Merge pull request TheAlgorithms#16 from EternalEnvy/add-fibonacci

Added bottom up DP implementation of Fibonacci

Author: ms10398

Algorithms/dynamic_programming/fibonacci.js

@@ -0,0 +1,25 @@
+// Calculates fib(n) such that fib(n) = fib(n - 1) + fib(n - 2)
+// fib(0) = fib(1) = 1
+// Uses a bottom up dynamic programming approach
+// Solve each subproblem once, using results of previous subproblems,
+// which are n-1 and n-2 for Fibonacci numbers
+
+// Although this algorithm is linear in space and time as a function
+// of the input value n, it is exponential in the size of n as
+// a function of the number of input bits
+
+function fib(n) {
+    var table = [];
+    table.push(1);
+    table.push(1);
+    for (var i = 2; i < n; ++i) {
+        table.push(table[i - 1] + table[i - 2]);
+    }
+    console.log("Fibonacci #%d = %d", n, table[n - 1]);
+}
+
+fib(1);
+fib(2);
+fib(200);
+fib(5);
+fib(10);