Median of Two Sorted Arrays

Author: applewjg

MedianofTwoSortedArrays.java

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+/*
+ Author:     King, [email protected]
+ Date:       Dec 12, 2014
+ Problem:    Median of Two Sorted Arrays
+ Difficulty: Hard
+ Source:     http://leetcode.com/onlinejudge#question_4
+ Notes:
+ There are two sorted arrays A and B of size m and n respectively. 
+ Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).
+
+ Solution: 1. O(m+n)
+           2. O(log(m+n))
+*/
+
+public class Solution {
+    public double findMedianSortedArrays_1(int A[], int B[]) {
+        int m = A.length, n = B.length;
+        int total = n + m, m1=0, m2=0, i=0, j=0;
+        for (int k = 1; k <= total/2 + 1; ++k) {
+            int a = (i==m) ? Integer.MAX_VALUE : A[i];
+            int b = (j==n) ? Integer.MAX_VALUE : B[j];
+            m1 = m2;
+            m2 = Math.min(a,b);
+            if (a > b) ++j;
+            else ++i;
+        }
+        if ((total&1) == 1) return m2;
+        else return (m1+m2)/2.0;
+    }
+    public double findMedianSortedArrays_2(int A[], int B[]) {
+        int m = A.length, n = B.length;
+        int total = m + n;
+        int k = total / 2;
+        if ((total&1) == 1) return findKth(A,B,k+1,0,m-1,0,n-1);
+        else return (findKth(A,B,k,0,m-1,0,n-1)+findKth(A,B,k+1,0,m-1,0,n-1))/2.0;
+    }
+    public double findKth(int A[], int B[], int k, int astart, int aend, int bstart, int bend) {
+        int alen = aend - astart + 1;
+        int blen = bend - bstart + 1;
+        if (alen > blen) return findKth(B,A,k, bstart, bend, astart, aend);
+        if (alen == 0) return B[bstart + k - 1];
+        if (k == 1) return Math.min(A[astart],B[bstart]);
+        int sa = Math.min(alen, k/2), sb = k- sa;
+        if (A[astart+sa-1] == B[bstart+sb-1]) return A[astart+sa-1];
+        else if (A[astart+sa-1] > B[bstart+sb-1]) return findKth(A,B,k - sb,astart,aend,bstart+sb,bend);
+        else return findKth(A,B,k - sa,astart+sa,aend,bstart,bend);
+    }
+    
+}