우리는 C++ 프로그래밍 언어의 이진 검색에 대해 논의할 것입니다. 이진 검색은 배열을 연속적으로 절반으로 나눈 다음 절반 배열에서 지정된 요소를 검색하여 정렬된 배열에서 지정된 요소를 찾는 데 사용되는 메커니즘입니다. 그리고 일치하는 항목을 찾을 때까지 프로세스가 계속됩니다. 정렬된 데이터 구조에서만 작동합니다. 이진 검색 알고리즘의 시간 복잡도는 O(log n)입니다.
참고: C++에서 이진 검색 기술을 수행하려면 프로그래머나 사용자는 주어진 배열이 오름차순 또는 내림차순으로 정렬되어야 함을 확인해야 합니다.
C++의 이진 검색 알고리즘
다음은 C++에서 이진 검색을 수행하는 알고리즘입니다.
beg = 0; end = size - 1; while ( beg num) { End = mid - 1; } Else if (arr [mid] <num) { beg="mid" + 1; } if the element does not exist in array, return -1. -1; < pre> <h3>Steps to perform the binary search in C++</h3> <p> <strong>Step 1:</strong> Declare the variables and input all elements of an array in sorted order (ascending or descending).</p> <p> <strong>Step 2:</strong> Divide the lists of array elements into halves.</p> <p> <strong>Step 3:</strong> Now compare the target elements with the middle element of the array. And if the value of the target element is matched with the middle element, return the middle element's position and end the search process.</p> <p> <strong>Step 4:</strong> If the target element is less than the middle element, we search the elements into the lower half of an array.</p> <p> <strong>Step 5:</strong> If the target element is larger than the middle element, we need to search the element into the greater half of the array.</p> <p> <strong>Step 6:</strong> We will continuously repeat steps 4, 5, and 6 till the specified element is not found in the sorted array.</p> <p> <strong>Example 1: Program to find the specified number from the sorted array using the binary search</strong> </p> <p>Let's write a program to find the specified number from a sorted array using the binary search in the C++ programming language.</p> <pre> #include #include using namespace std; int main () { // declaration of the variables and array int arr[100], st, mid, end, i, num, tgt; cout << ' Define the size of the array: ' <> num; // get size // enter only sorted array cout << ' Enter the values in sorted array either ascending or descending order: ' << endl; // use for loop to iterate values for (i = 0; i < num; i++) { cout << ' arr [' << i <> arr[i]; } // initialize the starting and ending variable's values st = 0; end = num - 1; // size of array (num) - 1 // define the item or value to be search cout << ' Define a value to be searched from sorted array: ' <> tgt; // use while loop to check 'st', should be less than equal to 'end'. while ( st <= end) { get middle value by splitting into half mid="(" st + end ) 2; * if we the target at index, print position and exit from program. (arr[mid]="=" tgt) cout << ' element is found index < arr[mid]) 1; set new for variable } check of less than element' else ( tgt - number not found. endl; return 0; pre> <p> <strong>Output</strong> </p> <pre> Define the size of the array: 10 Enter the values in sorted array either ascending or descending order: Arr [0] = 12 Arr [1] = 24 Arr [2] = 36 Arr [3] = 48 Arr [4] = 50 Arr [5] = 54 Arr [6] = 58 Arr [7] = 60 Arr [8] = 72 Arr [9] = 84 Define a value to be searched from sorted array: 50 Element is found at index 5 </pre> <p> <strong>Example 2: Program to perform the binary search using the user-defined function</strong> </p> <pre> /* program to find the specified element from the sorted array using the binary search in C++. */ #include using namespace std; /* create user-defined function and pass different parameters: arr[] - it represents the sorted array; num variable represents the size of an array; tgt variable represents the target or specified variable to be searched in the sorted array. */ int bin_search (int arr[], int num, int tgt) { int beg = 0, end = num - 1; // use loop to check all sorted elements while (beg <= end) { * get the mid value of sorted array and then compares with target element. int + 2; if (tgt="=" arr[mid]) return mid; when is equal to tgt } check less than value, discard left element else < end="mid" - 1; greater all elements beg="mid" -1 not exists in -1; main () declaration arrays arr[]="{" 5, 10, 15, 20, 25, 30, 37, 40}; specified num="sizeof" (arr) sizeof (arr[0]); declare pos variable position (arr, num, tgt); (pos !