# Algorithm to find the product of three numbers

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I need to write a program to find the Max product of three numbers for a given array of size N. Is there any effective algorithm for this? I just need to know the algorithm steps. Non of algorithms that i thought works for all the test cases. The method get the max product of 3 consists in basically find the biggest 3 numbers from the array and the smallest 2 numbers from the array in just 1 iteration over the array. There are of course a large variety of solutions but this is the optimal 1 because the time to solve the problem is O nthe other solutions time is O n lg n.

Here is the java code: by the way there is a guarantee that the input array is non empty and contains minimum 3 elements so there is no need to extra checks for empty and so on. More succinctly, you can just make one pass through the rest of the list:. Not an efficient solution, but a useful backup to show the use of data structures.

Create a max heap and min heap out of these integers. Then delete the root from max heap till you get 3 distinct integers top 3 and get the least two distinct integers from the min heap. Please use a BubbleSort procedure and break within three iterations.

Take the bottom of three and multiply. That should provide you the solution. Learn more. Max product of the three numbers for a given array of size N Ask Question. Asked 10 years, 2 months ago. Active 3 years, 3 months ago. Viewed 10k times. BlueRaja - Danny Pflughoeft Active Oldest Votes. Find the three largest numbers in the array n1, n2, n3 and the two smallest numbers m1, m2. The answer is either n1 x n2 x n3 or n1 x m1 x m2.GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together.

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community. Already on GitHub? Sign in to your account. A palindromic number reads the same both ways. In fact, it is possible to calculate the value of these palindrome for the product of two numbers up-to 8 digits in around 5 seconds. Finding the right strategy for finding a fast solution is not straightforward.

Use experiments to find a good strategy. The 'fast' solution doesn't require tons of math A first solution was just to use nested loops to calculate the product and keeping track of the max. But loops are dull, why not ' flatMap that shit '? So I came to this bit awkward flatMapped solution. Flatmap is cool, and can be written like a for-comprehension. And in this case also a dirty trick to set the max variable in the closure when we find a better max.

To get to the 8-digits in 5 seconds solutionmake the following observation in the product table:. The nested loops solutions from before calculated the products in this table from top to bottom from left to right, but you can find another order that generates the biggest product first and works it way down Using nested loops and stopping once the first palindromic product is found, you get to the fast solution.

I'm pretty sure it will result in a real 8-digits in 5 seconds solution. You're a genius! I have over quite some time, found a number of solutions using different approaches, but had never spotted the pattern that allows the calculation of products to generate results that are monotonously descending Next, your implementation the last one using a mutable variable is difficult to beat in terms of performance.

Time to find the 8 digit numbers that have the greatest palindromic product is about 9 seconds on my Mac. The Iterator-find combination just does that trick for you! And just for the sake of it, here a scary adaptation of your solution with for-comprehension. I posted some solutions that I came up with over time. The one that I originally started with used the brute force technique like shown by Michel Verbist with one optimization to avoid doing every possible multiplication twice - e.

A first minor improvement was to limit the range of numbers over which to perform the multiplications. In fact, I thought that there might exist numbers that, if squared, generate a palindrome. If the range of numbers 1 to in the problem contains 1 or more of such numbers, then we pick the largest one and the corresponding palindrome specialNumber.

For the stated problem, this number iswhich, if squared, generates the palindrome In the original case, we domultiplications, whereas here, we only do 25, a reduction by a factor of almost Of course we first have to find this special number but we can do this with a linear search like as follows:.

The code in my solution dates from quite a while ago and is different from what I show above. It demonstrates that experience will improve your code. Another solution I came up with uses another approach. It looks at all possible palindromic numbers, in reverse order, that can potentially generated from the base number It then calculates all divisors below or equal to the base number and checks if the result of the division of the palindrome by the divisors is lower than the base number.Why don't fictional characters say "goodbye" when they hang up a phone? All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. Hottest Questions. Previously Viewed. Unanswered Questions. Math and Arithmetic. Algorithm for greatest of three numbers and flowchart?

