Question

For a given integer N, find the number of minimum elements the N has to be broken into such that their product is maximum. Input User Task: Since this will be a functional problem, you don't have to take input. You just have to complete the function MaximumProduct() that takes integer N as parameter. Constraints:- 1 <= N <= 10000 Output Return the minimum number of elements the N has to be broken into

Answer 1

Answer : Breaking an Integer to get Maximum Product

Last Updated: 27-09-2020

Given an number n, the task is to broken in such a way that multiplication of its parts is maximized.

Input : n = 10

Output : 36

10 = 4 + 3 + 3 and 4 * 3 * 3 = 36

is maximum possible product.

Input : n = 8

Output : 18

8 = 2 + 3 + 3 and 2 * 3 * 3 = 18

is maximum possible product.

Mathematically, we are given n and we need to maximize a1 * a2 * a3 …. * aK such that n = a1 + a2 + a3 … + aK and a1, a2, … ak > 0.

Note that we need to break given Integer in at least two parts in this problem for maximizing the product.

Answer 2

Answer:

Explanation:

Integer definition:

An integer is a whole number that can be positive, negative, or zero and is not a fraction.

Product definition:

The outcome of multiplication or an expression that specifies factors to be multiplied is a product. For instance, the product of $6$ and $5$ is $30$, and the product of  $x$ and  $(2+x)$  is $x .(2+x)$ (indicating that the two factors should be multiplied together).

Breaking an integer to get maximum product:

The assignment must be divided in a way that maximizes the multiplication of its parts, given a number $n$.

Input: $n=10$

Output: $36$

$10 = 4 + 3 + 3$ 

The greatest feasible product is $4\times 3 \times 3 = 36$

Data: $n = 8$

Output: $18$

$8 = 2 + 3 + 3$

The greatest feasible product is $2 \times 3 \times 3 = 36$

Assuming that $n = a1 + a2 + a3... + aK$ and that $a1, a2,... ak > 0$, we must mathematically maximize $a1 \times a2 \times a3.... \times aK.$

Keep in mind that in order to maximize the product in this issue, we must divide the provided integer into at least two pieces.

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