="1)" cout << ' found at 1)<< endl; array' 0; pre> <p> <strong>Output</strong> </p> <pre> Element is found at position 5 </pre> <p>In the above program, we declared an array arr[] = {5, 10, 15, 20, 25, 30, 35, 40); and then we specified number '25' to which search from the sorted array using the binary search method. Therefore, we create a user-defined function bin_search() that searches the given number and returns the statement 'Element is found at position 5'. If the number is not defined in the array, the bin_search() function shows ' Element is not found in the array.' </p> <p> <strong>Example 3: Program to find the specified element using the recursion function</strong> </p> <p>Let's create an example to check whether the specified element is found in the sorted array using the binary search inside the recursion function.</p> <pre> /* find the specified number using the binary search technique inside the recursion method. */ #include using namespace std; // define a function int binary_search (int [], int, int, int); int main () { // declaration of the variables int i, arr[100], tgt, num, ind, st, end; cout <> num; cout << ' Enter ' << num << ' elements in ascending order: ' << endl; // use for loop to ieterate the number for ( i = 0; i < num; i++) { cout << ' arr [' << i <> arr[i]; } // define the element to be search cout <> tgt; // ind define the index number ind = binary_search (arr, 0, num - 1, tgt); // check for existemce of the specified element if (ind == 0) cout << tgt << ' is not available in the array-list'; else cout << tgt << ' is available at position ' << ind < end) { return 0; } mid = (st + end) / 2; // get middle value of the sorted array // check middle value is equal to target number if (arr[mid] == tgt) { return (mid + 1); } // check mid is greater than target number else if (arr[mid]> tgt) { binary_search (arr, st, mid - 1, tgt); } // check mid is less than target number else if (arr [mid] <tgt) { binary_search (arr, mid + 1, end, tgt); } < pre> <p> <strong>Output</strong> </p> <pre> Define the size of an array: 10 Arr [0] = 2 Arr [1] = 4 Arr [2] = 5 Arr [3] = 8 Arr [4] = 12 Arr [5] = 13 Arr [6] = 27 Arr [7] = 36 Arr [8] = 49 Arr [9] = 51 Enter an element to be searched in ascending array: 12 12 is available at position 6. </pre> <p>In the above program, we input all elements of an array in ascending order and then define a number as the target element is '12', which is searched from a sorted array using the binary search method. So, we create a user-defined function binary_search() that searches the defined element's position from an array and returns the particular element available at this position. And if the element is not available in the sorted array, it returns 0. </p> <hr></tgt)></pre></=></pre></=></pre></num)> 예제 2: 사용자 정의 함수를 사용하여 이진 검색을 수행하는 프로그램
/* program to find the specified element from the sorted array using the binary search in C++. */ #include using namespace std; /* create user-defined function and pass different parameters: arr[] - it represents the sorted array; num variable represents the size of an array; tgt variable represents the target or specified variable to be searched in the sorted array. */ int bin_search (int arr[], int num, int tgt) { int beg = 0, end = num - 1; // use loop to check all sorted elements while (beg <= end) { * get the mid value of sorted array and then compares with target element. int + 2; if (tgt="=" arr[mid]) return mid; when is equal to tgt } check less than value, discard left element else < end="mid" - 1; greater all elements beg="mid" -1 not exists in -1; main () declaration arrays arr[]="{" 5, 10, 15, 20, 25, 30, 37, 40}; specified num="sizeof" (arr) sizeof (arr[0]); declare pos variable position (arr, num, tgt); (pos !="1)" cout << \' found at 1)<< endl; array\' 0; pre> <p> <strong>Output</strong> </p> <pre> Element is found at position 5 </pre> <p>In the above program, we declared an array arr[] = {5, 10, 15, 20, 25, 30, 35, 40); and then we specified number '25' to which search from the sorted array using the binary search method. Therefore, we create a user-defined function bin_search() that searches the given number and returns the statement 'Element is found at position 5'. If the number is not defined in the array, the bin_search() function shows ' Element is not found in the array.' </p> <p> <strong>Example 3: Program to find the specified element using the recursion function</strong> </p> <p>Let's create an example to check whether the specified element is found in the sorted array using the binary search inside the recursion function.