A new algorithm has been developed to find ground state properties of finite two-dimensional lattices of Ising spins with +J, -J, or O interaction strengths. The algorithm is based on a list of all possible string assignments on a boundary which divides the sample in two. Averaged ground state properties are presented for random lattices in which +J occurs with probability p, -J with probability q, and O with probability r (p+q+r = 1). Evidence for zero temperature phase transitions between paramagnetic, ferromagnetic, antiferromagnetic, and possible spin glass phases is discussed.