4-Median-Of-Two-Sorted-Arrays.cpp

/*
    Given 2 sorted arrays of size m & n, return the median of these arrays
    Ex. nums1 = [1,3] nums2 = [2] -> 2, nums1 = [1,2] nums2 = [3,4] -> 2.5

    Binary search, partition each array until partitions are correct, get median
    [1,2,3,4,5]
    |  a|b    |
    [1,2,3,4,5,6,7,8]    -->    a <= d ? yes, c <= b ? no, so need to fix
    |      c|d      |

    Time: O(log min(m, n))
    Space: O(1)
*/

class Solution {
public:
    double findMedianSortedArrays(vector<int>& nums1, vector<int>& nums2) {
        int m = nums1.size();
        int n = nums2.size();
        
        if (m > n) {
            return findMedianSortedArrays(nums2, nums1);
        }
        
        int total = m + n;
        
        int low = 0;
        int high = m;
        
        double result = 0.0;
        
        while (low <= high) {
            // nums1
            int i = low + (high - low) / 2;
            // nums2
            int j = (total + 1) / 2 - i;
            
            int left1 = (i > 0) ? nums1[i - 1] : INT_MIN;
            int right1 = (i < m) ? nums1[i] : INT_MAX;
            int left2 = (j > 0) ? nums2[j - 1] : INT_MIN;
            int right2 = (j < n) ? nums2[j] : INT_MAX;
            
            // partition is correct
            if (left1 <= right2 && left2 <= right1) {
                // even
                if (total % 2 == 0) {
                    result = (max(left1, left2) + min(right1, right2)) / 2.0;
                // odd
                } else {
                    result = max(left1, left2);
                }
                break;
            } else if (left1 > right2) {
                high = i - 1;
            } else {
                low = i + 1;
            }
        }
        
        return result;
    }
};