# lower_bound

Category: algorithms | Component type: function

### Prototype

`Lower_bound` is an overloaded name; there are actually two `lower_bound` functions.

    template <class ForwardIterator, class LessThanComparable>
    ForwardIterator lower_bound(ForwardIterator first, ForwardIterator last,
                                const LessThanComparable& value);

    template <class ForwardIterator, class T, class StrictWeakOrdering>
    ForwardIterator lower_bound(ForwardIterator first, ForwardIterator last,
                                const T& value, StrictWeakOrdering comp);

### Description

`Lower_bound` is a version of binary search: it attempts to find the element `value` in an ordered range `[first, last)` [1]. Specifically, it returns the first position where `value` could be inserted without violating the ordering. [2] The first version of `lower_bound` uses `operator<` for comparison, and the second uses the function object `comp`.

The first version of `lower_bound` returns the furthermost iterator `i` in `[first, last)` such that, for every iterator `j` in `[first, i)`, `*j < value`.

The second version of `lower_bound` returns the furthermost iterator `i` in `[first, last)` such that, for every iterator `j` in `[first, i)`, `comp(*j, value)` is `true`.

### Definition

Defined in the standard header algorithm, and in the nonstandard backward-compatibility header algo.h.

### Requirements on types

For the first version:

- `ForwardIterator` is a model of Forward Iterator.
- `LessThanComparable` is a model of LessThan Comparable.
- The ordering on objects of type `LessThanComparable` is a strict weak ordering, as defined in the LessThan Comparable requirements.
- `ForwardIterator`'s value type is the same type as `LessThanComparable`.

For the second version:

- `ForwardIterator` is a model of Forward Iterator.
- `StrictWeakOrdering` is a model of Strict Weak Ordering.
- `ForwardIterator`'s value type is the same type as `T`.
- `ForwardIterator`'s value type is convertible to `StrictWeakOrdering`'s argument type.

### Preconditions

For the first version:

- `[first, last)` is a valid range.
- `[first, last)` is ordered in ascending order according to `operator<`. That is, for every pair of iterators `i` and `j` in `[first, last)` such that `i` precedes `j`, `*j < *i` is `false`.

For the second version:

- `[first, last)` is a valid range.
- `[first, last)` is ordered in ascending order according to the function object `comp`. That is, for every pair of iterators `i` and `j` in `[first, last)` such that `i` precedes `j`, `comp(*j, *i)` is `false`.

### Complexity

The number of comparisons is logarithmic: at most `log(last - first) + 1`. If `ForwardIterator` is a Random Access Iterator then the number of steps through the range is also logarithmic; otherwise, the number of steps is proportional to `last - first`. [3]

### Example

    int main()
    {
      int A[] = { 1, 2, 3, 3, 3, 5, 8 };
      const int N = sizeof(A) / sizeof(int);

      for (int i = 1; i <= 10; ++i) {
        int* p = lower_bound(A, A + N, i);
        cout << "Searching for " << i << ".  ";
        cout << "Result: index = " << p - A << ", ";
        if (p != A + N)
          cout << "A[" << p - A << "] == " << *p << endl;
        else
          cout << "which is off-the-end." << endl;
      }
    }

The output is:

    Searching for 1.  Result: index = 0, A[0] == 1
    Searching for 2.  Result: index = 1, A[1] == 2
    Searching for 3.  Result: index = 2, A[2] == 3
    Searching for 4.  Result: index = 5, A[5] == 5
    Searching for 5.  Result: index = 5, A[5] == 5
    Searching for 6.  Result: index = 6, A[6] == 8
    Searching for 7.  Result: index = 6, A[6] == 8
    Searching for 8.  Result: index = 6, A[6] == 8
    Searching for 9.  Result: index = 7, which is off-the-end.
    Searching for 10.  Result: index = 7, which is off-the-end.

### Notes

[1] Note that you may use an ordering that is a strict weak ordering but not a total ordering; that is, there might be values `x` and `y` such that `x < y`, `x > y`, and `x == y` are all `false`. (See the LessThan Comparable requirements for a more complete discussion.) Finding `value` in the range `[first, last)`, then, doesn't mean finding an element that is equal to `value` but rather one that is equivalent to `value`: one that is neither greater than nor less than `value`. If you're using a total ordering, however (if you're using `strcmp`, for example, or if you're using ordinary arithmetic comparison on integers), then you can ignore this technical distinction: for a total ordering, equality and equivalence are the same.

[2] If an element that is equivalent to [1] `value` is already present in the range `[first, last)`, then the return value of `lower_bound` will be an iterator that points to that element.

[3] This difference between Random Access Iterators and Forward Iterators is simply because `advance` is constant time for Random Access Iterators and linear time for Forward Iterators.

### See also

`upper_bound`, `equal_range`, `binary_search`

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