Add notes on fibonacci sequence

2 files changed, 55 insertions, 10 deletions

diff --git a/README.md b/README.md
index e93e732..8463bc1 100644
--- a/README.md
+++ b/README.md
@@ -184,6 +184,13 @@ Workbench
 * terminal:
 
 
+* variable declaration
+* assignment
+* conditional expression
+* loops
+* functions
+* structs / data
+
 # Version Control
 
 - Version (1 - many)
@@ -192,13 +199,43 @@ Workbench
 # Recursion
 
 The Fibonacci numbers are the numbers in the following integer sequence.
-0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
+
+|0|1|2|3|4|5|6| 7| 8| 9|10|11| 12|
+---------------
+|0|1|1|2|3|5|8|13|21|34|55|89|144| ...
+
+12th number
+
+n = 12
+n - 1 = 11
+n - 2 = 11
+
+n0 = 0
+n1 = 1
+n = (n-1) + (n-2)
+
+144 = 89 + 55
 
 ```plaintext
   Fn = Fn-1 + Fn-2
   F0 = 0 and F1 = 1
 ```
 
+How to solve a problem?
+
+1. Understand the problem
+2. Pick a solution
+3. Implement
+4. Review
+
+Test Driven Development/Design
+
+1. Red -> failing testing
+2. Green -> make it pass, be responsible
+3. Refactor -> reflect. can we improve this?
+  * time/space complexity
+  * program design
+
 Problem:
 
 Given a number n, print n-th Fibonacci Number.
diff --git a/fib.c b/fib.c
index 7525d1b..fffd94f 100644
--- a/fib.c
+++ b/fib.c
@@ -1,26 +1,34 @@
 #include <stdio.h>
 #include <assert.h>
 
+// 1. base case -> ends the loops
+// 2. recurrence
 int fib(int n)
 {
-  if (n == 1) {
-    return 0;
+  if (n <= 1) {
+    printf("%d: %d + %d = %d\n", n, n, n + n);
+    return n;
   }
 
-  if (n == 2 || n == 3) {
-    return 1;
-  }
+  int y = fib(n - 2);
+  int x = fib(n - 1);
+  printf("%d: %d + %d = %d\n", n, x, y, x+y);
 
-  return 2;
+  return x + y;
 }
 
 int main(int argc, char *argv[])
 {
-  assert(fib(1) == 0);
+  assert(fib(-2) == 0);
+  assert(fib(-1) == 0);
+  assert(fib(0) == 0);
+  assert(fib(1) == 1);
   assert(fib(2) == 1);
-  assert(fib(3) == 1);
-  assert(fib(4) == 2);
+  assert(fib(3) == 2);
+  assert(fib(4) == 3);
+  assert(fib(12) == 144);
 
+  printf("%d\n", fib(100));
 
   printf("YAY!\n");
   return 0;