Binary search is an important component in competitive programming or any algorithmic competition, having knowledge of shorthand functions reduces the time to code them. Binary search is the most efficient search algorithm.
Binary Search is a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(Log N).
General operations performed using binary search:
-
finding an element
-
lower_bound
-
upper_bound
Tóm Tắt
1. binary_search:
binary_search(start_ptr, end_ptr, num): This function returns true if the element is present in the container, else returns false. The start_ptr variable holds the starting point of the binary search and end_ptr holds the ending position of binary search space and num is the value to be found.
Coding implementation of binary_search function:
CPP
#include <bits/stdc++.h>
using namespace std;
int main()
{
vector<int> arr = { 10, 15, 20, 25, 30, 35 };
if (binary_search(arr.begin(), arr.end(), 15))
cout << "15 exists in vector";
else
cout << "15 does not exist";
cout << endl;
if (binary_search(arr.begin(), arr.end(), 23))
cout << "23 exists in vector";
else
cout << "23 does not exist";
cout << endl;
}
Output
15 exists in vector 23 does not exist
Time Complexity: O(log N) – where N is the number of elements in the array.
Auxiliary Space: O(1)
2. lower_bound:
lower_bound(start_ptr, end_ptr, num): Returns pointer to the position of num if the container contains only one occurrence of num. Returns a pointer to the first position of num if the container contains multiple occurrences of num. Returns pointer to the position of a number just higher than num, if the container does not contain an occurrence of num which is the position of the number when inserted in the already sorted array and sorted again. Subtracting the first position i.e vect.begin() from the pointer, returns the actual index. The start_ptr variable holds the starting point of the binary search and end_ptr holds the ending position of binary search space and num is the value to be found.
Coding implementation of lower_bound function:
CPP
#include <bits/stdc++.h>
using namespace std;
int main()
{
vector<int> arr1 = { 10, 15, 20, 25, 30, 35 };
vector<int> arr2 = { 10, 15, 20, 20, 25, 30, 35 };
vector<int> arr3 = { 10, 15, 25, 30, 35 };
cout << "The position of 20 using lower_bound "
" (in single occurrence case) : ";
cout << lower_bound(arr1.begin(), arr1.end(), 20)
- arr1.begin();
cout << endl;
cout << "The position of 20 using lower_bound "
"(in multiple occurrence case) : ";
cout << lower_bound(arr2.begin(), arr2.end(), 20)
- arr2.begin();
cout << endl;
cout << "The position of 20 using lower_bound "
"(in no occurrence case) : ";
cout << lower_bound(arr3.begin(), arr3.end(), 20)
- arr3.begin();
cout << endl;
}
Output
The position of 20 using lower_bound (in single occurrence case) : 2 The position of 20 using lower_bound (in multiple occurrence case) : 2 The position of 20 using lower_bound (in no occurrence case) : 2
Time Complexity: O(log N) – where N is the number of elements in the array.
Auxiliary Space: O(1)
3. upper_bound:
upper_bound(start_ptr, end_ptr, num): Returns pointer to the position of next higher number than num if the container contains one occurrence of num. Returns pointer to the first position of the next higher number than the last occurrence of num if the container contains multiple occurrences of num. Returns pointer to position of next higher number than num if the container does not contain an occurrence of num. Subtracting the first position i.e vect.begin() from the pointer, returns the actual index. The start_ptr variable holds the starting point of the binary search and end_ptr holds the ending position of binary search space and num is the value to be found.
Coding implementation of upper_bound function:
CPP
#include <bits/stdc++.h>
using namespace std;
int main()
{
vector<int> arr1 = { 10, 15, 20, 25, 30, 35 };
vector<int> arr2 = { 10, 15, 20, 20, 25, 30, 35 };
vector<int> arr3 = { 10, 15, 25, 30, 35 };
cout << "The position of 20 using upper_bound"
" (in single occurrence case) : ";
cout << upper_bound(arr1.begin(), arr1.end(), 20)
- arr1.begin();
cout << endl;
cout << "The position of 20 using upper_bound "
"(in multiple occurrence case) : ";
cout << upper_bound(arr2.begin(), arr2.end(), 20)
- arr2.begin();
cout << endl;
cout << "The position of 20 using upper_bound"
" (in no occurrence case) : ";
cout << upper_bound(arr3.begin(), arr3.end(), 20)
- arr3.begin();
cout << endl;
}
Output
The position of 20 using upper_bound (in single occurrence case) : 3 The position of 20 using upper_bound (in multiple occurrence case) : 4 The position of 20 using upper_bound (in no occurrence case) : 2
Time Complexity: O(log N) – where N is the number of elements in the array.
Auxiliary Space: O(1)
This article is contributed by Manjeet Singh(HBD.N). If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to [email protected]. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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