In C++

This is the Letter Frequencies

Problem (3): (40 points) Given a language with letter alphabet , of size n = [2], the entropy of the letters is Hu = log n if all letters of the alphabet are equally probable. In actual use of the language, this might not be the case and the computed entropy Hexp from texts of the language would be different from Hu. The letter redundancy of the language may be taken as R = 1- Hexp / Hu. This means that only [(1 R)n]letters can be used effectively to write most of the language texts. The file 'Letter Frequency.xlsx' gives the letter frequencies observed for four different languages (Arabic, English, French and Greek). Given these frequencies, compare the redundancies of the given four languages. English Letter A B French Letter No. 1 2 3 C B C D 4 -) D E 5 6 F G 7 NIO 8 9 10 11 12 1 J K L M Arabic Letter Probability Tiisi 17.33 4.64 4.13 1.13 T 1.86 0.83 0.93 3 2.58 3 0.83 4.23 j 0.41 2.37 0.72 0.93 0.41 b 0.52 0.10 4.02 0.31 2.79 2.68 1.96 12.38 6.50 6.60 5.16 6.04 7.61 100.00 7.7 313 31:31-9-9 Probability 8.12 1.49 2.71 4.32 12.02 2.30 2.03 5.92 7.31 0.10 0.69 3.98 2.61 6.95 7.68 1.82 0.11 6.02 6.28 9.10 2.88 1.11 2.09 0.17 2.11 0.08 E F G H 1 J L M N o Greek Probability Letter Probability 8.74 A 13.32 0.93 B 0.75 3.16 r 1.65 3.55 A 1.58 17.83 E 9.65 0.97 0.34 0.97 4.87 1.08 1.18 6.98 1 9.35 0.71 3.73 0.16 A 2.59 5.68 M 3.62 3.23 N 6.28 6.42 E 0.43 5.34 0 9.65 3.08 n 4.02 0.89 P 4.20 6.43 6.79 7.91 T 8.03 7.11 Y 4.03 6.14 0.73 1.83 1.28 0.04 0.15 0.42 1.77 0.19 0.21 N 15 0 P P Q R Q 111111 R 16 17 18 19 20 21 22 23 S T w.w397 32.5 S T U V w V W X Y 24 25 26 27 Y Z z 28 Sum 100.00 100 100