624. Maximum Distance in Arrays

Given m arrays, and each array is sorted in ascending order. Now you can pick up two integers from two different arrays (each array picks one) and calculate the distance. We define the distance between two integers a and b to be their absolute difference |a-b|. Your task is to find the maximum distance.

Example 1:
Input: 
[[1,2,3],
 [4,5],
 [1,2,3]]
Output: 4
Explanation: 
One way to reach the maximum distance 4 is to pick 1 in the first or third array and pick 5 in the second array.
Note:
Each given array will have at least 1 number. There will be at least two non-empty arrays.
The total number of the integers in all the m arrays will be in the range of [2, 10000].
The integers in the m arrays will be in the range of [-10000, 10000].



// sol 1 : tle 
123 / 124 test cases passed.


class Solution {
    public int maxDistance(List<List<Integer>> arrays) {
        // brute force solution is to try all possible ways 
        int res = 0;
        for(int i = 0; i < arrays.size() - 1; i++){
            for(int num1 : arrays.get(i)){
                for(int j = i + 1; j < arrays.size(); j++){
                    for(int num2 : arrays.get(j)){
                        res = Math.max(res, Math.abs(num1 - num2));
                    }
                }
            }
            
        }
        return res; 
    }
}


// sol 2 : find out a way, so that we don’t have to try all possible combinations to get the max 
123 / 124 test cases passed.
Tle , 

In the last approach, we didn't make use of the fact that every array in the listlist is sorted. Thus, instead of considering the distances among all the elements of all the arrays(except intra-array elements), we can consider only the distances between the first(minimum element) element of an array and the last(maximum element) element of the other arrays and find out the maximum distance from among all such distances.




class Solution {
    public int maxDistance(List<List<Integer>> arrays) {
        int res = 0;
        // pick any two arrays and check only the first one and the last one 
        for(int i = 0; i < arrays.size() - 1; i++){
            int s1 = arrays.get(i).get(0);
            int e1 = arrays.get(i).get(arrays.get(i).size() - 1);
            for(int j = i + 1; j < arrays.size(); j++){
                int s2 = arrays.get(j).get(0);
                int e2 = arrays.get(j).get(arrays.get(j).size() - 1);
                res = Math.max(res, Math.abs(s1 - e2));
                res = Math.max(res, Math.abs(s2 - e1));
            }
        }
        return res;
    }
}


// sol 3 : time n 

http://www.cnblogs.com/grandyang/p/7073343.html

用两个变量start和end分别表示当前遍历过的数组中最小的首元素，和最大的尾元素，那么每当我们遍历到一个新的数组时，只需计算新数组尾元素和start绝对差，跟end和新数组首元素的绝对差，取二者之间的较大值来更新结果res即可，



class Solution {
    public int maxDistance(List<List<Integer>> arrays) {
        int start = arrays.get(0).get(0);
        int n = arrays.get(0).size();
        int end = arrays.get(0).get(n - 1);
        int res = 0;
        for(int i = 1; i < arrays.size(); i++){
            List<Integer> list = arrays.get(i);
            int newStart = list.get(0);
            int len = list.size();
            int newEnd = list.get(len - 1);
            res = Math.max(res, Math.abs(newStart - end));
            res = Math.max(res, Math.abs(newEnd - start));
            end = Math.max(end, newEnd);
            start = Math.min(start, newStart);
        }
        return res;
        
    }
}