Question

16. Kleinberg, Jon. Algorithm Design (p. 68, q. 6). You’re given an array A consisting of n integers. You’d like to output a two-dimensional n-by-n array B in which B[i, j] (for i < j) contains the sum of array entries A[i] through A[j] — that is, the sum A[i] + A[i + 1] + ... + A[j]. (Whenever i >= j, it doesn’t matter what is output for B[i, j].) Here’s a simple algorithm to solve this problem. for i = 1 to n for j = i + 1 to n add up array entries A [ i ] through A [ j ] store the result in B [i , j ] endfor endfor (a) For some function f that you should choose, give a tight bound of the form O(f (n)) on the running time of this algorithm on an input of size n (i.e., a bound on the number of operations performed by the algorithm).

          16. Kleinberg, Jon. Algorithm Design (p. 68, q. 6). You’re given an array A consisting of n integers. You’d
like to output a two-dimensional n-by-n array B in which B[i, j] (for i < j) contains the sum of array
entries A[i] through A[j] — that is, the sum A[i] + A[i + 1] + ... + A[j]. (Whenever i >= j, it doesn’t
matter what is output for B[i, j].) Here’s a simple algorithm to solve this problem.
for i = 1 to n
for j = i + 1 to n
add up array entries A [ i ] through A [ j ]
store the result in B [i , j ]
endfor
endfor
(a) For some function f that you should choose, give a tight bound of the form O(f (n)) on the running
time of this algorithm on an input of size n (i.e., a bound on the number of operations performed
by the algorithm).

Added by Domingo V.

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