From f942937de1496e38f2d58d6383d03f5e254abfb6 Mon Sep 17 00:00:00 2001
From: Charles <sircharlesaze@gmail.com>
Date: Thu, 5 Sep 2019 14:48:42 +0200
Subject: problem 58 haskell

---
 haskell/058-spiral_primes.hs     | 51 ++++++++++++++++++++++++++++++++++++
 haskell/wip/058-spiral_primes.hs | 56 ----------------------------------------
 2 files changed, 51 insertions(+), 56 deletions(-)
 create mode 100644 haskell/058-spiral_primes.hs
 delete mode 100644 haskell/wip/058-spiral_primes.hs

(limited to 'haskell')

diff --git a/haskell/058-spiral_primes.hs b/haskell/058-spiral_primes.hs
new file mode 100644
index 0000000..d2c10d1
--- /dev/null
+++ b/haskell/058-spiral_primes.hs
@@ -0,0 +1,51 @@
+------
+-- Spiral primes
+-- Problem 58
+--
+-- Starting with 1 and spiralling anticlockwise in the following way,
+-- a square spiral with side length 7 is formed.
+--
+-- 37 36 35 34 33 32 31
+-- 38 17 16 15 14 13 30
+-- 39 18  5  4  3 12 29
+-- 40 19  6  1  2 11 28
+-- 41 20  7  8  9 10 27
+-- 42 21 22 23 24 25 26
+-- 43 44 45 46 47 48 49
+--
+-- It is interesting to note that the odd squares lie along the bottom right diagonal,
+-- but what is more interesting is that 8 out of the 13 numbers lying along both diagonals
+-- are prime; that is, a ratio of 8/13 ≈ 62%.
+-- If one complete new layer is wrapped around the spiral above, a square spiral
+-- with side length 9 will be formed. If this process is continued, what is the side
+-- length of the square spiral for which the ratio of primes along both diagonals
+-- first falls below 10%?
+------
+
+
+main = do
+    print $ firstDropBellow 0.1 0 0
+
+firstDropBellow :: Double -> Int -> Int -> Int
+firstDropBellow percent counter n
+    | counter /= 0 && primesRatio < percent = 2 * n + 1
+    | otherwise = firstDropBellow percent (counter + countPrimes) (n + 1)
+    where primesRatio =  (fromIntegral countPrimes + fromIntegral counter)
+                         / fromIntegral (4 * n + 1)
+          countPrimes = length $ filter id (map isPrime diags)
+          diags = [dur, ddl, dul]
+          dur = 4 * n ^ 2 - 2 * n + 1
+          ddl = 4 * n ^ 2 + 2 * n + 1
+          dul = 4 * n ^ 2 + 1
+
+isPrime :: Int -> Bool
+isPrime 2 = True
+isPrime 3 = True
+isPrime x
+    | x < 2 = False
+    | x `mod` 2 == 0 || x `mod` 3 == 0 = False
+    | otherwise = divCheck 5
+    where divCheck d
+           | d * d > x = True
+           | x `mod` d == 0 || x `mod` (d + 2) == 0 = False
+           | otherwise = divCheck (d + 6)
diff --git a/haskell/wip/058-spiral_primes.hs b/haskell/wip/058-spiral_primes.hs
deleted file mode 100644
index 3c620ec..0000000
--- a/haskell/wip/058-spiral_primes.hs
+++ /dev/null
@@ -1,56 +0,0 @@
-------
--- Spiral primes
--- Problem 58
---
--- Starting with 1 and spiralling anticlockwise in the following way,
--- a square spiral with side length 7 is formed.
---
--- 37 36 35 34 33 32 31
--- 38 17 16 15 14 13 30
--- 39 18  5  4  3 12 29
--- 40 19  6  1  2 11 28
--- 41 20  7  8  9 10 27
--- 42 21 22 23 24 25 26
--- 43 44 45 46 47 48 49
---
--- It is interesting to note that the odd squares lie along the bottom right diagonal,
--- but what is more interesting is that 8 out of the 13 numbers lying along both diagonals
--- are prime; that is, a ratio of 8/13 ≈ 62%.
--- If one complete new layer is wrapped around the spiral above, a square spiral
--- with side length 9 will be formed. If this process is continued, what is the side
--- length of the square spiral for which the ratio of primes along both diagonals
--- first falls below 10%?
-------
-
-
-main = do
-    print $ firstDropBellow 0.1 3 0
-
-firstDropBellow :: Double -> Int -> Int -> (Int, Int, Double)
-firstDropBellow percent counter n
-    | primesRatio < percent = (n, 2 * n + 1, primesRatio)
-    | otherwise = firstDropBellow percent (counter + countPrimes) (n + 1)
-    where primesRatio =  (fromIntegral countPrimes + fromIntegral counter)
-                         / fromIntegral (4 * n + 1)
-          countPrimes = length $ filter id (map isPrime corners)
-          corners = [dur, ddl, dul]
-          dur = 4 * n ^ 2 - 2 * n + 1
-          ddl = 4 * n ^ 2 + 2 * n + 1
-          dul = 4 * n ^ 2 + 1
-
-isPrime :: Int -> Bool
-isPrime 2 = True
-isPrime 3 = True
-isPrime x
-    | x < 2 = False
-    | x `mod` 2 == 0 || x `mod` 3 == 0 = False
-    | otherwise = divCheck 5
-    where divCheck d
-           | d * d > x = True
-           | x `mod` d == 0 || x `mod` (d + 2) == 0 = False
-           | otherwise = divCheck (d + 6)
-
--- diagUpRight = [4 * x ^ 2 - 2 * x + 1 | x <- [1..]]
--- diagdownLeft = [4 * x ^ 2 + 2 * x + 1 | x <- [1..]]
--- diagUpLeft = [4 * x ^ 2 + 1 | x <- [1..]]
--- diags = [diagUpRight, diagdownLeft, diagUpLeft]
-- 
cgit