Let A be a field of N integers and A = A[N+1] = infinity. Element A is called a local minimum if A[I-1] >= A <= A[I+1]. Find an alogrithm that will find some local minimum in a time asymptotically better then O(n). Hint: Consider that in each field deffined as before there must exist at least one local minimum. The best algorithm (or programme in Pascal) I´ve found is the following: ...... while (A[I+1] > A[I+2] and I<N-1) do I:=I+1; LOCMIN:=A[I+1]; ..... which needs maximally N-1 steps to find a local minimum, but this is not enough if we want the asymptotical difficulty better then O(n). Could anybody help me with improving the algorithm? Thanks.