Initial data commit

Task/Stern-Brocot-sequence/R/stern-brocot-sequence-1.r

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+## Stern-Brocot sequence
+## 12/19/16 aev
+SternBrocot <- function(n){
+  V <- 1; k <- n/2;
+  for (i in 1:k)
+    { V[2*i] = V[i]; V[2*i+1] = V[i] + V[i+1];}
+  return(V);
+}
+
+## Required tests:
+require(pracma);
+{
+cat(" *** The first 15:",SternBrocot(15),"\n");
+cat(" *** The first i@n:","\n");
+V=SternBrocot(40);
+for (i in 1:10) {j=match(i,V); cat(i,"@",j,",")}
+V=SternBrocot(1200);
+i=100; j=match(i,V); cat(i,"@",j,"\n");
+V=SternBrocot(1000); j=1;
+for (i in 2:1000) {j=j*gcd(V[i-1],V[i])}
+if(j==1) {cat(" *** All GCDs=1!\n")} else {cat(" *** All GCDs!=1??\n")}
+}

Task/Stern-Brocot-sequence/R/stern-brocot-sequence-2.r

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+genNStern <- function(n)
+{
+  sternNums <- c(1, 1)
+  i <- 2
+  while((endIndex <- length(sternNums)) < n)
+  {
+    #To show off R's vectorization, the following line is deliberately terse.
+    #It assigns sternNums[i-1]+sternNums[i] to sternNums[endIndex+1]
+    #and it assigns sternNums[i], the "considered" number, to sternNums[endIndex+2], now the end of the sequence.
+    #Note that we do not have to initialize a big sternNums array to do this.
+    #True to the algorithm, the new entries are appended to the end of the old sequence.
+    sternNums[endIndex + c(1, 2)] <- c(sum(sternNums[c(i - 1, i)]), sternNums[i])
+    i <- i + 1
+  }
+  sternNums[seq_len(n)]
+}
+#N=5000 was picked arbitrarily. The code runs very fast regardless of this number being much more than we need.
+firstFiveThousandTerms <- genNStern(5000)
+match(1:10, firstFiveThousandTerms)
+match(100, firstFiveThousandTerms)
+all(sapply(1:999, function(i) gmp::gcd(firstFiveThousandTerms[i], firstFiveThousandTerms[i + 1])) == 1)