While going through ROD CUTTING problem of DP from CLRS, I noticed the optimal structure of the rod cutting problem is :
In overhead approach, after the initial cut, each sub part of the rod is being considered as an independent problem statement, which makes sense as we don't know which will give the optimal solution. But the turnaround happens after 15.1 is transformed to 15.2 which is :
After the first cut lets take one case of (p3+r4) Since r4 will return the max revenue after further cuts(if required), the first part i.e. p3 of length 3 is not being touched here. What if that length of 3 would yield maximum revenue from cutting it to length 2 and 1 ?
I hope to find an explanantion here. PS: Please excuse the equations syntax. I am not well versed with MathJax and too keen to find answer to this. Cheers!