std::upper_bound and std::lower_bound for Vector in C++ STL

The std::upper_bound() and std::lower_bound() perform binary search on random-access STL containers and are defined in <algorithm>. Here, we focus on their use with vectors in C++ STL.

lower_bound() for Vectors

The std::lower_bound() method can be used to find the first value that is greater than or equal to given value in the vector. It needs the vector to be sorted because it implements binary search to find the value.

#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    // Sorted vector
    vector<int> v = {10, 20, 30, 40, 50};

    // Finding lower bound of 30
    cout << *lower_bound(v.begin(), v.end(), 30);

    return 0;
}

30

upper_bound() for Vectors

The std::upper_bound() method can be used to find the first value that is greater than to given value in the vector. It needs sorted vector because it implements binary search to find the value.

// C++ Program to illustrate use of std::upper_bound() for vector
#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    // Sorted vector
    vector<int> v = {10, 20, 30, 40, 50};

    // Finding upper bound of 30
    cout << *upper_bound(v.begin(), v.end(), 30);

    return 0;
}

40

Time Complexity: O(log n), where n is the number of elements in vector.
Auxiliary Space: O(1)

Examples

The below examples demonstrate the use of std::upper_bound and std::lower_bound in a vector in different scenarios

1 Finding the Lower and Upper Bound in a Part of Unsorted Vector

#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    vector<int> v = {89, 11, 56, 34, 67};

    // Sorting v before finding upper and lower bound
    sort(v.begin(), v.end());

    // Finding the lower bound of value 30 in the first three elements of the vector v
    cout << *lower_bound(v.begin(), v.begin() + 3, 30) << endl;

    // Finding the upper bound of value 30 in the last three elements of the vector v
    cout << *upper_bound(v.end() - 3, v.end(), 30);

    return 0;
}

34
56

Time Complexity: O(log n), not considering time required for sorting.
Auxiliary Space: O(1), not considering memory required for sorting.

Explanation: As we know that std::upper_bound() and std::lower_bound() doesn't works for unsorted vector, so we use std::sort() function to sort the vector. After that, we find the lower and upper bound in the desired range.

2 Checking if an Element Exists in Vector using lower_bound()

// C++ Program to check if an element exists in a vector using lower_bound()
#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    vector<int> v = {11, 34, 56, 67, 89};
    int val = 56;

    // Checking if val exists in the vector v
    auto it = lower_bound(v.begin(), v.end(), val);

    if (it != v.end() && *it == val)
        cout << val << " is found.";
    else
        cout << val << " is NOT found.";

    return 0;
}

56 is found.

Time Complexity: O(log n), where n is the number of elements in vector.
Auxiliary Space: O(1)

Explanation

• lower_bound() returns an iterator to the given value if it exists in the vector.
• If the value is not present, it returns an iterator to the first element greater than the value; upper_bound() cannot be used the same way to check existence.

3 Finding the Number of Elements Smaller and Greater than a Value

#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    vector<int> v = {11, 34, 56, 67, 89};
    int val = 50;

    // Finding lower and upper bound of val in v
    auto lb = lower_bound(v.begin(), v.end(), val);
    auto up = upper_bound(v.begin(), v.end(), val);

    // Finding the number of smaller elements
    cout << "No. of Smaller Elements: " << lb - v.begin() << endl;

    // Finding the number of larger elements
    cout << "No. of Larger Elements: " << v.end() - up << endl;

    return 0;
}

No. of Smaller Elements: 2
No. of Larger Elements: 3

Time Complexity: O(log n), where n is the number of elements in vector.
Auxiliary Space: O(1)

Explanation

• Lower_bound() returns an iterator to the first element ≥ the given value in a sorted vector.
• All elements before this iterator are smaller, so subtracting v.begin() from it gives their count.

Difference Between lower_bound() and upper_bound()

• lower_bound() returns the first element ≥ given value; upper_bound() returns the first element > given value.
• lower_bound() can be used to check if a value exists; upper_bound() cannot.
• For duplicates, lower_bound() points to the first occurrence, upper_bound() points just after the last occurrence.