Write a recurrence relation describing the worst case running time of each the following algorithms and make a guess about the asymptotic complexity of the functions defined by the recurrence relation using either expanding into a series or a recursion tree. Justify your solutions using the substitution method. A[i j] represents an array of n = j i +1 numbers starting at index i and ending at index j and A[k] represents the value at index k. (20 points each) 3.) FUNCTION F3(A[1...n]) IF n 5 THEN RETURN(A[n]) x0 FOR 1 TO 5 DO BEGIN (FOR i) END FOR j1 TO n - 4 DO A[i] A[j] + A[j+2] x x + F3(A[1 .. [n/2]]) RETURN(x) 4.) FUNCTION F(A[i... j]) nj-i+1 IF n 1 THEN RETURN(A[i]) x F(A[i.. [i + 2n/3]]) FOR in/4] TO [n/4] + 12 DO x+x+A[i] RETURN(x)