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Richard Pieters edited section_Deel_A_Optelreeksen_1__.tex
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\section{Deel A: Optelreeksen 1 tot 32}
1: 1
\noindent
2: $1+1=2$
\noindent
3: $1+1=2$; $1+2=3$
\noindent
4: $1+1=2$; $2+2=4$
\noindent
5: $1+1=2$; $2+2=4$; $4+1=5$
\noindent
6: $1+1=2$; $2+2=4$; $4+2=6$
\noindent
7: $1+1=2$; $2+1=3$; $2+2=4$; $3+4=7$
\noindent
8: $1+1=2$; $2+2=4$; $4+4=8$
\noindent
9: $1+1=2$; $2+1=3$; $3+3=6$; $3+6=9$
\noindent
10: $1+1=2$; $2+2=4$; $4+4=8$; $2+8=10$
\noindent
11: $1+1=2$; $2+2=4$; $4+1=5$; $5+1=6$; $6+5=11$
\noindent
12: $1+1=2$; $2+2=4$; $4+4=8$; $8+4=12$
\noindent
13: $1+1=2$; $2+2=4$; $4+1=5$; $4+4=8$; $5+8=13$
\noindent
14: $1+1=2$; $2+2=4$; $4+2=6$; $6+6=12$; $2+12=14$
\noindent
15: $1+1=2$; $2+1=3$; $3+3=6$; $6+6=12$; $3+12=15$
\noindent
16: $1+1=2$; $2+2=4$; $4+4=8$; $8+8=16$
\noindent
17: $1+1=2$; $2+2=4$; $4+4=8$; $8+8=16$; $1+16=17$
\noindent
18: $1+1=2$; $2+2=4$; $4+4=8$; $8+8=16$; $2+16=18$
\noindent
19: $1+1=2$; $1+2=3$; $1+3=4$; $4+4=8$; $8+8=16$; $3+16=19$
\noindent
20: $1+1=2$; $2+2=4$; $4+4=8$; $8+8=16$; $4+16=20$
\noindent
21: $1+1=2$; $2+2=4$; $4+4=8$; $8+8=16$; $16+4=20$; $20+1=21$
\noindent
22: $1+1=2$; $2+2=4$; $4+2=6$; $6+4=10$; $6+6=12$; $10+12=22$
\noindent
23: $1+1=2$; $2+1=3$; $3+2=5$; $5+5=10$; $10+10=20$; $20+3=23$
\noindent
24: $1+1=2$; $2+2=4$; $4+4=8$; $8+8=16$; $16+8=24$
\noindent
25: $1+1=2$; $2+1=3$; $3+2=5$; $5+5=10$; $10+10=20$; $20+5=25$
\noindent
26: $1+1=2$; $2+2=4$; $4+4=8$; $8+2=10$; $8+8=16$; $16+10=26$
\noindent
27: $1+1=2$; $2+1=3$; $3+3=6$; $6+6=12$; $12+12=24$; $24+3=27$
\noindent
28: $1+1=2$; $2+2=4$; $4+4=8$; $8+8=16$; $16+8=24$; $24+4=28$
\noindent
29: $1+1=2$; $2+1=3$; $3+3=6$; $6+6=12$; $12+12=24$; $24+2=26$; $26+3=29$
\noindent
30: $1+1=2$; $2+1=3$; $3+3=6$; $6+6=12$; $12+12=24$; $24+6=30$
\noindent
31: $1+1=2$; $2+1=3$; $3+3=6$; $6+6=12$; $12+12=24$; $24+6=30$; $30+1=31$
\noindent
32: $1+1=2$; $2+2=4$; $4+4=8$; $8+8=16$; $16+16=32$ ;
\noindent
\noindent Zoals je ziet is het niet zo dat de complexiteit per se groter wordt naarmate het getal groter wordt.
\noindent
\begin{table}[]
\centering
\caption{c(n) Tabel}
\begin{tabular}{|l|l|l|}
\hline
n & een korste optelketen & c(n) \\ \hline
1 & 1 & 0 \\ \hline
2 & 1, 2 & 1 \\ \hline
3 & 1, 2, 3 & 2 \\ \hline
4 & 1, 2, 4 & 2 \\ \hline
5 & 1, 2, 4, 5 & 3 \\ \hline
6 & 1, 2, 4, 6 & 3 \\ \hline
7 & 1, 2, 3, 4, 7 & 4 \\ \hline�
8 & 1, 2, 4, 8 & 3 \\ \hline
9 & 1, 2, 3, 6, 9 & 4 \\ \hline
10 & 1, 2, 4, 8, 10 & 4 \\ \hline
11 & 1, 2, 4, 5, 6, 11 & 5 \\ \hline
12 & 1, 2, 4, 8, 12 & 4 \\ \hline
13 & 1, 2, 4, 5, 8, 13 & 5 \\ \hline
14 & 1, 2, 6, 12, 14 & 4 \\ \hline
15 & 1, 2, 3, 6, 12, 15 & 5 \\ \hline
16 & 1, 2, 4, 8, 16 & 4 \\ \hline
17 & 1, 2, 4, 8, 16, 17 & 5 \\ \hline
18 & 1, 2, 4, 8, 16, 18 & 5 \\ \hline
19 & 1, 2, 3, 4, 8, 16, 19 & 6 \\ \hline
20 & 1, 2, 4, 8, 16, 20 & 5 \\ \hline
21 & 1, 2, 4, 8, 16, 20, 21 & 6 \\ \hline
22 & 1, 2, 4, 6, 10, 12, 22 & 6 \\ \hline
23 & 1, 2, 3, 5, 10, 20, 23 & 6 \\ \hline
24 & 1, 2, 4, 8, 16 ,24 & 5 \\ \hline
25 & 1, 2, 3, 5, 10, 20, 25 & 6 \\ \hline
26 & 1, 2, 4, 8, 10, 16, 26 & 6 \\ \hline
27 & 1, 2, 3, 6, 12, 24, 27 & 6 \\ \hline
28 & 1, 2, 4, 8, 16, 24, 28 & 6 \\ \hline
29 & 1, 2, 3, 6, 12, 24, 26, 29 & 7 \\ \hline
30 & 1, 2, 3, 6, 12, 24, 30 & 6 \\ \hline
31 & 1, 2, 3, 6, 12, 24, 30, 31 & 7 \\ \hline
32 & 1, 2, 4, 8, 16, 32 & 5 \\ \hline
\end{tabular}
\end{table}
\noindent
\noindent Wat opvalt is dat vooral machten van twee een kleinere complexiteit hebben (zie tabel bladzijde 4).
