difference-of-squares v2

difference-of-squares/src/difference_of_squares.gleam

@@ -1,14 +1,25 @@
 pub fn square_of_sum(n: Int) -> Int {
-  let sum = sum_to(n)
-  sum * sum
+  // (1 + 2 + ... n)^2
+  square_of_sum_loop(n, 0)
 }
 
-fn sum_to(n: Int) -> Int {
-  n * { n + 1 } / 2
+fn square_of_sum_loop(n: Int, acc: Int) -> Int {
+  case n {
+    0 -> acc * acc
+    _ -> square_of_sum_loop(n - 1, acc + n)
+  }
 }
 
 pub fn sum_of_squares(n: Int) -> Int {
-  n * { n + 1 } * { 2 * n + 1 } / 6
+  // TODO (1^2 + 2^2 ... + n^2)
+  sum_of_squares_loop(n, 0)
+}
+
+fn sum_of_squares_loop(n: Int, acc: Int) -> Int {
+  case n {
+    0 -> acc
+    _ -> sum_of_squares_loop(n - 1, acc + { n * n })
+  }
 }
 
 pub fn difference(n: Int) -> Int {