Merge pull request TheAlgorithms#29 from shashank152k/BasicMaths

Basic Maths - Fibonacci, Factorial, Maximum Sub Array Sum (Kadane)

Author: RationalAsh

src/Maths/Factorial.hs

@@ -0,0 +1,9 @@
+module Maths.Factorial where
+
+fac :: Integer -> Integer 
+fac 0 = 1
+fac n = n * fac (n - 1)
+
+main :: IO ()
+main = do
+    print (fac 4)

src/Maths/Fibonacci.hs

@@ -0,0 +1,10 @@
+module Maths.Fibonacci where
+
+fib :: Integer -> Integer
+fib 0 = 0
+fib 1 = 1
+fib n = fib (n-1) + fib (n-2)
+
+main :: IO ()
+main = do
+    print (fib 10)

src/Maths/KadaneAlgorithm.hs

@@ -0,0 +1,36 @@
+module Maths.KadaneAlgorithm where
+
+-- Sample Input List 
+inputList :: [Integer]
+inputList = [1, -2, 3, 4, -5, 6, -7, 8, 9, 10]
+
+
+-- Helper function that updates values of maxSoFar and maxEndingHere
+-- and call itself recursively over the values of the list 
+-- and when the list is empty, return the maxSoFar value
+-- with the start and end indices.
+maxSubArrayHelper :: Integer -> Integer -> Integer -> Integer -> Integer -> [Integer] -> (Integer, Integer, Integer)
+maxSubArrayHelper maxSoFar _ _ start end [] = (maxSoFar, start, end)
+maxSubArrayHelper maxSoFar maxEndingHere i start end (x:xs) = 
+    let i' = i + 1
+        maxEndingHere' = maxEndingHere + x
+    in 
+        if maxSoFar < maxEndingHere' then 
+            maxSubArrayHelper maxEndingHere' maxEndingHere' i' start i xs
+        else if maxEndingHere' < 0 then
+            maxSubArrayHelper maxSoFar 0 i' i' i' xs
+        else 
+            maxSubArrayHelper maxSoFar maxEndingHere' i' start end xs
+
+-- Initially maxSoFar (maximum sum till the previous iteration), 
+-- maxEndingHere (maximum sum till end index of the current iteration),
+-- start (start index) and end (end index) are sent as 0
+maxSubArray :: [Integer] -> (Integer, Integer, Integer)
+maxSubArray = maxSubArrayHelper 0 0 0 0 0
+
+-- Outputs (sum, start, end)
+-- sum - sum from start to end indices of the input array
+-- start:end - the subarray with max sum
+main :: IO ()
+main = do
+    print (maxSubArray inputList)