HS23 Theory

Loop Invariant

This loop invariant was really hard. The functions sums $n+(n-1)+\cdots +1=n+n+n-1-2-3$, basically doing ${\sum }_{i=1}^n(n-i)={\sum }_{i=1}^{n}n-{\sum }_{i=1}^{n}i=n\cdot n-\frac{n(n+1)}{2}$.

As c = c + 1 in the loop body, we work with c - 1. Therefore our Loop Invariant was $c\cdot n-\frac{c(c-1)}{2}$ which is $c\cdot n$ minus the gaussian summation of $n$.