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Showing content from https://cplusplus.com/reference/algorithm/max/ below:

function template

<algorithm>

std::max default (1) 
template <class T> const T& max (const T& a, const T& b);
custom (2) 
template <class T, class Compare>  const T& max (const T& a, const T& b, Compare comp);
default (1) 
template <class T> const T& max (const T& a, const T& b);
custom (2) 
template <class T, class Compare>  const T& max (const T& a, const T& b, Compare comp);
initializer list (3) 
template <class T> T max (initializer_list<T> il);template <class T, class Compare>  T max (initializer_list<T> il, Compare comp);
default (1) 
template <class T> constexpr const T& max (const T& a, const T& b);
custom (2) 
template <class T, class Compare>  constexpr const T& max (const T& a, const T& b, Compare comp);
initializer list (3) 
template <class T> constexpr T max (initializer_list<T> il);template <class T, class Compare>  constexpr T max (initializer_list<T> il, Compare comp);

Return the largest

Returns the largest of a and b. If both are equivalent, a is returned.

The versions for initializer lists (3) return the largest of all the elements in the list. Returning the first of them if these are more than one.

The function uses operator< (or comp, if provided) to compare the values.

The behavior of this function template (C++98) is equivalent to:


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template <class T> const T& max (const T& a, const T& b) {
  return (a<b)?b:a;     // or: return comp(a,b)?b:a; for version (2)
}

Parameters
a, b
Values to compare.
comp
Binary function that accepts two values of type T as arguments, and returns a value convertible to bool. The value returned indicates whether the element passed as first argument is considered less than the second.
The function shall not modify any of its arguments.
This can either be a function pointer or a function object.
il
An initializer_list object.
These objects are automatically constructed from initializer list declarators.

T shall support being compared with operator<.

Return value The largest of the values passed as arguments.

Example 
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// max example
#include <iostream>     // std::cout
#include <algorithm>    // std::max

int main () {
  std::cout << "max(1,2)==" << std::max(1,2) << '\n';
  std::cout << "max(2,1)==" << std::max(2,1) << '\n';
  std::cout << "max('a','z')==" << std::max('a','z') << '\n';
  std::cout << "max(3.14,2.73)==" << std::max(3.14,2.73) << '\n';
  return 0;
}

Output: 
max(1,2)==2
max(2,1)==2
max('a','z')==z
max(3.14,2.73)==3.14


Complexity Linear in one less than the number of elements compared (constant for (1) and (2)).

Exceptions Throws if any comparison throws.
Note that invalid arguments cause undefined behavior.

See also
min
Return the smallest (function template)
max_element
Return largest element in range (function template)

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