Space complexity is a measure of the amount of working storage an algorithm needs. That means how much memory, in the worst case, is needed at any point in the algorithm. As with time complexity, we’re mostly concerned with how the space needs grow, in big-Oh terms, as the size N of the input problem grows.

For any algorithm, memory is required for the following purposes

  1. Memory required to store program instructions
  2. Memory required to store constant values
  3. Memory required to store variable values
  4. And for few other things

Example :-

int sum(int x, int y, int z) {
  int r = x + y + z;
  return r;

This requires 3 units of space for the parameters and 1 for the local variable, and this never changes, so space complexity is O(1).

int sum(int a[], int n) {
  int r = 0;
  for (int i = 0; i < n; ++i) {
    r += a[i];
  return r;

This requires N units for a, plus space for n, r and i, so it’s O(N). 

If a function A uses M units of its own space (local variables and parameters), and it calls a function B that needs N units of local space, then A overall needs M + N units of temporary workspace. What if A calls B 3 times? When a function finishes, its space can be reused, so if A calls B 3 times, it still only needs M + N units of workspace. What if A calls itself recursively N times? Then its space can’t be reused because every call is still in progress, so it needs O(N2) units of workspace. If things are passed by pointer or reference, then space is shared. If A passes a C-style array to B, there is no new space allocated. If A passes a C++ object by reference to B, there is no new space. What if A passes a vector or string by value? Most likely, new space will be allocated.