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What is complexity of an algorithm? What is the basic relation between the time and space complexities of an algorithm? Justify your answer by giving an example.
Complexity of an algorithm is the measure of analysis of the algorithm. Analyzing an Algorithm means predicting the resources that the algorithm needs such as memory, communication bandwidth, time and logic gates. Most often it is computational or calculation time that is measured for finding a more suitable algorithm. This is called as time complexity of the algorithm. The running time of a program is described or defined as a function of the size of its input. On a specific input, it is traditionally measured as the number of primitive operations or steps executed.
The analysis of algorithm focuses on time complexity and space complexity both. As compared to time analysis, the analysis of space requirement for an algorithm is generally easier and faster, but wherever necessary, both the techniques can be used. The space is referred to as storage needed in addition to the space required storing the input data. The amount of memory needed by the program to run to completion is referred to as space complexity. For an algorithm, time complexity depends only upon the size of the input, thus, it is a function of input size 'n'. So the amount of time required by an algorithm to run to its completion is referred as time complexity.
The best algorithm to solve a given problem is the one that requires less memory and takes less time to complete its execution of the algorithm. But in practice it is not always likely to achieve both of these objectives. There may be number of approaches to solve a same problem. One such approach may require more space but takes less time to complete its execution while on other hand the other approach requires less space but
more time to complete its execution. Thus we may have to compromise one thing to improve the other. That is, we may be able to reduce space requirement by increasing running time or we can reduce running time by allocating more memory space. This situation where we compromise one to improve the other is known as Time-space trade off.
Compare zero-address, one-address, two-address, and three-address machines by writing programs to compute: Y = (A – B X C) / (D + E X F) for each of the four machines. The inst
Write an algorithm in form of a flowchart that takes temperatures input over a 100 day period (once per day) and outputs the number of days when temperature was below 20C and numbe
Handout 15 COMP 264: Introduction to Computer Systems (Section 001) Spring 2013 R. I. Greenberg Computer Science Department Loyola University Water TowerCampus, Lewis Towers 524 82
Q. Explain the technique to calculate the address of an element in an array. A 25 × 4 matrix array DATA is stored in memory in 'row-major order'. If base address is 200 and
An undirected graph G with n vertices and e edges is shown by adjacency list. What is the time required to generate all the connected components? O (e+n)
An algorithm is a sequence of steps to solve a problem; there may be more than one algorithm to solve a problem. The choice of a particular algorithm depends upon following cons
The worst case of quick sort has order O(n 2 )
Best - Fit Method: - This method obtains the smallest free block whose size is greater than or equal to get such a block by traversing the whole free list follows.
Mid Square method with good example
For a queue a physical analogy is a line at booking counter. At booking counter, customers go to the rear (end) of the line & customers are attended to several services from the fr
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