Wiki User Related Questions Asked in Math and Arithmetic Write an algorithm to find the largest number amongst three numbers and draw a flowchart? Asked in Computer Programming What is flowchart to find the largest of three numbers? Asked in Computer Programming, Math and Arithmetic, C Programming Give a sample problem with the use of algorithm and flowchart symbols? Asked in Computer History, Database Programming, C Programming Draw a flow chart to find out the greatest number among the three given numbers ab c?

Asked in Computer Programming What is the algorithm for average of three numbers? Algorithm for average of 3 numbers: Sum the 3 numbers. Divide the sum by 3. Asked in Math and Arithmetic, C Programming What an algorithm to find largest of three numbers draw flow chart? Asked in C Programming Draw a flowchart that will determine and display the largest among the three numbers being inputted?

The greatest common factor, or GCF of the numbers three and five is one. Both three and five are prime numbers. Accept 3 natural numbers and check whether it firms pythagorean triplet. Asked in Prime Numbers What is the sum of the three greatest prime numbers that are less than 39? The sum of the three greatest prime numbers that are less than 39 is Asked in C Programming, Algebra How do you draw a flowchart to find maximum and minimum of given 3 input numbers?

You draw a flowchart to find maximum and minimum of given 3 input numbers by using all three numbers. You take the low, high and input the middle number between them. You can see the rise, or decline of the chart that way. Algorithm to find the largest of three numbers Compare the first two numbers to find the larger of the two. Then compare the larger number with the third number to find the largest of all three. Asked in Factoring and Multiples What three numbers have a greatest common factor of 13?

## C program to find product of digits of a number

Asked in Factoring and Multiples Name the greatest common factor of the following numbers three and 37? The greatest common factor for the numbers 3 and 37 is 1. It is: Asked in Factoring and Multiples What three numbers have a greatest common factor of 1?

Any three consecutive integers. The numbers three and five have the greatest common factor of one. Asked in Factoring and Multiples What three numbers have a greatest common factor of 25? One possibility: 25, 50 and 75 are three numbers with a GCF of Asked in Factoring and Multiples What three sets of numbers have a greatest common Factor of 16?

Asked in Math and Arithmetic, Computers, Computer Programming List down the names of any three parameters on which you analyze an algorithm?Given an integer array, find three numbers whose product is maximum and output the maximum product. The simplest solution is to consider every triplet out of the given n u m s nums n u m s array and check their product and find out the maximum product out of them.

We need to consider every triplet from n u m s nums n u m s array of length n n n. Space complexity : O 1 O 1 O 1. Constant extra space is used. Another solution could be to sort the given n u m s nums n u m s array in ascending order and find out the product of the last three numbers. But, we can note that this product will be maximum only if all the numbers in n u m s nums n u m s array are positive. But, in the given problem statement, negative elements could exist as well.

Thus, it could also be possible that two negative numbers lying at the left extreme end could also contribute to lead to a larger product if the third number in the triplet being considered is the largest positive number in the n u m s nums n u m s array.

Thus, we need to find the larger one from out of these values. We need not necessarily sort the given n u m s nums n u m s array to find the maximum product. Time complexity : O n O n O n. Only one iteration over the n u m s nums n u m s array of length n n n is required. The second and the third solutions didn't consider the situation when all elements in nuns are negative.

The problem has week tests. Maximmum Product of Three Numbers. Multiplication of any three numbers in the input won't exceed the range of bit signed integer. Rate this article:. Most Votes. Newest to Oldest. Oldest to Newest. Login to Comment. July 21, PM. Show 1 Reply. July 5, AM. November 24, AM. In 2nd approach, why is the space complexity O nlogn?

We are not using any extra space right? Show 6 Replies. January 1, PM. November 17, AM. July 26, AM. June 27, PM. Read More.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information.

I have a question about running time of an algorithm that express the product of n numbers. I think the best solution is divide and conquer which is based on halving the n element by 2 recursively and multiply 2 elements. The confusing part is the number of simple operations. In case of Divide and Conquer the complexity should be O logn So if we have 8 numbers to multiply we should end up with 3 basic steps E. However, in this result we need 7 simple multiplication.

Can someone clarify this to me.? Divide and conquer is for cases when you can divide your original set into multiple subsets which, after you've identified and created them, do not interact anymore or only in a way that's neglectably cheap compared to the operation on each subset. In your case, you're violating the "subsets do not interact after identifying them" rule.

