From 9f3faba1e0b63fb201b17fbe9c218ef6840d9b8f Mon Sep 17 00:00:00 2001
From: Dimitri Lozeve <dimitri@lozeve.com>
Date: Sun, 10 May 2020 19:21:07 +0200
Subject: [PATCH] Add second solution for problem 5 task 1

---
 Contest2020/Contest2020.dyalog | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/Contest2020/Contest2020.dyalog b/Contest2020/Contest2020.dyalog
index 7e53ff5..0834c30 100644
--- a/Contest2020/Contest2020.dyalog
+++ b/Contest2020/Contest2020.dyalog
@@ -67,6 +67,23 @@
                   r←((↑∘amounts)((1+⊢)⊥⊣)(↑∘rates))¨⍳⍴rates
                 ∇
 
+                ∇ r←amounts rr2 rates;recur
+                  ⍝ Second solution
+                  ⍝ The recurrence relation (⍺ is the previous value,
+                  ⍝ ⍵[1] is the current amount, and ⍵[2] is the
+                  ⍝ current rate).
+                  recur←{⍵[1]+⍺×1+⍵[2]}
+                  ⍝ Because APL evaluates from right to left, we can't
+                  ⍝ use Scan directly, as recur is not associative. We
+                  ⍝ need something like Haskell's scanl, that will
+                  ⍝ accumulate left-to-right and accumulate
+                  ⍝ left-to-right. Scan accumulates left-to-right but
+                  ⍝ evaluates right-to-left. This solution therefore
+                  ⍝ folds for all subarrays, but it is not good in
+                  ⍝ terms of performance.
+                  r←{⊃⊃f⍨/(⌽⍵↑amounts,¨rates),⊂0 0}¨⍳⍴amounts
+                ∇
+
                 ∇ r←cashFlow pv rates
                   ⍝ 2020 APL Problem Solving Competition Phase II
                   ⍝ Stub function for Problem 5, Task 2 - pv