Add 858

Author: trung-hn

Diff for: Readme.md

@@ -160,6 +160,7 @@
 | 849 | Maximize Distance to Closest Person | Medium | O(N) | O(1) | Array | | |
 | 851 | Loud and Rich | Medium | O(N^2) | O(N^2) | DFS | | |
 | 853 | Car Fleet | Medium | O(NlogN) | O(N) | Sort | | |
+| 858 | Mirror Reflection | Medium | O(logN) | O(1) | Math | | |
 | 859 | Buddy Strings | Easy | O(N) | O(1) | String | | |
 | 875 | Koko Eating Bananas | Medium | O(NlogN) | O(1) | Binary Search | | |
 | 886 | Possible Bipartition | Medium | O(N + E) | O(N + E) | Depth First Search | Good problem | |

Diff for: src/858.mirror-reflection.py

@@ -0,0 +1,40 @@
+#
+# @lc app=leetcode id=858 lang=python3
+#
+# [858] Mirror Reflection
+#
+
+# @lc code=start
+# TAGS: Math
+# REVIEWME: Math
+import fractions
+class Solution:
+    # 24 ms, 91.58%. Time: O(logN). Space: O(1)
+    def mirrorReflection(self, p: int, q: int) -> int:
+        if q == 0: return 0
+        val = 0
+        while val == 0 or val % p:
+            val += q
+            
+        if (val // p) % 2 == 0: return 0
+        if (val // q) % 2 : return 1
+        return 2
+    
+    # 24 ms, 91.58%. using fraction. Simplified version of above.
+    def mirrorReflection(self, p: int, q: int) -> int:
+        num = fractions.Fraction(q, p)
+        val = num.numerator * num.denominator
+        if (val // num.denominator) % 2 == 0: return 0
+        if (val // num.numerator) % 2 : return 1
+        return 2
+    
+    # 24 ms, 91.58%. Use gcd. Simplified version of above.
+    def mirrorReflection(self, p: int, q: int) -> int:
+        gcd = math.gcd(p, q)
+        p //= gcd
+        q //= gcd
+        if q % 2 == 0: return 0
+        if p % 2 : return 1
+        return 2
+# @lc code=end
+

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