Finding sum of absolute difference of every pair of integer from

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Now I would not give you the exact solution to this problem rather I would give you an intuition to solve this problem.

If we try to generalize count of the number of times a particular number at index i is getting added and number of times it is being subtracted then for every index i we can use that mathematically derived formula to compute the sum of contributions of every number in the absolute difference in O N time and O 1 extra space.

Range[-n, n, 2] creates a list with numbers from -n to n in steps of 2e. Have a look at this small piece of working code in JAVA. Hope it helps and make sense. Learn more. Asked 9 years, 5 months ago.

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Active 3 months ago. Viewed 10k times. Given an array, find the sum of the absolute difference of every pair of integers. The original array isn't necessarily sorted. Shamim Hafiz Shamim Hafiz 19k 36 36 gold badges silver badges bronze badges. I know the obvious brute force solution. I was also thinking that, difference between successive numbers will appear exactly n-1 times. But the result doesn't match with that of the brute-force solution. Active Oldest Votes.

Actually can't you do it in O n using radix or counting sort and then do the post processing as you mentioned it. I think I have found the answer. I got it by looking into the result expression in my post.In digital image processingthe sum of absolute differences SAD is a measure of the similarity between image blocks. It is calculated by taking the absolute difference between each pixel in the original block and the corresponding pixel in the block being used for comparison.

These differences are summed to create a simple metric of block similarity, the L 1 norm of the difference image or Manhattan distance between two image blocks. The sum of absolute differences may be used for a variety of purposes, such as object recognitionthe generation of disparity maps for stereo images, and motion estimation for video compression. This example uses the sum of absolute differences to identify which part of a search image is most similar to a template image.

In this example, the template image is 3 by 3 pixels in size, while the search image is 3 by 5 pixels in size. Each pixel is represented by a single integer from 0 to 9. There are exactly three unique locations within the search image where the template may fit: the left side of the image, the center of the image, and the right side of the image. To calculate the SAD values, the absolute value of the difference between each corresponding pair of pixels is used: the difference between 2 and 2 is 0, 4 and 1 is 3, 7 and 8 is 1, and so forth.

Calculating the values of the absolute differences for each pixel, for the three possible template locations, gives the following:. For each of these three image patches, the 9 absolute differences are added together, giving SAD values of 20, 25, and 17, respectively.

From these SAD values, it could be asserted that the right side of the search image is the most similar to the template image, because it has the lowest sum of absolute differences as compared to the other two locations. The sum of absolute differences provides a simple way to automate the searching for objects inside an image, but may be unreliable due to the effects of contextual factors such as changes in lighting, color, viewing direction, size, or shape.

The SAD may be used in conjunction with other object recognition methods, such as edge detectionto improve the reliability of results. SAD is an extremely fast metric due to its simplicity; it is effectively the simplest possible metric that takes into account every pixel in a block. Therefore it is very effective for a wide motion search of many different blocks. Once candidate blocks are found, the final refinement of the motion estimation process is often done with other slower but more accurate metrics, which better take into account human perception.

These include the sum of absolute transformed differences SATDthe sum of squared differences SSDand rate-distortion optimization. From Wikipedia, the free encyclopedia.

Categories : Video compression Signal processing metrics Loss functions. Hidden categories: Use dmy dates from January Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version.Given a sorted array of distinct elements, the task is to find the summation of absolute differences of all pairs in the given array. A simple solution for this problem is to one by one look for each pair take their difference and sum up them together.

The time complexity for this approach is O n 2.

finding sum of absolute difference of every pair of integer from

An efficient solution for this problem needs a simple observation. What if array is not sorted? The efficient solution is also better for the cases where array is not sorted.

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We can sort the array first in O n Log n time and then find the required value in O n. So overall time complexity is O n Log n which is still better than O n 2. This article is contributed by Shashank Mishra Gullu.

Absolute Difference Calculator

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Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Attention reader! Writing code in comment? Please use ide. Python3 program to find sum of. Function to calculate sum of absolute. This code is contributed by Anant Agarwal. Write sumPairs arr, n. Load Comments. We use cookies to ensure you have the best browsing experience on our website.To calculate the difference between two values or times may be easy for most of Excel users, but have you tried to calculate the absolute difference between values as below screenshot shown?

Here in this article, I introduce some tricks on quickly getting the ABS difference between values in Excel. Calculate absolute differences with formula. Calculate absolute differences with Kutools for Excel. To calculate the absolute differences, you just need one of below formulas, paste one of below formulas to the blank cell you want to place the result, press Enter key, and drag fill handle over cells needed this formula. See screenshot:. If you have Kutools for Excel installed, its Change Sign of Values utility also can quickly calculate the absolute differences between two numbers.

Click Ok or Applyand a dialog pops out to remind you some information, click Yes to continue. Now all negative differences have been converted to absolute. Remember Me. Log in. About Us Our team. Calculate absolute differences with formula Calculate absolute differences with Kutools for Excel Calculate absolute differences with formula To calculate the absolute differences, you just need one of below formulas, paste one of below formulas to the blank cell you want to place the result, press Enter key, and drag fill handle over cells needed this formula.

finding sum of absolute difference of every pair of integer from

See screenshot: Calculate absolute differences with Kutools for Excel If you have Kutools for Excel installed, its Change Sign of Values utility also can quickly calculate the absolute differences between two numbers. Kutools for Excelwith more than handy functions, makes your jobs more easier. Free Download Full future 30 days free trial.

