From ae631d3c0a44e76741a5cde1a1b80ee258923b70 Mon Sep 17 00:00:00 2001
From: Seongbeom Park <sparkamita90@gmail.com>
Date: Mon, 7 Mar 2022 22:00:25 +0900
Subject: [PATCH] finish level5/dodge-the-lasers

---
 README.md                                      |  9 +++++----
 .../dodge-the-lasers/constraints.txt           |  0
 {others => level5}/dodge-the-lasers/readme.txt |  0
 .../dodge-the-lasers/solution.py               | 18 ++++++++----------
 4 files changed, 13 insertions(+), 14 deletions(-)
 rename {others => level5}/dodge-the-lasers/constraints.txt (100%)
 rename {others => level5}/dodge-the-lasers/readme.txt (100%)
 rename {others => level5}/dodge-the-lasers/solution.py (57%)

diff --git a/README.md b/README.md
index 3b6085e..487e9f3 100644
--- a/README.md
+++ b/README.md
@@ -28,11 +28,12 @@
 * Completed in: 6 hrs, 49 mins, 26 secs.
 * DP & Optimization
 
-## Encrypted message
-CFcSBwgCCBoHRhkKU1cGAA4AGU5YQR5THBwNFwoGGAxTQQMQVBUSBg4EAAwQRhUQVBUHFAQTGRpT QQMQVBkPERkECQAWDVwXX1BGEwgJBAwCBFRVHQRGUlFBShwaDVZTGBUFVUdBShsVA1tZBwNGUlFB ShoVB1wXX1BGFAQOSklOQR5HGh5AVRY=
-
-## Others
 ### dodge-the-laser
+* Completed in: 2 days, 20 hrs, 22 mins, 39 secs.
 * Reference
   * [Beatty sequence](https://en.wikipedia.org/wiki/Beatty_sequence)
   * How to find A001951 A Beatty sequence: a(n)=floor(n\*sqrt(2)), stackexchange, https://math.stackexchange.com/questions/2052179/how-to-find-sum-i-1n-left-lfloor-i-sqrt2-right-rfloor-a001951-a-beatty-s
+
+## Encrypted message
+CFcSBwgCCBoHRhkKU1cGAA4AGU5YQR5THBwNFwoGGAxTQQMQVBUSBg4EAAwQRhUQVBUHFAQTGRpT QQMQVBkPERkECQAWDVwXX1BGEwgJBAwCBFRVHQRGUlFBShwaDVZTGBUFVUdBShsVA1tZBwNGUlFB ShoVB1wXX1BGFAQOSklOQR5HGh5AVRY=
+
diff --git a/others/dodge-the-lasers/constraints.txt b/level5/dodge-the-lasers/constraints.txt
similarity index 100%
rename from others/dodge-the-lasers/constraints.txt
rename to level5/dodge-the-lasers/constraints.txt
diff --git a/others/dodge-the-lasers/readme.txt b/level5/dodge-the-lasers/readme.txt
similarity index 100%
rename from others/dodge-the-lasers/readme.txt
rename to level5/dodge-the-lasers/readme.txt
diff --git a/others/dodge-the-lasers/solution.py b/level5/dodge-the-lasers/solution.py
similarity index 57%
rename from others/dodge-the-lasers/solution.py
rename to level5/dodge-the-lasers/solution.py
index f3dc8df..3891747 100644
--- a/others/dodge-the-lasers/solution.py
+++ b/level5/dodge-the-lasers/solution.py
@@ -2,25 +2,23 @@ import math
 from decimal import *
 
 def solution(s):
-    getcontext().prec = 10000
-    sqrt_2 = Decimal(2).sqrt()
+    getcontext().prec = len(s)+1
+    return str(beatty_sum_sqrt2(int(s)))
 
-    return str(beatty_sum(sqrt_2, int(s)))
-
-def beatty_sum(r, n):
+def beatty_sum_sqrt2(n):
     if n == 0:
         return 0
     if n == 1:
         return 1
-    floor_r_n = int(math.floor(r*n))
-    
-    return natural_number_sum(floor_r_n) - 2 * natural_number_sum(floor_r_n - n) - beatty_sum(r, floor_r_n - n)
+    floor_r_n = int(Decimal(2*(n**2)).sqrt())
+
+    return natural_number_sum(floor_r_n) - 2 * natural_number_sum(floor_r_n - n) - beatty_sum_sqrt2(floor_r_n - n)
 
 def natural_number_sum(n):
     return n*(n+1)/2
 
 def ten(n):
-    return 10**n
+    return str(10**n)
 
 tests = [
         ['77', '4208'],
@@ -34,7 +32,7 @@ tests = [
         ['8', '47'],
         ['9', '59'],
         ['10', '73'],
-        [ten(100), '0']
+        [ten(100), '70710678118654752440084436210484903928483593768847403658833986899536623923105351942519376716382078638821760123411090095254685423841027253480565451739737157454059823250037671948325191776995310741236436']
         ]