UVa problem 10696: sample code, sample algorithm

To solve this problem, one needs to be able to discover the observation that:
if N is greater than 100, the output is N - 10; otherwise it is always 91.

One can discover this observation by running a simple simulation of the recursive F91 function:

001 #include "stdio.h"
002 
003 int f91(int n) {
004   if (n <= 100) {
005     return f91(f91(n + 11));
006   }
007   else {
008     return n - 10;
009   }
010 }
011 
012 int main() {
013   char line[100];
014 
015   int n;
016 
017   while (fgets(line, 100, stdin)) {
018     sscanf(line, "%d", &n);
019  
020     if (n == 0) {
021       break;
022     }
023 
024     printf("%d\n", f91(n));
025   }
026 
027   return 0;
028 }

After discovering the pattern, one can then simplify his code like as follows:

001 #include "stdio.h"
002 
003 int main() {
004   char line[100];
005   int   n
006       , n1;
007 
008   while(fgets(line, 100, stdin)) {
009     sscanf(line, "%d", &n);
010 
011     if (n == 0) {
012       break;
013     }
014 
015     if (n > 100) {
016       n1 = n - 10;
017     }
018     else {
019       n1 = 91;
020     }
021 
022     printf("f91(%d) = %d\n", n, n1); 
023   }
024 
025   return 0;
026 }