Summary: Given a pair \(p\), \(q\) of relative prime positive integers, we have uniquely determined positive integers \(x\), \(y\), \(u\) and \(v\) such that \(vx-uy=1\), \(p= x+y\) and \(q= u+v\). Using this property, we show that \[ \sum_{1\leq i\leq x,1\leq j\leq v} t^{(i-1)q+(j-1)p}-\sum_{1\leq k\leq y,1\leq l\leq u} t^{1+(k-1)q+(l-1)p} \] is the Alexander polynomial \(\Delta_{p,q}(t)\) of a torus knot \(t(p,q)\). Hence the number \(N_{p,q}\) of nonzero terms of \(\Delta_{p,q}(t)\) is equal to \(vx+ uy= 2vx-1\). Owing to well-known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its \((1,1)\)-diagram. In particular we prove (see Corollary 2.8). Let \(q\) be a positive integer \(>1\) and let \(k\) be a positive integer. Then we have \[ \begin{aligned} N_{kq+1,q} &= 2k(q-1)+ 1,\tag{1}\\ N_{kq+q-1,q} &= 2(k+1)(q-1)-1,\tag{2}\\ N_{kq+2,q} &={1\over 2} k(q^2-1)+ q,\tag{3}\\ N_{kq+q-2,q} &= {1\over 2}(k+1)(q^2-1)-q,\tag{4}\end{aligned} \] where we further assume \(q\) is odd in formula (3) and (4). Consequently we confirm that the complexities of \((1,1)\)-diagrams of torus knots of type \(t(kq+ 2,q)\) and \(t(kq+ q-2,q)\) by \textit{S. H. Kim} and \textit{Y. Kim} [J. Knot Theory Ramifications 13, No. 8, 1103--1119 (2004; Zbl 1065.57002)] agree with \(N_{kq+2,q}\) and \(N_{kq+q-2,q}\), respectively.