The longest increasing subsequence problem is as follows: Given numbers a1, a2, . . . , aN,

Question:

The longest increasing subsequence problem is as follows: Given numbers a1, a2, . . . , aN, find the maximum value of k such that ai1 < ai2 < · · · < aik, and i1 < i2 < · · · < ik. As an example, if the input is 3, 1, 4, 1, 5, 9, 2, 6, 5, the maximum increasing subsequence has length four (1, 4, 5, 9 among others). Give an O(N2) algorithm to solve the longest increasing subsequence problem.