Question
Consider the following problem. You are given array X consisting of integers X[1], X[2], . . . X[n], and you need to output an n
Consider the following problem. You are given array X consisting of integers X[1], X[2], . . . X[n], and you need to output an n n matrix Y in which the entries Y [i, j] = X[i] + X[i + 1] + . . . + X[j] for i < j (for i j, Y [i, j] may contain any value). Consider the following algorithm for this problem. Algorithm 1 Compute Y (given input X, an array of n integers)
initialize Y to an n n matrix of 0s
for i = 1 to n do
for j = i + 1 to n do
for k = i to j do
Y [i, j] = Y [i, j] + X[k]
end for
end for
end for
return Y
Design an algorithm for this problem with asymptotically faster than n^3. Explain your answer
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