# What constitutes a minimal-sum section of an integer array I’m having trouble understanding what constitutes a “minimal sum section” of an integer array. My book defines it as the following:

Let $$a,\dots, a[n-1]$$ be the integer values of an array $$a$$.
A section of $$a$$ is a continuous piece $$a[i],\dots,a[j]$$, where $$0\le i \le j < n$$. We write $$S_i,_j$$ for the sum of that section: $$a[i] + a[i+1]+\dots+a[j]$$.
A minimal-sum section is a section $$a[i],\dots,a[j]$$ of $$a$$ such that the sum $$S_{i,j}$$ is less than or equal to the sum $$S_{i’,j’}$$ of any other section $$a[i’],\dots,a[j’]$$ of $$a$$.

My confusion comes with one of the examples that follow this definition:

The array [1,-1,3,-1,1] has two minimal-sum sections [1,-1] and [-1,1] with minimal sum 0.

But, wouldn’t the minimal sum section be $$[-1]$$ ?

In a later example they give:

array $$[-1,3,-2]$$

Minimal sum

section $$[-2]$$

So, in the last example they definitely counted one element as the minimal sum section, but not in the first one. Any clarification on why this is so would be greatly appreciated. Posted on Categories proxies