Finding Triangles

This Quora post answered the question: “How many triangles with integer-length sides have a perimeter of 40?” So, I wrote the following R code to obtain the answer, 33, plus the lengths of the triangles' sides. Notice how to define an empty list and how to make it “grow” to a data frame.

find_xyz <- function(s = 40)
{re <- vector(mode = "list") # an empty list
 the_counter <- 0
 m <- ceiling(s / 3)
 for(x in 1:m) 
   for(y in x:s)
     for(z in y:s) {
       chk_sum <- sum(c(x, y, z)) == s
       chk_triangle <- (x + y) > z 
       if(all(chk_sum, chk_triangle)) {
         the_counter <- the_counter + 1
         re[[the_counter]] <- c(x, y, z)
       }
     }
 df <- do.call('rbind', re)
 return(list(the_counter, df))
}       
       
find_xyz(40)

## [[1]]
## [1] 33
## 
## [[2]]
##       [,1] [,2] [,3]
##  [1,]    2   19   19
##  [2,]    3   18   19
##  [3,]    4   17   19
##  [4,]    4   18   18
##  [5,]    5   16   19
##  [6,]    5   17   18
##  [7,]    6   15   19
##  [8,]    6   16   18
##  [9,]    6   17   17
## [10,]    7   14   19
## [11,]    7   15   18
## [12,]    7   16   17
## [13,]    8   13   19
## [14,]    8   14   18
## [15,]    8   15   17
## [16,]    8   16   16
## [17,]    9   12   19
## [18,]    9   13   18
## [19,]    9   14   17
## [20,]    9   15   16
## [21,]   10   11   19
## [22,]   10   12   18
## [23,]   10   13   17
## [24,]   10   14   16
## [25,]   10   15   15
## [26,]   11   11   18
## [27,]   11   12   17
## [28,]   11   13   16
## [29,]   11   14   15
## [30,]   12   12   16
## [31,]   12   13   15
## [32,]   12   14   14
## [33,]   13   13   14