Print every way of writing as a sum of natural numbers, with repetitions, in nondecreasing order.

Question

1.00/5 (1 vote)

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Input: .
Output: Print every way of writing as a sum of natural numbers, with repetitions, in nondecreasing order.
Format:
Each number in the sum should be separated by a '+'.
The numbers should be listed in non-decreasing order.
End each line with \n
Examples:
Input instance: 3 \n
Output:
1+1+1 \n
1+2 \n
3 \n
Input instance: 5 \n
Output:
1+1+1+1+1 \n
1+1+1+2 \n
1+1+3 \n
1+2+2 \n
1+4 \n
2+3 \n
5 \n
Observation: In each line, the numbers appear in non-decreasing order.

What I have tried:

#include <stdio.h>
int main()
{
    int i,j;
    int n;
    scanf("%d",&n);
    int sum=0;
    if(sum!=n){
        for(i=1;i<n;i++){
        for(j=i;j<n;j++){
            printf("%d+",1);
        }
        printf("%d\n",i);
        }
    }
    printf("%d",n);

}

Posted 10-Feb-22 7:08am

shaym roy

Updated 10-Feb-22 9:14am

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Comments

Luc Pattyn 10-Feb-22 13:18pm

can you come up with any value of n for which your code generates the correct output?
did you try n=3? n=5?

shaym roy 10-Feb-22 13:23pm

when I tried n=5.Its output is
1+1+1+1+1
1+1+1+2
1+1+3
1+4
5 . I cant understand how should I print 1+2+2 and 2+3

Luc Pattyn 10-Feb-22 13:31pm

when it fails for one or more cases, the algorithm is wrong.
Before you start coding, you should think about the problem, formulate a potential approach and test it manually.

I will not help you any further except for this one hint: when searching all correct summations in the required order you can't solve this by printing before you got a correct sum. Reduce the problem to a slightly smaller one.

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OriginalGriff · Answer 1 · 2022-02-10T08:57:00

Solution 1

To add to what Luc - rightly - said, have a look here: How to Write Code to Solve a Problem, A Beginner's Guide[^]
It won't give you the code, but it may help you work out a way to solve it.

Posted 10-Feb-22 8:57am

OriginalGriff

Patrice T · Answer 2 · 2022-02-10T09:14:00

Quote:
I cant understand how should I print 1+2+2 and 2+3

It is just that your code do not try to answer those cases, your algorithm is just wrong.
Your code just print a bunch of '1' and the last digit.
For a given n, your code will print n lines, how do you know the number of lines in answer is n ?

Advice: try to write the solution by hand with decreasing digits, figure out the rules leading to solutions.
Since each line of solution have a variable number of digits, recursive code or backtracking code may help.
Recursion (computer science) - Wikipedia[^]
Backtracking - Wikipedia[^]

5
4+1
3+2
3+1+1
2+2+1
...

Your code do not behave the way you expect, or you don't understand why !

There is an almost universal solution: Run your code on debugger step by step, inspect variables.
The debugger is here to show you what your code is doing and your task is to compare with what it should do.
There is no magic in the debugger, it don't know what your code is supposed to do, it don't find bugs, it just help you to by showing you what is going on. When the code don't do what is expected, you are close to a bug.
To see what your code is doing: Just set a breakpoint and see your code performing, the debugger allow you to execute lines 1 by 1 and to inspect variables as it execute.

Debugger - Wikipedia, the free encyclopedia[^]

Mastering Debugging in Visual Studio 2010 - A Beginner's Guide[^]
Basic Debugging with Visual Studio 2010 - YouTube[^]

1.11 — Debugging your program (stepping and breakpoints) | Learn C++[^]

The debugger is here to only show you what your code is doing and your task is to compare with what it should do.