How to find all unique possible ways of partition from specific data given of an integer

Question

I want to make java program that count all unique possible ways from specific data (array list) given of an integer.

 Example : input: 3 6 1 2 3 output: 7 explanation: the first line contains two separated integers of value x,y. the second line contains x separated integers For y = 6 and x = {1, 2, 3} there are exactly seven ways: 1. {1, 1, 1, 1, 1, 1} <— sum up to 6 2. {1, 1, 1, 1, 2} <- sum up to 6 3. {1, 1, 1, 3} <- sum up to 4 4. {2, 2, 2} <— sum up to 6 5. {2, 2, 1, 1} <— sum up to 6 6. {1, 2, 3} <— sum up to 6 7. {3, 3} <- sum up to 6 

Answer 1

Your question is unclear, but I think what you're asking is "count the number of ways to add up to y using only a set of numbers as possible summands".

I assume that the numbers in the second line are all distinct, are all less than y (well, this is not really necessary), and are positive.

One solution is to use a recursive approach. Say f(y, {x_1, ..., x_n}) is the number of ways to add up to y using only x_i 's.

Then f(y, {x_1, ..., x_n}) = sum of f(y - x_i, {x_1, ..., x_n}) for i = 1, ..., n .

You can write a recursive function now. What's the base case? Well, y could be 0, so the answer would be 1. Or y could be negative, and the answer would be 0.

That should do it. But it will probably be very inefficient. I encourage you to read up on recursion and calculating Fibonacci numbers to learn how you can be more efficient (hint: memoization, and a bottoms-up approach instead of a top-down approach are your friends).