The Smallest Difference

LintCode-387.The Smallest Difference

Given two array of integers(the first array is array A, the second array is array B), now we are going to find a element in array A which is A[i], and another element in array B which is B[j], so that the difference between A[i] and B[j] (|A[i] - B[j]|) is as small as possible, return their smallest difference.

Example: For example, given array A = [3,6,7,4], B = [2,8,9,3], return 0

Challenge: O(n log n) time

public class Solution {
    /**
     * @param A, B: Two integer arrays.
     * @return: Their smallest difference.
     */
    public int smallestDifference(int[] A, int[] B) {
        if (A == null || A.length == 0 || B == null || B.length == 0) {
            return -1;
        }
        
        Arrays.sort(A);
        Arrays.sort(B);
        
        int diff = Math.abs(A[0] - B[0]);
        
        for (int i = 0; i < A.length; i++) {
            int low = 0, high = B.length - 1;
            
            while (low + 1 < high) {
                int middle = low + (high - low) / 2;
                
                if (diff > Math.abs(A[i] - B[middle])) {
                    diff = Math.abs(A[i] - B[middle]);
                }
                
                if (A[i] == B[middle]) {
                    return 0;
                } else if (A[i] > B[middle]) {
                    low = middle;
                } else {
                    high = middle;
                }
            }
            
            if (diff > Math.abs(A[i] - B[low])) {
                diff = Math.abs(A[i] - B[low]);
            }
            if (diff > Math.abs(A[i] - B[high])) {
                diff = Math.abs(A[i] - B[high]);
            }
        }
        
        return diff;
    }
}

Here is another simpler solution.

public class Solution {
    /**
     * @param A, B: Two integer arrays.
     * @return: Their smallest difference.
     */
    public int smallestDifference(int[] A, int[] B) {
        if (A == null || A.length == 0 || B == null || B.length == 0) {
            return -1;
        }
        
        Arrays.sort(A);
        Arrays.sort(B);
        
        int diff = Math.abs(A[0] - B[0]);
        
        int i = 0, j = 0;
        
        while (i < A.length && j < B.length) {
            diff = Math.min(diff, Math.abs(A[i] - B[j]));
            
            if (A[i] < B[j]) {
                i++;
            } else {
                j++;
            }
        }
        
        return diff;
    }
}

Hope this helps,
Michael