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Median of Two Sorted Arrays.cpp
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Median of Two Sorted Arrays.cpp
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//Last Modified: 2015/01/10
//Author: Junbo Xin
/*
************************Problem Description*********************
Here 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<assert.h>
using namespace std;
class Solution {
public:
double findMedianSortedArrays(int A[], int m, int B[], int n) {
if(( m+n) %2 == 0){
int k = (m+n)/2;
return (findMergeKth(A,m,B,n,k) + findMergeKth(A,m,B,n,k+1))/2;
} else {
int k = (m+n+1)/2;
return findMergeKth(A,m,B,n,k);
}
}
double findMergeKth(int A[], int m, int B[], int n, int k){
if( m == 0)
return B[k-1];
if( n == 0)
return A[k-1];
// before Ai, there are i numbers, before Bj, there are j numbers.
int i = int( m*(k-1)/(m+n) );
int j = k-i-1;
int Ai_1 = (i==0)? INT_MIN:A[i-1];
int Ai = (i==m)? INT_MAX:A[i];
int Bj_1 = (j ==0)? INT_MIN:B[j-1];
int Bj = (j==n)? INT_MAX:B[j];
if(Ai_1 <= Bj && Bj <= Ai)
return Bj;
if(Bj_1 <= Ai && Ai <= Bj)
return Ai;
// assert( (Ai < Bj && Ai < Bj_1) || ( Bj < Ai && Bj < Ai_1) );
if(Ai <= Bj)
return findMergeKth(A+i+1, m-i-1,B,n,k-i-1);
else
return findMergeKth(A,m,B+j+1,n-j-1,k-j-1);
}
};
int main(){
Solution s;
//int A[] = { 3, 4, 12, 23, 32, 33, 67, 102};
//int B[] = { -3,2,6,10,14,39,45,55,89,104};
int A[] = {1,1,2};
int B[] = {1,2,2};
//int key = s.findMergeKth(A, sizeof(A)/sizeof(int),
//B, sizeof(B)/sizeof(int), 4);
double key = s.findMedianSortedArrays(A,sizeof(A)/sizeof(int),B,sizeof(B)/sizeof(int));
cout << key << endl;
printf("%d",1<<2);
getchar();
return 0;
}