Consolidated Questions from the Uploaded Images
Question 2: Stable Sub-segments
In an organization, there are n
servers, each with a capacity of capacity[i]
. A contiguous subsegment [l, r]
of servers is said to be stable if:
- The first and last server's capacities are equal to the sum of the capacities of all interior servers:
capacity[l] = capacity[r] = sum[l+1, r-1]
.
Task:
Find the number of stable subsegments of length 3 or more.
Example:
For n = 5
and capacity = [9, 3, 3, 3, 9]
:
Segment | First & Last Capacity | Interior Capacity Sum | Balanced |
---|---|---|---|
[9, 3, 3] | 9 | 6 | No |
[3, 3, 3] | 3 | 3 | Yes |
[3, 3, 9] | 3 | 3 | No |
[9, 3, 3, 3] | 9 | 6 | No |
[3, 3, 3, 9] | 3 | 9 | No |
[9, 3, 3, 3, 9] | 9 | 9 | Yes |
- Stable subsegments are
[3, 3, 3]
and[9, 3, 3, 3, 9]
.
Output:2
Constraints:
- The number of servers,
n
, is between 1 and 300,000. - Each server's capacity,
capacity[i]
, is between 1 and 1,000,000,000.
Input Format for Custom Testing:
- First line: An integer
n
(number of servers). - Second line: A list of
n
integers representing the arraycapacity
.
Output Format:
- An integer representing the number of stable subsegments.
Question 3: Bitwise-OR Goodness
A coding competition organized to hire software developers includes an interesting problem on Bitwise-OR.
The goodness of a sequence is defined as the bitwise-OR of its elements. Given an array arr
of length n
, find all possible distinct values of goodness that can be obtained by choosing any strictly increasing subsequence of the array. The result must be sorted in non-decreasing order.
Example:
Input: n = 4
, arr = [4, 2, 4, 1]
Strictly increasing subsequences and their goodness values:
- Empty subsequence: Goodness = 0
[1]
: Goodness = 1[2]
: Goodness = 2[4]
: Goodness = 4[2, 4]
: Goodness = 6
Output: [0, 1, 2, 4, 6]
Function Description:
Complete the function getDistinctGoodnessValues
in the editor below.
Parameters:
int arr[n]
: An array of integers.
Returns:
int[]
: A list of all possible distinct goodness values.
Constraints:
- The length of the array,
n
, is between 1 and 10,000. - Each element in the array,
arr[i]
, is between 1 and 1,023.
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