Maximum of minimum for every window size

Hard

0/120

Average time to solve is 45m

202 upvotes

Asked in companies

Problem statement

You are given an array of ‘N’ integers, you need to find the maximum of minimum for every window size. The size of the window should vary from 1 to ‘N’ only.

For example:

ARR = [1,2,3,4]
Minimums of window size 1 = min(1), min(2), min(3), min(4) = 1,2,3,4
Maximum among (1,2,3,4)  is 4

Minimums of window size 2 = min(1,2), min(2,3),   min(3,4) = 1,2,3
Maximum among (1,2,3) is 3

Minimums of window size 3 = min(1,2,3), min(2,3,4) = 1,2
Maximum among (1,2) is 2

Minimums of window size 4 = min(1,2,3,4) = 1
Maximum among them is 1
The output array should be [4,3,2,1].

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The first line of the input contains an integer ‘T’ denoting the number of test cases.

The first line of each test case contains a single positive integer ‘N’ denoting the number of the elements present in the array.

The second line of each test case contains ‘N’ space-separated integers denoting the elements of the array.

Output Format:

The only line of output of each test case should contain ‘N’ space-separated integer such that he ith integer indicates the maximum of minimums of the windows of size ‘i’.

Constraints:

1 <= T <= 100
1 <= N <= 10 ^ 4 
-10 ^ 9 <= ARR[i] <= 10 ^ 9

Where ‘T’ is the number of test cases, ‘N’ is the size of the array and ‘ARR[i]’ is the size of the array elements.

Time Limit: 1 sec

Sample Input 1:

Sample Output 1:

4 3 2 1
4 3 3 2 2

Explanation for sample input 1:

Test case 1:
Already explained in the question.

Test case 2:
Minimums of window size 1 = min(3), min(3), min(4), min(2), min(4) = 3, 3, 4, 2, 4
Maximum among (3, 3, 4, 2, 4) is 4

Minimums of window size 2 = min(3,3), min(3,4), min(4,2), min(2,4) = 3, 3, 2, 2
Maximum among (3, 3, 2, 2) is 3

Minimums of window size 3 = min(3,3,4), min(3,4,2), min(4,2,4) = 3, 2, 2
Maximum among (3, 2, 2) is 3

Minimums of window size 4 = min(3,3,4,2), min(3,4,2,4) = 2, 2
Maximum among (2, 2) is 2

Minimums of window size 4 = min(3,3,4,2,4) = 2
Maximum among them is 2
The output array should be [4,3,3,2,2].

Sample Input 2:

2
5 
45 -2 42 5 -11 
6 
-2 12 -1 1 20 1

Sample Output 2:

 45 5 -2 -2 -11
 20 1  1 -1 -1 -2

Console