  The Fukui-Todo algorithm is an important element of the array of simulational
approaches to tackling critical phenomena in statistical physics. The
partition-function-zero approach is of fundamental importance to understanding
such phenomena and a precise tool to measure their properties. However, because
the Fukui-Todo algorithm bypasses sample-by-sample energy computation, zeros
cannot easily be harnessed through the energy distribution. Here this obstacle
is overcome by a novel reweighting technique and zero-detection protocol. The
efficacy of the approach is demonstrated in simple iconic models which feature
transitions of both first and second order.
