I have a problem where I need to find the maximum distance between two different elements in an array.
For example: given an array 4,6,2,2,6,6,4 , the method should return 5 as the max distance.
I am able to solve the problem using two for loops but it is not an optimized solution. Am trying to optimize it by doing it in a single for loop.
here is my current solution:
int [] A = {4,6,2,2,6,6,4};
int N = A.length;
int result = 0;
for (int i = 0; i < N; i++){
for (int j = i; j < N; j++) {
if(A[i] != A[j]){
result = Math.max(result, j - i);
}
}
}
// tried below code but it is not efficient
// for (int i = 0; i < N; i++){
//
// if(A[N-1] != A[i]){
// result = Math.max(result, N-1-i);
// }
// }
System.out.println(result);
How to make this better in terms of time complexity?
Solution:
Simple (not nested) loop is enough, but two cases should be taken into
account: either the best result is
4,6,2,2,6,6,4
^ ^ - moving first
or
4,6,2,2,6,6,4
^ ^ - moving last
for instance: [4, 2, 4, 4, 4] moving first brings the answer, when in case of [4, 4, 4, 2, 4] moving last should be used.
int first = 0;
int last = A.length - 1;
// 1st case: moving "first"
while (first < last) {
if (A[first] == A[last])
first++;
else
break;
}
int diff1 = last - first;
first = 0;
last = A.length - 1;
// 2nd case: moving "last"
while (first < last) {
if (A[first] == A[last])
last--;
else
break;
}
int diff2 = last - first;
// result is the max between two cases
int result = diff1 > diff2
? diff1
: diff2;
So we have O(N) time complexity.
Edit: Let’s proof that at least one of the indexes is either 0 or length - 1. Let’s do it by contradiction. Suppose we have a solution like
a, b, c, .... d, e, f, g
^ ..... ^ <- solution indexes (no borders)
Items to the left of c must be d, otherwise we can take a or b indexes and have an improved solution. Items to right of d must be c or we can once again push last index to the right and have a better solution. So we have
d, d, c .... d, c, c, c
^ .... ^ <- solution indexes
Now, since d <> c (c..d is a solution) we can improve the solution into
d, d, c .... d, c, c, c
^ .... ^ <- solution indexes
^ .... ^ <- better solution
We have a contradiction (the supposed solution is not one – we have a better choice) and that’s why at least one index must be 0 or length - 1.
Now we have 2 scenarions to test:
a, b, ..... y, z
^ ...... ^ <- moving first
^ ...... ^ <- moving last
We can combine both conditions into if and have just one loop:
int result = 0;
for (int i = 0; i < A.length; ++i)
if (A[i] != A[A.length - 1] || A[0] != A[A.length - 1 - i]) {
result = A.length - i - 1;
break;
}