f 1
const int n) i > 0; i--) 0; j < i; j++) Mjl > a[j+U 1 swwb[jl ,a[j+ll);
55 22 99 66 44 88 33 77 3.3 44 55 66 77 88 99
The sort ( > function uses two nested loops. The inside for loop compares pairs of adjacent elements and swaps them whenever they are in reverse order. This way, each element bubbles up past all the elements that are less than it.
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5.8 THE BINARY SEARCH ALGORITHM
The binary search uses the divide and conquer strategy. It repeatedly divides the array into two pieces and refocuses on the piece that could contain the target value.
EXAMPLE 5.13 The Binary Search Algorithm This program tests a function that implements the Binary Search Algorithm: // Binary Search: void search(int& found, int& location, int a[], int n, int target); main0 int a[] = (22, 33, 44, 55, 66, 77, 88, 99}, target, found, lot; tout CC "Target: '; tin >> target; search(found,loc,a,8,target); if (found) tout CC target << ' is at a[' CC lot CC "].\n"; else tout CC target CC ' was not found.\n"; } while (target != 0);
void search(int& found, int& location, int a[], int n, int target) { int left = 0, rignt = n-l; found = 0; while (!found &SC left c= right) { location = (left + right)/2; // the midpoint found = (a[location] == target); if (a[location] c target) left = location + 1; else right = location - 1; ) 1
Target : 3 3 1 , .: _ . . : 3,3-: i~ti. at a [ 1 J * . . . .i, .. : . _. . . r 159 er . . :,, .. 1. . . . ., . ,. .. 99. is . f& a *,., , 8 .5 . _. &&g&; : %Jfj ; : , * : * . , , ,: , ; .; ,-. ,., ,:..I : .;, ., ., .:. _ : .; . ,., .;~ ., ;.:. : : . .;I:;. :,:. . ,: so~.~;~L..-.;.. .tit . . . . . e.b&..Y.a ~ ; .:, . ,. ,:. ., . , ;. .:. ..! .:. ,:I;, .,. ,:. ,. .: ...: .,: . ~ ,. : 1 , . , , . ~y:;.;I.:; .;, ,. T&g&t-: . .2 $$ . ; :. :,: : , ,.: j , : ; m. J : ,:,. 1-y ; , ,, .,. - , ; ,. . 2.2 :,,,isr,;$k :@,[Q:],; ; : : . Y.. :r .:.,:., . : , _ :. ;. ,, , ..:; . . , _ . . .:.,.:,;.; , .:.: 7.: . .:,. j : : ~$i&lTg&Ls. -0 : ,:. :,., , - : < : ..:. .:; ,(, ,: , ,: ~ . _ , : , ., : , (., :, , Y,. _ ;. ./.;.. . .:, . :I ,:.~.: : ,I .: i_, :! . 1, y . : :I, ,;:. : r, .&@&.; && f.&&& _ . _ , , .: . On each iteration of the whi 1 e loop, the middle element a [ 1 oca t i on] of the sub-array (from a [ 1 e f t ] to a [ right ] ) is checked for the target. If it is not found there, then either the left half is discarded by resetting left = location + 1, or the right half is discarded by resetting right = location - 1, accordingtowhether (a[location] c target).
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