Is it more energy efficient to desalinate seawater by flash boiling or by flash freezing?
The cheapest way is probably to use the sun, as it is done in Tunisia. In Tunisia, they dig long channels on the beach along the sea. The channels must be long and narrow, and they are filled by sea water. Now the channel is covered by an inclined glass roof. The sun heats the water through the roof, and the steam  is slowly evaporated and condensed on the roof. It makes mist that streams and flow in a drainpipe placed at the lower part of the glass, just above but nearly on a level with the sea. It produce pure water for free.