Question

According to Stroustrup : The C++ programming language :-

“When a vector is resized to accommodate more (or fewer) elements, all of its elements may be
moved to new locations.”

Is this holds true, even if the vector is re-sized to smaller size ?

Answer 1

Case 1: If the new size being requested is greater than the current std::vector::capacity() then all elements will be relocated.
Case 2: If the new size being requested is lesser than the current std::vector::capacity() then there will be no relocation of elements.

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Standerdese Evidence:

The standard defines effect of vector::resize() as:

C++11 Standard 23.3.6.3/12 vector capacity:

void resize(size_type sz, const T& c);

Effect:

if (sz > size())
     insert(end(), sz-size(), c);
else if (sz < size())
    erase(begin()+sz, end());
else
; // do nothing

As @DavidRodríguez-dribeas correctly points out, Iterator invalidation rules for std::vector::insert() operation are:

23.3.6.5 vector modifiers

1 [insert,push_back,emplace,emplace_back]

Remarks: Causes reallocation if the new size is greater than the old capacity. If no reallocation happens, all the iterators and references before the insertion point remain valid.

Essentially this means:
All iterators and references before the point of insertion will be unaffected, unless the new container size is greater than the previous capacity because in such a scenario all elements might be moved to new locations thus invalidating pointers/iterators to original location.Since resize() only erases/inserts elements at the end of the container^{[Note 1]}.The governing factor boils down to size being requested as against current capacity.

Hence the Case 1 result.

In Case 2 std::vector::erase() will be called and the invalidation rule in this case is:

23.3.6.5 vector modifiers

iterator erase(const_iterator position);

3 Effects: Invalidates iterators and references at or after the point of the erase.

Since ^{[Note 1]}, elements will be only removed at end and there is no need of relocation of all elements.