HW3: FFT

1.  We are given an array A with n elements, where each element of A is an integer in the range $[0,n]$. We are also given an integer $t$. The algorithm must answer the following yes-or-no question:
Do there exist indices $i, j, k$, not necessarily distinct, such that $A[i] + A[j] + A[k] = t$?
Design an $O(n \log n)$ time algorithm for this problem.
2. Modify your algorithm to count the total number of ordered triples $(i,j,k)$ for which the sum of entries is at most $t$.