4_Median_of_Two_Sorted_Arrays

Author: qiyuangong

README.md

@@ -9,6 +9,7 @@
 | 1 | [Two Sum](https://leetcode.com/problems/two-sum/) | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/1_Two_Sum.py) | 1. Hash O(n) and O(n) space<br>2. Sort and search with two points O(n) and O(1) space |
 | 2 | [Add Two Numbers](https://leetcode.com/problems/add-two-numbers/) | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/2_Add_Two_Numbers.py) | Note the carry from lower digit. |
 | 3 | [Longest Substring Without Repeating Characters](https://leetcode.com/problems/longest-substring-without-repeating-characters/) | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/3_Longest_Substring_Without_Repeating_Characters.py) |1. Check every possible substring O(n^2) <br>2. Remember the character index and current check pos, if character index >= current pos, then there is duplicate |
+| 4 | [Median of Two Sorted Arrays](https://leetcode.com/problems/median-of-two-sorted-arrays/) | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/.py) | 1. Merge two sorted lists and compute median, O(m + n) and O(m + n)<br>2. An extension of median of two sorted arrays of equal size problem|
 | 5 | [Longest Palindromic Substring](https://leetcode.com/problems/longest-palindromic-substring/) | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/5_Longest_Palindromic_Substring.py) | [Background knowledge](http://en.wikipedia.org/wiki/Longest_palindromic_substring)<br>1. DP if s[i]==s[j] and P[i+1, j-1] then P[i,j]<br>2. A palindrome can be expanded from its center<br>3. Manacher algorithm|
 | 7 | [Reverse Integer](https://leetcode.com/problems/reverse-integer/) | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/7_Reverse_Integer.py) | Overflow when the result is greater than 2147483647
 | 8 | [String to Integer (atoi)](https://leetcode.com/problems/string-to-integer-atoi/) | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/8_String_to_Integer(atoi).py) | Overflow, Space, and negative number |
@@ -79,4 +80,11 @@
 | 288 | [Unique Word Abbreviation](https://leetcode.com/problems/unique-word-abbreviation/) &hearts; | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/288_Unique_Word_Abbreviation.py) | hash |
 | 337 | [House Robber III](https://leetcode.com/problems/house-robber-iii/) | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/337_House_Robber_III.py) | 1. Recursion with hash map, O(n) and O(n)<br>2. Recursion on two steps, O(n) and O(1) |
 | 339 | [Nested List Weight Sum](https://leetcode.com/problems/nested-list-weight-sum/) &hearts; | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/339_Nested_List_Weight_Sum.py) | Depth-first recursion |
-| 340 | [Longest Substring with At Most K Distinct Characters](https://leetcode.com/problems/longest-substring-with-at-most-k-distinct-characters/) &hearts; | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/340_Longest_Substring_with_At_Most_K_Distinct_Characters.py) | Maintain a sliding window with at most k distinct characters and a count for this window. Note that the start position need a loop to update.|
+| 340 | [Longest Substring with At Most K Distinct Characters](https://leetcode.com/problems/longest-substring-with-at-most-k-distinct-characters/) &hearts; | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/340_Longest_Substring_with_At_Most_K_Distinct_Characters.py) | Maintain a sliding window with at most k distinct characters and a count for this window. Note that the start position need a loop to update.|
+| 351 | [Android Unlock Patterns](https://leetcode.com/problems/android-unlock-patterns/) &hearts; | [Python](https://github.com/qiyuangong/leetcode/blob/master/python/351_Android_Unlock_Patterns.py) |  |
+
+
+| # | ToDo |
+|---| ----- |
+
+| 351 | [Android Unlock Patterns](https://leetcode.com/problems/android-unlock-patterns/) &hearts; |

python/4_Median_of_Two_Sorted_Arrays.py

@@ -1,36 +1,55 @@
 class Solution(object):
+    # def findMedianSortedArrays(self, nums1, nums2):
+    #     """
+    #     :type nums1: List[int]
+    #     :type nums2: List[int]
+    #     :rtype: float
+    #     """
+    #     p1 = p2 = 0
+    #     ls1 = len(nums1)
+    #     ls2 = len(nums2)
+    #     all_nums = []
+    #     median = 0.0
+    #     while p1 < ls1 and p2 < ls2:
+    #         if nums1[p1] < nums2[p2]:
+    #             all_nums.append(nums1[p1])
+    #             p1 += 1
+    #         else:
+    #             all_nums.append(nums2[p2])
+    #             p2 += 1
+    #     if p1 < ls1:
+    #         while p1 < ls1:
+    #             all_nums.append(nums1[p1])
+    #             p1 += 1
+    #     if p2 < ls2:
+    #         while p2 < ls2:
+    #             all_nums.append(nums2[p2])
+    #             p2 += 1
+    #     # print all_nums
+    #     if (ls1 + ls2) % 2 == 1:
+    #         median = all_nums[(ls1 + ls2) / 2]
+    #     else:
+    #         median = 1.0 * (all_nums[(ls1 + ls2) / 2] + all_nums[(ls1 + ls2) / 2 - 1]) / 2
+    #     return median
+
     def findMedianSortedArrays(self, nums1, nums2):
-        """
-        :type nums1: List[int]
-        :type nums2: List[int]
-        :rtype: float
-        """
-        p1 = p2 = 0
-        ls1 = len(nums1)
-        ls2 = len(nums2)
-        all_nums = []
-        median = 0.0
-        while p1 < ls1 and p2 < ls2:
-            if nums1[p1] < nums2[p2]:
-                all_nums.append(nums1[p1])
-                p1 += 1
+        N1, N2 = len(nums1), len(nums2)
+        if N1 < N2:
+            nums1, N1, nums2, N2 = nums2, N2, nums1, N1
+        l, r = 0, N2 * 2
+        while l <= r:
+            mid2 = (l + r) >> 1
+            mid1 = N1 + N2 - mid2
+            L1 = -sys.maxint - 1 if mid1 == 0 else nums1[(mid1 - 1) >> 1]
+            L2 = -sys.maxint - 1 if mid2 == 0 else nums2[(mid2 - 1) >> 1]
+            R1 = sys.maxint if mid1 == 2 * N1 else nums1[mid1 >> 1]
+            R2 = sys.maxint if mid2 == 2 * N2 else nums2[mid2 >> 1]
+            if L1 > R2:
+                l = mid2 + 1
+            elif L2 > R1:
+                r = mid2 - 1
             else:
-                all_nums.append(nums2[p2])
-                p2 += 1
-        if p1 < ls1:
-            while p1 < ls1:
-                all_nums.append(nums1[p1])
-                p1 += 1
-        if p2 < ls2:
-            while p2 < ls2:
-                all_nums.append(nums2[p2])
-                p2 += 1
-        # print all_nums
-        if (ls1 + ls2) % 2 == 1:
-            median = all_nums[(ls1 + ls2) / 2]
-        else:
-            median = 1.0 * (all_nums[(ls1 + ls2) / 2] + all_nums[(ls1 + ls2) / 2 - 1]) / 2
-        return median
+                return (max(L1, L2) + min(R1, R2)) / 2.0
 
 
 if __name__ == '__main__':