What would you like to do?
What is Time space trade off between algorithm?
what do you mean by time and space complexity and how to represent these complexity
Yes, there should be.
An algorithm is a statement of how a particular problem will be solved. Coding is the implementation of that algorithm in a particular language.
The algorithm will have both a constant time complexity and a constant space complexity: O(1)
In a trade-off you give up something for something else. If you exchange some item with someone for something of equal value, you have made a trade-off. in opportunity co…st you are forced to make an alternate choice that you did not intend to make. Here you are giving up something of better value for something of lesser value. Usually there is remorse here. You actually are not as happy as you would have been if you had the opportunity to make the original choice. If you go to the store to purchase an item and for some reason you left that item in the store and bring something else home. This could happen because the price s too high, the quality was not as advertised, or you just did not see yourself buying this item. You opportunity cost is the item you left behind in the store.
BASIC DIFFERENCES BETWEEN SPACE COMPLEXITY AND TIME COMPLEXITY SPACE COMPLEXITY: The space complexity of an algorithm is the amount of memory it requires to run to complet…ion. the space needed by a program contains the following components: 1) Instruction space: -stores the executable version of programs and is generally fixed. 2) Data space: It contains: a) Space required by constants and simple variables.Its space is fixed. b) Space needed by fixed size stucture variables such as array and structures. c) dynamically allocated space.This space is usually variable. 3) enviorntal stack: -Needed to stores information required to reinvoke suspended processes or functions. the following data is saved on the stack - return address. -value of all local variables -value of all formal parameters in the function.. TIME COMPLEXITY: The time complexity of an algorithm is the amount of time it needs to run to completion. namely space To measure the time complexity we can count all operations performed in an algorithm and if we know the time taken for each operation then we can easily compute the total time taken by the algorithm.This time varies from system to system. Our intention is to estimate execution time of an algorithm irrespective of the computer on which it will be used. Hence identify the key operation and count such operation performed till the program completes its execution. The time complexity can be expressd as a function of a key operation performed. The space and time complexity is usually expressed in the form of function f(n),where n is the input size for a given instance of a problem being solved. f(n) helps us to predict the rate of growthof complexity that will increase as size of input to the problem increases. f(1) also helps us to predict complexity of two or more algorithms in order ro find which is more efficient.
Insertion sort is an in-place sorting algorithm, meaning that it requires little to no extra storage. In the case of insertion sort, only a single list element needs to be st…ored outside of the initial data, making the space complexity O(1).
Decisions are directly related to trade offs because what one person chooses can have an effect on outcome. Trade-offs may need to be analyzed carefully if there are risks… involved. For every decision you make their is a trade-off, because you always have to give something up in exchange for another decision.
the main difference between the A*(A star) and AO*(AO star) algorithms is that A* algo is a OR graph algorithm and AO* is a AND-OR graph algorithm. In OR graph algorithm it ju…st find only one solution (i.e either OR solution means this OR this OR this). But in the AND-OR graph algo it find more than one solution by ANDing two or more branches. for more details on AND-OR graph & OR graph please refer the book "Artificial Intelligence" by Elaine Rich & Kevin Knight. -AAA
Residence time is the time it takes a particle to complete the cycle. Space time is volume of the reactor over the velocity. If the volume does not change and the velocity… remains constant then Residence time = space time, however, if there is a disturbance in the reactor (i.e., change in pressure, temp, ect.), then residence time does not equal to space time.
Algorithms are basically sequences of instructions to solve a problem or to perform a calculation. A logarithm is a specific mathematical concept. For more information on each…, look at the sites listed below: Algorithms: http://en.wikipedia.org/wiki/Algorithm Logarithms: http://en.wikipedia.org/wiki/Logarithm
An algorithm is a sequence of steps which can be followed to solve a particular problem. A flowchart is one way in which to describe an algorithm.
Generally, a faster algorithm will take up more memory, whereas a slower algorithm will use less memory.
The relationship between time and space is, r=ct or space = the speed of light times time. Time t = r/c or time is space divided by the speed of light. Space r is a re…al number as time t and c the speed of light.
Picture "Liquidity" as being on one end of a straight line and "Profitability" on the other end of the line. If you are on the line and move toward one, you automatically move… away from the other. In other words, there is the trade-off between liquidity and profitability. This is easy to illustrate with a simple example. The items on the asset side of a company's balance sheet are listed in order of liquidity, i.e., the ease with which they can be converted into cash. In order, the most important of these assets are:CashMarketable SecuritiesAccounts ReceivableInventoryFixed Assets Notice that as we go from the top of the list to the bottom, the liquidity decreases. However, as we go from top to bottom, the profitability increases. In other words, the most profitable investment for company is normally in its fixed assets; the least profitable investment is cash. Bankruptcy Risk Is it possible for a company to go bankrupt if it has a lot of cash but is not profitable? Sure it is! It may take a while, but if it remains unprofitable, it will eventually go bankrupt. Its available cash will be used to finance the losses, but when the cash runs out, the assets of the company will have to shrink because there will be insufficient funds to replace them as they wear out. The company will become smaller and smaller and will eventually fail.Is it possible for a company to go bankrupt if it is very, very profitable but is not very liquid (i.e., does not have much cash)? Certainly! For example, if a company expands so rapidly that it is constantly building new buildings and buying new equipment, it may very well get behind on its payments to the contractors and vendors due to the lack of cash. In other words, the company is spending money much faster than it is making it, even though it is making a lot. Eventually, the creditors (i.e., contractors and vendors) will demand their money and, if the company does not have enough cash to pay up, the creditors will take the company to court. A judge may very well decide that the creditors are entitled to their money and will start selling off the assets of the company in order to raise cash to pay them. (Half-finished construction projects don't bring in much cash at a sheriff's auction.) At that point, the owners of the company have lost control and may very well be forced into bankruptcy. So, you can see that it's dangerous to be on either extreme of the line: (1) highly liquid but not very profitable, and (2) highly profitable but not very liquid. There's a broad middle ground between the two extremes where the company wants to reside. Fortunately, we have tools at our disposal that will allow us to measure where we are on the line. These tools are primarily financial ratios, which measure the company's liquidity and profitability. We can compare the company's liquidity and profitability ratios to those of other companies (particularly, to the industry average) to see where we are on the line, and can, if necessary, make corrections.
