Design and analyze an exhaustive$-$search algorithm for the following problem:

INPUT: an array $A[0,$dots,$n-1]$ of real values, and a target real value $t$

OUTPUT: TRUE iff there are three indices $A[i]+A[j]+A[k]=tA[0,$dots,$n-1]AA[i]=A[j]iin$ A such that $A[i]=A[j].$

OPTIONAL, NOT FOR CREDIT: Can you design faster algorithms for the two problems

above?i such that $A[i]+A[j]+A[k]=t.$

Design and analyze a decrease$-$conquer algorithm for the following problem:

INPUT: $an$ array $A[0,$dots,$n-1]of$ integers

OUTPUT: TRUE iff there are two indices $iin$ A such that $A[i]=A[j].$

OPTIONAL, NOT FOR CREDIT: Can you design faster algorithms for the two problems

above?