2. Space Time complexity (Theory)

Time Complexity-

it is not the time taken by code to run on system, as diff system have diff speed.
it is rate at which time taken increases wrt input size.
Big O notation-  computed for worst case scenario

O(cn+k)=O(cn)

ω is lower bound
θ is avg complexity
O is upper bound

1 sec => O(10^8) time complexity

optimal:         1  >  logn > n > nlogn  >  (n^2)  >  n!

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                                                            Space Complexity

it is (auxiliary space + input space) = (space to solve + space to store)

int f1(vector<int>v)             --  pass by value -- space inefficient, as it creates a copy

int f1(const vector<int>&v) --  for read only operations without making a copy

int f1(vector<int>&v)          --  for write operations in the original one

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int : (-10^9, +10^9)
long: (-10^12, +10^12)
long long: (-10^18, +10^18)

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Standard TIME complexities-

ordered set/map-                                            logN
unordered set/map-                                        1 or (N: worst case)     

------------------

sorting( merge/ quick/.sort() )-                      NlogN
bubble/ selection/ insertion sort-                   (n^2) 

-----------------

max/min-                                                        n      
binary search-                                                logN 
all permutations-                                            n!     
stack/queue-                                                   O(1)
priority queue-                                                logN

-----------------

if in loop, division happen by t:                    logt(N)
finding all divisors-                                       sqrt(n) 
GCD-                                                             log( min[A,B] )
exponentiation-                                             logN

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