From f978ffbfa1484bfed368d3f53f9b54df96fbadd5 Mon Sep 17 00:00:00 2001
From: Quentin Boyer <quentin+dev@familleboyer.net>
Date: Wed, 27 Nov 2024 12:44:42 +0100
Subject: [PATCH] Optimize problem 1

---
 src/one.rs | 17 +++++++++++++++--
 1 file changed, 15 insertions(+), 2 deletions(-)

diff --git a/src/one.rs b/src/one.rs
index 1498a50..a29c802 100644
--- a/src/one.rs
+++ b/src/one.rs
@@ -6,12 +6,25 @@ pub struct Args {
     pub until: u64,
 }
 
+fn multiple_sum_until(m: u64, n: u64) -> u64 {
+    let k = n / m;
+    m * k * (k + 1) / 2
+}
+
 impl Problem for Args {
     type Solution = u64;
 
-    // We could derive it mathematically, ... or write a dump loop
+    // Multiple of threes:
+    // 3 6 9 12 ... = 3 * 1 + 3 * 2 + 3 * 3 ... = 3 * (1 + 2 + 3 ...)
+    // Identically multiples of 5: 5 * (1 + 2 + 3 ...)
+    //
+    // We need all multiples such that 3 * n < X, n < X / 3
     fn solve(self, _: GlobalArgs) -> color_eyre::Result<u64> {
-        let sum = (0..self.until).filter(|x| x % 3 == 0 || x % 5 == 0).sum();
+        let three_sum = multiple_sum_until(3, self.until - 1);
+        let five_sum = multiple_sum_until(5, self.until - 1);
+        let fifteen_sum = multiple_sum_until(15, self.until - 1);
+
+        let sum = three_sum + five_sum - fifteen_sum;
 
         Ok(sum)
     }