# How to find the number of runs in a sequence in R?

Sometimes data is recorded as a sequence of numerical values or strings and we might to find the frequency for each of the sequences. This helps us to check the variation in the runs but we must make sure the total frequency is equal to the total number values, otherwise our calculation of frequency would be incorrect. To find the number of runs, we can use rle function in R that stands for Run Length Encoding.

## Examples

x1<-rep(c(1:5),10)
x1
[1] 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3
[39] 4 5 1 2 3 4 5 1 2 3 4 5
rle(x1)
Run Length Encoding
lengths: int [1:50] 1 1 1 1 1 1 1 1 1 1 ...
values : int [1:50] 1 2 3 4 5 1 2 3 4 5 ...
x2<-rep(c(1:5),each=10)
x2
[1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4
[39] 4 4 5 5 5 5 5 5 5 5 5 5
rle(x2)
Run Length Encoding
lengths: int [1:5] 10 10 10 10 10
values : int [1:5] 1 2 3 4 5
x3<-rep(c(2,3,4,5),times=c(20,14,18,21))
x3
[1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4
[39] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
rle(x3)
Run Length Encoding
lengths: int [1:4] 20 14 18 21
values : num [1:4] 2 3 4 5
x4<-rep(c(0,1,1,0,1,0,1,0,1),times=c(4,8,6,4,9,16,7,8,12))
x4
[1] 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0
[39] 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
rle(x4)
Run Length Encoding
lengths: int [1:8] 4 14 4 9 16 7 8 12
values : num [1:8] 0 1 0 1 0 1 0 1
x5<-rep(c(0,1,1,0,1,0,1,0,1),times=c(40,18,26,24,19,16,27,28,12))
x5
[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[38] 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[75] 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1
[112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1
[149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[186] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
rle(x5)
Run Length Encoding
lengths: int [1:8] 40 44 24 19 16 27 28 12
values : num [1:8] 0 1 0 1 0 1 0 1
x6<-rep(c(LETTERS[1:9]),times=c(40,18,26,24,19,16,27,28,12))
x6
[1] "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A"
[19] "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A" "A"
[37] "A" "A" "A" "A" "B" "B" "B" "B" "B" "B" "B" "B" "B" "B" "B" "B" "B" "B"
[55] "B" "B" "B" "B" "C" "C" "C" "C" "C" "C" "C" "C" "C" "C" "C" "C" "C" "C"
[73] "C" "C" "C" "C" "C" "C" "C" "C" "C" "C" "C" "C" "D" "D" "D" "D" "D" "D"
[91] "D" "D" "D" "D" "D" "D" "D" "D" "D" "D" "D" "D" "D" "D" "D" "D" "D" "D"
[109] "E" "E" "E" "E" "E" "E" "E" "E" "E" "E" "E" "E" "E" "E" "E" "E" "E" "E"
[127] "E" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "G"
[145] "G" "G" "G" "G" "G" "G" "G" "G" "G" "G" "G" "G" "G" "G" "G" "G" "G" "G"
[163] "G" "G" "G" "G" "G" "G" "G" "G" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H"
[181] "H" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H" "H"
[199] "I" "I" "I" "I" "I" "I" "I" "I" "I" "I" "I" "I"
rle(x6)
Run Length Encoding
lengths: int [1:9] 40 18 26 24 19 16 27 28 12
values : chr [1:9] "A" "B" "C" "D" "E" "F" "G" "H" "I"
x7
[1] "India" "India" "India" "India"
[5] "India" "India" "India" "India"
[9] "India" "India" "India" "India"
[13] "India" "Russia" "Russia" "Russia"
[17] "Russia" "Russia" "Russia" "Russia"
[21] "Russia" "Russia" "Russia" "Russia"
[25] "China" "China" "China" "China"
[29] "China" "China" "China" "China"
[45] "Belarus" "Belarus" "Belarus" "Belarus"
[49] "Belarus" "Belarus" "Belarus" "Belarus"
[53] "Belarus" "Belarus" "Belarus" "Belarus"
[57] "Indonesia" "Indonesia" "Indonesia" "Indonesia"
[61] "Indonesia" "Indonesia" "Indonesia" "Indonesia"
[65] "Indonesia" "Indonesia" "Indonesia" "United Kingdom"
[69] "United Kingdom" "United Kingdom" "United Kingdom" "United Kingdom"
[73] "United Kingdom" "United Kingdom" "United Kingdom" "United Kingdom"
[77] "United Kingdom" "United Kingdom" "United Kingdom" "United Kingdom"
[81] "United Kingdom" "Sudan" "Sudan" "Sudan"
[85] "Sudan" "Sudan" "Sudan" "Sudan"
[89] "Sudan" "Sudan" "Sudan" "Sudan"
[93] "Sudan"
rle(x7)
Run Length Encoding
lengths: int [1:8] 13 11 10 10 12 11 14 12
values : chr [1:8] "India" "Russia" "China" "Canada" "Belarus" "Indonesia" ...

Updated on: 24-Aug-2020

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