</p> <pre> /* find the specified number using the binary search technique inside the recursion method. */ #include using namespace std; // define a function int binary_search (int [], int, int, int); int main () { // declaration of the variables int i, arr[100], tgt, num, ind, st, end; cout <> num; cout << ' Enter ' << num << ' elements in ascending order: ' << endl; // use for loop to ieterate the number for ( i = 0; i < num; i++) { cout << ' arr [' << i <> arr[i]; } // define the element to be search cout <> tgt; // ind define the index number ind = binary_search (arr, 0, num - 1, tgt); // check for existemce of the specified element if (ind == 0) cout << tgt << ' is not available in the array-list'; else cout << tgt << ' is available at position ' << ind < end) { return 0; } mid = (st + end) / 2; // get middle value of the sorted array // check middle value is equal to target number if (arr[mid] == tgt) { return (mid + 1); } // check mid is greater than target number else if (arr[mid]> tgt) { binary_search (arr, st, mid - 1, tgt); } // check mid is less than target number else if (arr [mid] <tgt) { binary_search (arr, mid + 1, end, tgt); } < pre> <p> <strong>Output</strong> </p> <pre> Define the size of an array: 10 Arr [0] = 2 Arr [1] = 4 Arr [2] = 5 Arr [3] = 8 Arr [4] = 12 Arr [5] = 13 Arr [6] = 27 Arr [7] = 36 Arr [8] = 49 Arr [9] = 51 Enter an element to be searched in ascending array: 12 12 is available at position 6. </pre> <p>In the above program, we input all elements of an array in ascending order and then define a number as the target element is '12', which is searched from a sorted array using the binary search method. So, we create a user-defined function binary_search() that searches the defined element's position from an array and returns the particular element available at this position. And if the element is not available in the sorted array, it returns 0. </p> <hr></tgt)></pre></=> 위 프로그램에서는 배열 arr[] = {5, 10, 15, 20, 25, 30, 35, 40);을 선언했습니다. 그런 다음 이진 검색 방법을 사용하여 정렬된 배열에서 검색할 번호 '25'를 지정했습니다. 따라서 주어진 숫자를 검색하고 '요소는 위치 5에서 발견되었습니다'라는 명령문을 반환하는 사용자 정의 함수 bin_search()를 만듭니다. 배열에 숫자가 정의되어 있지 않으면 bin_search() 함수는 '배열에서 요소를 찾을 수 없습니다.'라고 표시합니다.
추상 클래스와 인터페이스
예제 3: 재귀 함수를 사용하여 지정된 요소를 찾는 프로그램
재귀 함수 내부에서 이진 검색을 이용하여 정렬된 배열에 지정한 요소가 있는지 확인하는 예제를 만들어 보겠습니다.
/* find the specified number using the binary search technique inside the recursion method. */ #include using namespace std; // define a function int binary_search (int [], int, int, int); int main () { // declaration of the variables int i, arr[100], tgt, num, ind, st, end; cout <> num; cout << ' Enter ' << num << ' elements in ascending order: ' << endl; // use for loop to ieterate the number for ( i = 0; i < num; i++) { cout << ' arr [' << i <> arr[i]; } // define the element to be search cout <> tgt; // ind define the index number ind = binary_search (arr, 0, num - 1, tgt); // check for existemce of the specified element if (ind == 0) cout << tgt << ' is not available in the array-list'; else cout << tgt << ' is available at position ' << ind < end) { return 0; } mid = (st + end) / 2; // get middle value of the sorted array // check middle value is equal to target number if (arr[mid] == tgt) { return (mid + 1); } // check mid is greater than target number else if (arr[mid]> tgt) { binary_search (arr, st, mid - 1, tgt); } // check mid is less than target number else if (arr [mid] <tgt) { binary_search (arr, mid + 1, end, tgt); } < pre> <p> <strong>Output</strong> </p> <pre> Define the size of an array: 10 Arr [0] = 2 Arr [1] = 4 Arr [2] = 5 Arr [3] = 8 Arr [4] = 12 Arr [5] = 13 Arr [6] = 27 Arr [7] = 36 Arr [8] = 49 Arr [9] = 51 Enter an element to be searched in ascending array: 12 12 is available at position 6. </pre> <p>In the above program, we input all elements of an array in ascending order and then define a number as the target element is '12', which is searched from a sorted array using the binary search method. So, we create a user-defined function binary_search() that searches the defined element's position from an array and returns the particular element available at this position. And if the element is not available in the sorted array, it returns 0. </p> <hr></tgt)> 위 프로그램에서는 배열의 모든 요소를 오름차순으로 입력한 후 이진 검색 방법을 사용하여 정렬된 배열에서 검색되는 대상 요소가 '12'이므로 숫자를 정의합니다. 따라서 우리는 배열에서 정의된 요소의 위치를 검색하고 이 위치에서 사용 가능한 특정 요소를 반환하는 사용자 정의 함수 binary_search()를 만듭니다. 그리고 정렬된 배열에서 해당 요소를 사용할 수 없으면 0을 반환합니다.