IN COMPUTER SCIENCE, A SPACE-TIME OR TIME-MEMORY TRADEOFF IS A SITUATION WHERE THE MEMORY USE CAN BE REDUCED AT THE COST OF SLOWER PROGRAM EXECUTION (OR, VICE VERSA, THE COMPU…TATION TIME CAN BE REDUCED AT THE COST OF INCREASED MEMORY USE). AS THE RELATIVE COSTS OF CPU CYCLES, RAM SPACE, AND HARD DRIVE SPACE CHANGE HARD DRIVE SPACE HAS FOR SOME TIME BEEN GETTING CHEAPER AT A MUCH FASTER RATE THAN OTHER COMPONENTS OF COMPUTERS. THE APPROPRIATE CHOICES FOR SPACE-TIME TRADEOFFS HAVE CHANGED RADICALLY. OFTEN, BY EXPLOITING A SPACE-TIME TRADEOFF, A PROGRAM CAN BE MADE TO RUN MUCH FASTER. THE MOST COMMON SITUATION IS AN ALGORITHM INVOLVING A LOOKUP TABLE: AN IMPLEMENTATION CAN INCLUDE THE ENTIRE TABLE, WHICH REDUCES COMPUTING TIME, BUT INCREASES THE AMOUNT OF MEMORY NEEDED, OR IT CAN COMPUTE TABLE ENTRIES AS NEEDED, INCREASING COMPUTING TIME, BUT REDUCING MEMORY REQUIREMENTS. A SPACE-TIME TRADEOFF CAN BE APPLIED TO THE PROBLEM OF DATA STORAGE. IF DATA IS STORED UNCOMPRESSED, IT TAKES MORE SPACE BUT LESS TIME THAN IF THE DATA WERE STORED COMPRESSED (SINCE COMPRESSING THE DATA REDUCES THE AMOUNT OF SPACE IT TAKES, BUT IT TAKES TIME TO RUN THECOMPRESSION ALGORITHM). DEPENDING ON THE PARTICULAR INSTANCE OF THE PROBLEM, EITHER WAY IS PRACTICAL. ANOTHER EXAMPLE IS DISPLAYING MATHEMATICAL FORMULAE ON PRIMARILY TEXT-BASED WEBSITES, SUCH AS WIKIPEDIA. Storing only the LaTeX source and rendering it as an image every time the page is requested would be trading time for space - more time used, but less space. Rendering the image when the page is changed and storing the rendered images would be trading space for time - more space used, but less time. Note that there are also rare instances where it is possible to directly work with compressed data, such as in the case of compressed bitmap indices, where it is faster to work with compression than without compression. Larger code size can be traded for higher program speed when applying loop unrolling. This technique makes the code longer for each iteration of a loop, but saves the computation time required for jumping back to the beginning of the loop at the end of each iteration. Algorithms that also make use of space-time tradeoffs include: BABY-STEP GIANT-STEP ALGORITHM FOR CALCULATING DISCRETE LOGARITHMS. RAINBOW TABLES IN CRYPTOGRAPHY, WHERE THE ADVERSARY IS TRYING TO DO BETTER THAN THE EXPONENTIAL TIME REQUIRED FOR A BRUTE FORCE ATTACK. RAINBOW TABLES USE PARTIALLY PRECOMPUTED VALUES IN THE HASH SPACE OF A CRYPTOGRAPHIC HASH FUNCTION TO CRACK PASSWORDS IN MINUTES INSTEAD OF WEEKS. DECREASING THE SIZE OF THE RAINBOW TABLE INCREASES THE TIME REQUIRED TO ITERATE OVER THE HASH SPACE. THE MEET-IN-THE-MIDDLE ATTACK USES A SPACE-TIME TRADEOFF TO FIND THE CRYPTOGRAPHIC KEY IN ONLY 2N + 1 ENCRYPTIONS (AND O(2N) SPACE) VERSUS THE EXPECTED 22N ENCRYPTIONS (BUT ONLY O(1) SPACE) OF THE NAIVE ATTACK. DYNAMIC PROGRAMMING, WHERE THE TIME COMPLEXITY OF A PROBLEM CAN BE REDUCED SIGNIFICANTLY BY USING MORE MEMORY.
There's more than one algorithms, the best one is the following: F(n) = 1/sqrt(5) * (q1^n + q2^n) where q1=(1+sqrt(5))/2, q2=(1-sqrt(5))/2