Algorithm DP-SAT(V, C, v)

  Given:
    + A list of variables V
    + A list of clauses C, with each
      clause consisting of a list of literals
      drawn from the variables of V
    + A partial assignment, a partial function v mapping
      some of the variables of V to either true or false

  Return:
    + A total assignment consistent with C and v
      or false if no such total assignment exists

for each c in C {
  if v is inconsistent with c
    return false
}
if v is a total assignment
  return v
select x in V such that x is unassigned in v
let v' = DP-SAT(V, C, v + [x -> true])
if v' is not false
  return v'
let v'' = DP-SAT(V, C, v + [x -> false])
if v'' is not false
  return v''
return false