Time Complexity
Definition:
“Time Complexity of an algorithm signifies the total time required by the program to run to completion.The Time complexity of algorithm is most commonly expressed using the big O notation”. “Time Complexity is most commonly estimated by counting the number of elementary functions performed by the algorithm.”
Big O Notation:
Big O notation is an upper bound, the worst-case time; Big O notation is required to run an algorithm on various inputs.
Example: if the time required by an algorithm on all inputs of size n is at most 5n3 + 3n.
Big Omega Notation:
Big Omega notation is a lower bound, the best-case time is proportional to the function multiplied by some constant factor.
Example: Quick sort
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Example: exchange the value of a and b if necessary so that a=<b^n is called constant time.
Linear Time:
An algorithm is said to be linear if its time complexity is O (n)
Function needs amount of time that is directly proportional to the number of input elements.
Example: Finding small values of n.
Quadratic Time: An algorithm is said to be quadratic if its time complexity is O (n^2)
Function needs amount of time that is quadratic proportional to the number of input elements.
Example: bubble sort algorithm, insertion sort algorithm, and selection sort algorithm.
Sub-Quadratic Time:
An algorithm is said to be Sub-quadratic time if T (n) =O (n^2)
Example: Shell Sort
Logarithmic time:
An algorithm is said to be Logarithmic time if T (n) =O (logn). When we performed operation on binary trees so we take logarithmic time.
Example: very easy example is that an algorithm that cuts a string in half.That is take O (logn) time (n is the length of the string)
Polylogarithmic time:
An algorithm is said to be Polylogarithmic time if T (n) = O ((logn) ^k)
Example: matrix chain
Thus total number of operations needed to execute the function for any given n, can be expressed as sum of 2 operations and the total number of operations needed to execute the function for n-1. Also when n=1, it just needs one operation to execute the function
Robinson, E. P., & Sahin, F. (2001). Economic production lot sizing with periodic costs and overtime. Decision Sciences, 32(3), 423-452. Retrieved from http://search.proquest.com/docview/198075992?accountid=32521
This equation shifts from the parent function based on the equation f(x) = k+a(x-h) . In this equation, k shifts the parent function vertically, up or down, depending on the value of k. The h value shifts the parent function to the left or right. If h equals 1, it goes to the right 1 unit, if it is negative 1, it goes to the left 1 unit. If a is negative, the parent function is reflected on the x-axis. If x is negative, the parent function is reflected on the y-axis.
allow for each subsequent step to take place. And after each step it becomes increasingly
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'You can time [someone], know exactly how long it takes him to do something... then you can make him do it faster.
area for a certain amount of time - as long as this is for no more
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What are the possible factors that contribute to the difficulty of the student in solving word problem?
where N_k are the constants and can be determined by the initial values of q_j and q ̇_j.