Absolute and Relative Differences

Read More Free Download You are guest Sign Up? Login Now. Loading comment The comment will be refreshed after To post as a guest, your comment is unpublished. If there are two list of values mixed with negative and positive numbers, now you want to get the absolute sum of two list in the same row, how can you quickly solve? The Sum absolute values utility in Kutools for Excel can do you a favor without remember formula. Click for full-featured 30 days free trial! Kutools for Excel: with more than handy Excel add-ins, free to try with no limitation in 30 days.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Code Review Stack Exchange is a question and answer site for peer programmer code reviews. It only takes a minute to sign up. Given a sorted array of N elements, I need to find the absolute sum of the differences of all elements. I'm looking for an efficient algorithm rather than the trivial one I am using O n 2 complexity.

Sum of absolute differences of all pairs in a given array

This is a requirement for a bigger program which requires this function. The input number of elements can be as big as 10 5. Let's see this mathematically. I am assuming that a is an ascendingly sorted array. I start with indexes from 1, to get better readability by avoiding n-1 as often as possible. This has a linear complexity, which is optimal, because you need to "visit" each member of the array at least once which is linear. I believe you can write your code by yourself. I would not give you the exact solution to this problem rather I would help you to get an intuition on how to solve this question.

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If we try to generalize count of the number of times a particular number at index i is getting added and the number of times it is being subtracted then for every index i we can use that mathematically derived formula to compute the sum of contributions of every number in the absolute difference in O N time and O 1 extra space. Sign up to join this community. The best answers are voted up and rise to the top.

Simplify function to sum the absolute value of the difference between all pairs of elements of a sorted array Ask Question. Asked 6 years, 11 months ago. Active 3 months ago. Viewed 2k times. What is min? Don't you need abs somewhere? Do we know anything about the numbers in the array i. Consider the list to be sorted in ascending order. Active Oldest Votes. Thanks a lot. The break up of the formula did the trick. You can refer to this video if you still find difficulties in understanding this concept.

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Vaibhav Varshney Vaibhav Varshney 1.Given an unsorted array and a number n, find if there exists a pair of elements in the array whose difference is n.

The simplest method is to run two loops, the outer loop picks the first element smaller element and the inner loop looks for the element picked by outer loop plus n. We can use sorting and Binary Search to improve time complexity to O nLogn. The first step is to sort the array in ascending order. If the element is found, return the pair.

finding sum of absolute difference of every pair of integer from

Both first and second steps take O nLogn. So overall complexity is O nLogn. The second step of the above algorithm can be improved to O n.

The first step remain same. The idea for second step is take two index variables i and j, initialize them as 0 and 1 respectively.

finding sum of absolute difference of every pair of integer from

Now run a linear loop. If arr[j] — arr[i] is smaller than n, we need to look for greater arr[j], so increment j.

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If arr[j] — arr[i] is greater than n, we need to look for greater arr[i], so increment i. Thanks to Aashish Barnwal for suggesting this approach.

The following code is only for the second step of the algorithm, it assumes that the array is already sorted. Hashing can also be used to solve this problem. Create an empty hash table HT. Traverse the array, use array elements as hash keys and enter them in HT. Attention reader! Writing code in comment? Please use ide. Python program to find a pair with the given difference.

The function assumes that the array is sorted. Initialize positions of two elements.

Find a pair with the given difference

Search for a pair. Driver function to test above function. This code is contributed by Devesh Agrawal. Write "Pair Found: ".Some changes have already been hinted at. Others have been partially published. In some areas, Emirates is making changes and hoping nobody notices. A new First Class suite has been touted by the airline for some time now.

Many commentators believe Emirates will be introducing a new and improved design at some point in the next 12-months. Last year, Emirates made a few minor improvements to its First Class product. All new seats now feature a 32-inch television although the basic design remained unchanged. Abu Dhabi-based, Etihad Airways has a super-sized First Class product on its A380 aircraft and Qatar Airways is introducing privacy screens on its new QSuite Business Class product.

In 2015, Emirates did unveil a new seat at ITB Berlin. The new Business Class seat for its Boeing 777 fleet was touted as a game changer for Emirates. Unfortunately, it left many frequent flyers underwhelmed.

With the new design, Emirates has eventually introduced a fully-flat seat for its 777 aircraft. But it maintained a 2-3-2 layout without direct aisle access for all passengers. The devices allow Cabin Crew to quickly take custom orders from passengers and then beam requests straight to the galley. Emirates should have the devices rolled out across the entire network by the end of the year.

Emirates is slowly being left behind by other airlines who already offer this service to passengers. Emirates President, Tim Clark has spoken of Premium Economy several times over the past year. Clark recently said a full analysis would be completed by April. Expect the new Premium Economy Class to be announced in the next few months. But, Premium Economy has been hugely successful on many European legacy airlines.

Is Emirates going for a more understated and grown-up look. That certainly seems to be the theme from its latest cabin upgrades. The bar was first unveiled at industry trade show ITB Berlin earlier this year and is said to take inspiration from luxury private yachts.

We predict future design elements to have a subtle nod to stripped back elegance. Emirates famously has an all widebody fleet of Airbus A380 and Boeing 777-300 aircraft, with the last A330 and A340 aircraft being retired from service last year. But as the airline suffers dwindling passenger numbers and rising costs, their hand might be forced.

However, we do know that senior pilots were evaluating both the twin-aisle Boeing 787 and Airbus A350 as contenders last year. Again, this is another prediction that has come straight from Tim Clark.

But new Gulf services may only be possible once Emirates has taken delivery of some smaller jets.


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