The space complexity of an algorithm or a data structure is the amount of memory space required to solve an instance of the computational problem as a function of characteristics of the input. It is the memory required by an algorithm until it executes completely. This includes the memory space used by its inputs, called input space, and any other (auxiliary) memory it uses during execution, which is called auxiliary space.
Similar to time complexity, space complexity is often expressed asymptotically in big O notation, such as O ( n ) , {\displaystyle O(n),} O ( n log n ) , {\displaystyle O(n\log n),} O ( n α ) , {\displaystyle O(n^{\alpha }),} O ( 2 n ) , {\displaystyle O(2^{n}),} etc., where n is a characteristic of the input influencing space complexity.
## R Code Example ```r Here is a simple R code demonstration of space complexity using two functions: one with linear space complexity (O(n)) and another with constant space complexity (O(1)).# Function for linear space complexity (O(n))
linear_space <- function(n) {
# Allocate a vector of size n
vec <- numeric(n)
return(vec)
}
# Function for constant space complexity (O(1))
constant_space <- function() {
# No additional memory is allocated, only the input 'x' is used
x <- 5
return(x)
}
# Demonstrate linear space complexity
linear_vec <- linear_space(10)
# Demonstrate constant space complexity
const_val <- constant_space()In this example, the