add medianOfTwoSortedArrays

Author: feng

medianOfTwoSortedArrays.cpp

@@ -0,0 +1,103 @@
+/*
+ * Author : Feng Wei
+ * Date   : Nov 15, 2014
+ *
+ * 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)).
+ */
+
+#include <iostream>
+#include <algorithm>
+using namespace std;
+
+/*
+ * we are required to find the median of array, 
+ *
+ * 		if array.len is odd {
+ * 			return array[(len + 1) / 2 ];
+ * 		}
+ * 		else {
+ * 			return (array[len / 2] + array[len / 2 + 1]) / 2;
+ * 		}
+ * 		note: len = m + n
+ */
+class Solution {
+public:
+	/*
+	 * the problem can be transformed to find the kth smallest number in two arrays,
+	 *
+	 * Supposed that two arrays A and B, A.size() > k / 2 and B.size() > k / 2:
+	 *
+	 * 		1. if A[k / 2 - 1] < B[k / 2 - 1], it means that A[0] ~  A[k / 2 - 1] in the top k of the array merged A and B;
+	 * 		2. if A[k / 2 - 1] > B[k / 2 - 1], this sitution is similar to 1;
+	 * 		3. if A[k / 2 - 1] = B[k / 2 - 1], return A[k / 2 - 1] or B[k / 2 - 1].
+	 *
+	 * 	but we must consider some edge cases:
+	 *
+	 * 		1. if A or B is empty, return B[k - 1] or A[k - 1];
+	 * 		2. if k == 1, return min(A[0], B[0]);
+	 * 		3. if A[k / 2 - 1] == B[k / 2 - 1], return one of them.
+	 */
+
+    double findMedianSortedArrays(int A[], int m, int B[], int n) {
+		int len = m + n;
+		double result;
+
+		if ((len & 1) != 0) {
+			return findKNum(A, m, B, n, len / 2 + 1);
+		}
+		else {
+			double a = findKNum(A, m, B, n, len / 2);
+			double b = findKNum(A, m, B, n, len / 2 + 1);
+			return (a + b) / 2;
+		}
+
+		return -1;
+    }
+
+	double findKNum(int *A, int m, int *B, int n, int k)
+	{
+		if (m > n) {
+			return findKNum(B, n, A, m, k);
+		}
+
+		if ( m == 0) {
+			return B[k - 1];
+		}
+		if (k == 1) {
+			return min(A[0], B[0]);
+		}
+		int pa = min(k / 2, m);
+		int pb = k - pa;
+		if (A[pa - 1] < B[pb - 1]) {
+			return findKNum(A + pa, m - pa, B, n, k - pa);
+		}
+		else if (A[pa - 1] > B[pb - 1]) {
+			return findKNum(A, m, B + pb, n - pb, k - pb);
+		}
+		else {
+			return A[pa - 1];
+		}
+
+		return -1;
+	}
+};
+
+int main()
+{
+	Solution s;
+
+	int a[] = {1,2};
+	int b[] = {1,2};
+	cout << s.findMedianSortedArrays(a, 2, b, 2) <<endl;
+
+	int c[] = {};
+	int d[] = {1,2};
+	cout << s.findMedianSortedArrays(c, 0, d, 2)<<endl;
+
+	int e[] = {1};
+	int f[] = {1};
+	cout << s.findMedianSortedArrays(e, 1, f, 1)<<endl;
+	return 0;
+}