Question

Cutting a stick A stick n inches long needs to be cut into n 1-inch pieces. Outline an algorithm that performs this task with the minimum number of cuts if several pieces of the stick can be cut at the same time. Also give a formula for the minimum number of cuts

Answer 1

the same time. the approach soly since we can cut several pieces at to solve this problem: cut the stick into 2 pleces : One of length and rest (8)=n-k k=gc where c=int/rogen) For example, if n=22 , c=int (209, 22)=4 and stick will be cut into k=26=24 = 16 minimum numbers of cuts For Kisc. in this example, minimum number of cuts far and r=22-16=6 parte=16 is 4curs. sototoy cuts = 1+4= 5 cuts. (b) we repeat the same procedure and we assume ner and repeat a untill r=1. • several pieces of the stick can be cut at the same time whenever apiece nas length zk, we assume it will be cut with the long piece in part (a). and these cuts will not counted here. above exemple - 8=6 Now let n=r=6 c= int(10926)=2 K=26=2²=41 Note we assume the cuts for k=4 are included into cut of the longer piece (16 inclus) when it is reduced to 4 inches. Here we have only one cut. No. of cur for 32 18 one cut o minimum co+ = =+I+I +wh.

Algorithm:- c= 0 8=n / intial value for r . S=O sls minimum no. ofcuts c=int (10qan) s=sto &=n-2c if (r=0) print"No. of cuts = ", S. STOP else n=r while n>1 do c= int(eoq24) 8=n-2c if (r=o) then print "No.of cuts="s+1 STOP else n=r sestione cut is added because the length of piece isak. continue S=5+1 print No.of wts="s. Stop Formula minimum No.of cuts. for (s(u) letc=int (10924) s(n)= c+1 , iF 2092 (0-2) is integer > s(h)= ct int (1092 (n=2+2)), if 1092 (n=2") is fraction