Question

Consider the following Python program, where x is assumed to be a list of integers.

def mystery_func(x):

n = len(x)

for i in range(n - 1):

for j in range(i + 1, n):

if x[j] - x[i] < j - i: return False

return True

3a. In plain English, describe what it accomplishes (i.e., the relationship between input and output, not how the code works).

3b. Analyze the running time and express it with big O.

3c. Rewrite this function so it accomplishes the same thing but is more efficient, and state the running time in a comment.

Answer 1

Answer:

3a) input is array and output is false or true on the basis of given comparison

Here two loops are used to travel array, i indexed array is outermost and j indexed array is innermost

if condition is checking whether "difference between value at jth location and value at ith location" is less than "difference between index value j and index value i". if the above mentioned condition right/true then it return false value otherwise it return true value.

3b) It has two nested for loop hence its time complexity is O(n²)

3c) Lets consider array x is already sorted in ascending order then no need of j indexed array. because condition is always true. only above mentioned case can reduce its running time.

def mystery_func(x):

n = len(x)

for i in range(n - 1):

if x[i+1] - x[i] < 1: return False

return True

Here running time is O(n)