September Morn Update

Task/Average-loop-length/R/average-loop-length.r

@@ -0,0 +1,34 @@
+expected <- function(size) {
+  result <- 0
+  for (i in 1:size) {
+    result <- result + factorial(size) / size^i / factorial(size -i)
+  }
+  result
+}
+
+knuth <- function(size) {
+  v <- sample(1:size, size, replace = TRUE)
+
+  visit <- vector('logical',size)
+  place <- 1
+  visit[[1]] <- TRUE
+  steps <- 0
+
+  repeat {
+    place <- v[[place]]
+    steps <- steps + 1
+    if (visit[[place]]) break
+    visit[[place]] <- TRUE
+  }
+  steps
+}
+
+cat(" N    average    analytical     (error)\n")
+cat("===  =========  ============  ==========\n")
+for (num in 1:20) {
+  average <- mean(replicate(1e6, knuth(num)))
+  analytical <- expected(num)
+  error <- abs(average/analytical-1)*100
+
+  cat(sprintf("%3d%11.4f%14.4f  ( %4.4f%%)\n", num, round(average,4), round(analytical,4), round(error,2)))
+}