How many different ways can one hundred be written as a sum of at least two positive integers?
I am not getting algo. please any one can give me write solution of this problem
Welcome to the Java Programming Forums
The professional, friendly Java community. 21,500 members and growing!
The Java Programming Forums are a community of Java programmers from all around the World. Our members have a wide range of skills and they all have one thing in common: A passion to learn and code Java. We invite beginner Java programmers right through to Java professionals to post here and share your knowledge. Become a part of the community, help others, expand your knowledge of Java and enjoy talking with like minded people. Registration is quick and best of all free. We look forward to meeting you.
>> REGISTER NOW TO START POSTING
Members have full access to the forums. Advertisements are removed for registered users.
How many different ways can one hundred be written as a sum of at least two positive integers?
I am not getting algo. please any one can give me write solution of this problem
Does "algo" mean algorithm?
Well...
This is related to a well-known topic in number theory: Integer Partitions
Here is an illustration of how calculation of a partition number (size of the set of partitions of a positive integer) relates to your assignment:
Let's look at the number of ways of writing a particular number, 5, as the sum of positive integers:
Note that p(5) = 7 and the seven ways of writing 5 as the sum of positive integers are:
5
4 + 1
3 + 2
3 + 1 + 1
2 + 2 + 1
2 + 1 + 1 + 1
1 + 1 + 1 + 1 + 1
Note also that, except for the first one, each of these lines (called parts or partitions of the number) consists of the sum of two or more positive integers.
Making a slight inductive leap (without formal proof):
The algorithm for finding the number of ways of writing 100 as the sum of two or more positive integers is:
- Calculate p(100).
- The answer is p(100)-1.
Finally, note that using partition number calculations as outlined in the Wikipedia article (and myriads of other references) depends on the following convention:
Two sums that differ only in the order of their terms are considered to be the same partition.
That is, 2+3 is the same as 3+2, so you don't count that as two different partitions.
Similarly, 2+2+1 is the same as 2+1+2, and is the same as 1+2+2.
Etc.
Cheers!
Z