Computer resources are limited that should be utilized efficiently. Show
Efficiency of an algorithm Computer resources are limited that should be utilized efficiently. The efficiency of an algorithm is defined as the number of computational resources used by the algorithm. An algorithm must be analyzed to determine its resource usage. The efficiency of an algorithm can be measured based on the usage of different resources. For maximum efficiency of algorithm we wish to minimize resource usage. The important resources such as time and space complexity cannot be compared directly, so time and space complexity could be considered for an algorithmic efficiency. Method for determining EfficiencyThe efficiency of an algorithm depends on how efficiently it uses time and memory space. The time efficiency of an algorithm is measured by different factors. For example, write a program for a defined algorithm, execute it by using any programming language, and measure the total time it takes to run. The execution time that you measure in this case would depend on a number of factors such as: · Speed of the machine · Compiler and other system Software tools · Operating System · Programming language used · Volume of data required However, to determine how efficiently an algorithm solves a given problem, you would like to determine how the execution time is affected by the nature of the algorithm. Therefore, we need to develop fundamental laws that determine the efficiency of a program in terms of the nature of the underlying algorithm. Space-Time tradeoffA space-time or time-memory tradeoff is a way of solving in less time by using more storage space or by solving a given algorithm in very little space by spending more time. To solve a given programming problem, many different algorithms may be used. Some of these algorithms may be extremely time-efficient and others extremely space-efficient. Time/space trade off refers to a situation where you can reduce the use of memory at the cost of slower program execution, or reduce the running time at the cost of increased memory usage. Asymptotic NotationsAsymptotic Notations are languages that uses meaningful statements about time and space complexity. The following three asymptotic notations are mostly used to represent time complexity of algorithms: (i) Big OBig O is often used to describe the worst-case of an algorithm. (ii) Big ΩBig Omega is the reverse Big O, if Bi O is used to describe the upper bound (worst - case) of a asymptotic function, Big Omega is used to describe the lower bound (best-case). (iii) Big ΘWhen an algorithm has a complexity with lower bound = upper bound, say that an algorithm has a complexity O (n log n) and (n log n), it’s actually has the complexity Θ (n log n), which means the running time of that algorithm always falls in n log n in the best-case and worst-case. Best, Worst, and Average ease EfficiencyLet us assume a list of n number of values stored in an array. Suppose if we want to search a particular element in this list, the algorithm that search the key element in the list among n elements, by comparing the key element with each element in the list sequentially. The best case would be if the first element in the list matches with the key element to be searched in a list of elements. The efficiency in that case would be expressed as O(1) because only one comparison is enough. Similarly, the worst case in this scenario would be if the complete list is searched and the element is found only at the end of the list or is not found in the list. The efficiency of an algorithm in that case would be expressed as O(n) because n comparisons required to complete the search. The average case efficiency of an algorithm can be obtained by finding the average number of comparisons as given below: Minimum number of comparisons = 1 Maximum number of comparisons = n If the element not found then maximum number of comparison = n Therefore, average number of comparisons = (n + 1)/2 Hence the average case efficiency will be expressed as O (n). Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail 12th Computer Science : Chapter 4 : Algorithmic Strategies : Efficiency of an algorithm | When determining the efficiency of an algorithm you must consider which of the following things?Time and space complexity are the two main measures for calculating algorithm efficiency, determining how many resources are needed on a machine to process it. Where time measures how long it takes to process the algorithm, space measures how much memory is used.
Which of the following is used to compare the efficiency of algorithms?To express the time complexity of an algorithm, we use something called the “Big O notation”. The Big O notation is a language we use to describe the time complexity of an algorithm. It's how we compare the efficiency of different approaches to a problem, and helps us to make decisions.
How does the efficiency of a program depend upon the algorithm?The efficiency of an algorithm depends upon its time complexity and space complexity. The complexity of an algorithm is a function that provides the running time and space for data, depending on the size provided by us.
What is effectiveness of an algorithm?An algorithm is considered efficient if its resource consumption, also known as computational cost, is at or below some acceptable level. Roughly speaking, 'acceptable' means: it will run in a reasonable amount of time or space on an available computer, typically as a function of the size of the input.
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Which of the following is a key factor in determining the efficiency of an algorithm?
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