Find 2nd minimum value from a row after addition

 [c,ix] = min(sum(A,2));

This code will give the minimum value from a row after addition, https://www.mathworks.com/matlabcentral/answers/82429-minimum-row-value-and-return-the-row

Similar to this, how to find the 2nd minimum value from the same row?

Can someone help me out?

Answer 1

[KSSV]

You can sort your row and pick what ever minimum you want.

A = rand(10) ;
% [c,ix] = min(sum(A,2));
[val,idx] = sort(sum(A,2)) ;
min1 = val(1)
min2 = val(2)
min3 = val(3)

[Asim Ismail]

Cant we do that without sorting?

[KSSV]

Replace the first minimum with NaN and use min again.

A = rand(10) ;
thesum = sum(A,2) ;
[c1,ix1] = min(thesum);
thesum(ix1) = NaN ;
[c2,ix2] = min(thesum);

[Stephen23]

@asim ismail: you can't. Not really. When you ask for the sequence of things (1st, 2nd,...), then this means sorting them into that sequence. Whether the values themselves are sorted, or whether you collect a sequence of indices, the algorithm is a sorting algorithm, and it will have to traverse the entire set of values before picking the 1st, 2nd, etc.

"Cant we do that without sorting?" To get the 2nd element you will have to exclude the 1st, 3rd, 4th... elements, which means that they need to be in some way distinguishable in that sequence, which means that all of them have to be traversed by a sorting algorithm. And you want to do that without sorting. How to sort without sorting... you could try magic.

[Asim Ismail]

Thanks @KSSV its perfect

[Asim Ismail]

@Stephen you can be right, but somehow sorting method was not working for my algorithm, thats why I asked for something similar to the above mentioned code. And I think @KSSV done it quite well.

[Stephen23]

@Asim Ismail: What KSSV gave you is not a general solution to the task. It works by replacing one element with NaN, and then traversing the elements again. As you can see by my tests of KSSV's FEX submission that uses this concept, it is extremely inefficient when used as a general solution:

n = 1e5;
vec = randi(1e4,1,1e6);

takes this long to run once:

Elapsed time is 0.068590 seconds. % using sort
Elapsed time is 1036.380380 seconds. % KSSV's code (sixteen minutes)

While it does work, this algorithm is extremely slow when used to find any arbitrary element. Sorting with sort is usually going to be the best solution (fastest, simplest, neatest, most efficient, easiest to understand the purpose,...). The sort algorithm that KSSV used is a version of a "selection sort", which are described on wikipedia as "...inefficient on large lists".

[Asim Ismail]

@Stephen Cobeldick, thanks for information, I will take it consideration, and you are right @KSSV's method is not a general solution.