Also, O x does not mean the number of operations is less than x. My native language is german, i hope i didn't change the meaning when translating. So the fact that you need 8 operations on 8 data items does not, per se, mean the complexity is larger than O log n. If I understand your objective correctly, then the complexity should be O nas you can just multiply the n values in sequence.

For n values, you need n-1 multiplications. No need for any divide and conquer. Whichever way you choose to perform multiplication of n numbers, you will need to multiply all of them, making n-1 multiplications. Thus, the time complexity of this multiplication will always be O n. Here is how I can explain that the number of steps required to multiply n numbers by your approach is close to nnot log n.

This process will end when you'll have only two numbers left - their multiplication will give you the result. Now, let's count the total number of multiplications needed. It was shown, that the sum of such sequence equals to n. Learn more. Algorithm for product of n numbers Ask Question.

Asked 6 years, 4 months ago. Active 6 years, 4 months ago. Viewed times. You've reached a meaningless result, so you should check your assumptions. One of them is "divide and conquer complexity should be O log n ". Perhaps think about what this means in detail eg: what does "divide and conquer" mean, and why its "complexity should be O log n " mean, and why it doesn't apply in the specific case you're interested in.

Active Oldest Votes.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I've to maximize the product of any 3 elements of the array. The elements can be non-contiguous.

I've tried solving it using Dynamic Programmingbut I'm not getting the expected result. It is returning the result often involving the same number twice in the multiplication. I've an intuition that, the first if condition is one of the reason of failure.

Because, it is only considering maximum element from an array, while the maximum product may comprise of negative numbers too. But I don't know how to take care of that. The reason I'm using Dynamic Programming is that I can then generalize this solution to work for any value of count. Sort the given array in ascending order and you have to take the maximum of these cases to get the answer. The largest positive value and the 2 smallest negative values assuming there IS a positive value.

It is always max of smallest two negative digits and biggest positive or last three big positive numbers. Assuming that the a positive product is bigger than a negative product, I can think of the following way it can be done. If negative numbers are chosen, at least 2 of them have to be in the product, so that product is positive. Therefore whatever be the case, the top positive number will always be part of the product.

Multiply last two negatives and 2nd and 3rd highest positives and compare. Out of these two pairs whichever has higher value, will be part of the final product along with the top positive shortlisted in line above.

I think this problem is confusion because each number can be positive, negative and zero. Thanks to interviewcake. Detailed Explanation of this Algorithm. This Solution is applicable only if there are 3 numbers needed. If It's dynamic or say user can ask for 4 or 5 then this solution is not suitable for it. Without sorting you can achieve it by find out max 3 numbers from array and multiply 3 numbers, because max product requires max number from array.Why don't fictional characters say "goodbye" when they hang up a phone?

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Prove that the product of three consecutive positive integers is divisible by 3 -- Real Numbers

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## C program to multiply two number without using multiplication(*) operator

C Programming. What is the algorithm to find the largest of three numbers? Wiki User Algorithm to find the largest of three numbers Compare the first two numbers to find the larger of the two. Then compare the larger number with the third number to find the largest of all three.

Asked in Math and Arithmetic Write an algorithm to find the largest number amongst three numbers and draw a flowchart? Asked in Computer Programming What is flowchart to find the largest of three numbers? Asked in C Programming How do you write an algorithm to find the biggest of three numbers? To find the largest of three numbers you first need to find the largest of two numbers.

First, place all the values in a container such as an array. Store the first value then compare all other values with the stored value. If the current value is larger, replace the stored value with the current value. When all values have been compared, the stored value holds the largest value.

### C program to Find the Largest Number Among Three Numbers

Asked in Math and Arithmetic How can i find an algorithm to determine the largest number? Asked in C Programming How do you write an algorithm to find the largest of two positive numbers? Asked in C Programming What are the examples of algorithm in the flow chart? TO find the sum of n numbers? Given a set of n numbers, to find the largest is a simple matter.

Iterate through the numbers with a controlled loop structure using a maxValue variable. If the next variable is greater than maxValue, then that variable is the new maxValue. This continues until there are no more variables. Once that occurs, maxValue will have the largest number in the set of n numbers. Asked in C Programming Algorithm to find the smallest number among three numbers in C programming language?