We divide the points in such a way that only consecutive points $($along the line$)$ may

fall into the same group.

Design an efficient algorithm for this problem. You should: $($the following is described

in terms of the design of a dynamic programming algorithm, since you almost certainly

should use it$)$

$$ In plain English or using some mathematical notation, give a recursive

formulation of the problem. $($Hint: one possible approach is to define $(,)$

to be the error of the optimal partition of the first $$ points $1,...,$

into $$

groups, where $<=$ and $<=.$ The value of $(,)$ can be found

recursively: consider all possible locations where the last $(-)$ group can

begin.$)$

$$ Write a program in C$++$ of the algorithm that is based on this formulation

$($Pseudocode may be accepted however some points will be lost$)$