How do you solve Count the Hidden Sequences on LeetCode?

Count the Hidden Sequences (LeetCode #2145) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The differences array allows us to derive the entire hidden sequence from any starting point.

What is the time complexity of Count the Hidden Sequences?

The optimal solution for Count the Hidden Sequences runs in O(n) time and uses O(1) space. The time complexity is O(n) because we only make a single pass through the differences array to compute min_sum and max_sum.

What is the brute force solution for Count the Hidden Sequences?

The brute force approach for Count the Hidden Sequences is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves trying every possible starting value for the hidden sequence and checking if the resulting sequence meets the difference requirements and falls within the specified bounds. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Count the Hidden Sequences?

Count the Hidden Sequences uses the following concepts: Array, Prefix Sum. The recommended patterns to study are: Prefix Sum, Cumulative Sum.

What are the interview tips for Count the Hidden Sequences?

Always consider edge cases, such as when the differences lead to values outside the bounds. Practice deriving relationships between elements in sequences to identify patterns. Be prepared to optimize your initial brute-force solution by recognizing patterns in the problem.

What are common mistakes when solving Count the Hidden Sequences?

Failing to check if all elements of the hidden sequence are within bounds in the brute-force approach. Not recognizing that the starting point can be derived from the min and max sums in the optimal approach.

#2145

Count the Hidden Sequences

Medium

ArrayPrefix SumPrefix SumCumulative Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

Instead of checking every possible starting value, we can calculate the minimum and maximum possible values of the hidden sequence based on the differences. This allows us to directly compute how many valid starting values exist within the bounds.

⚙️

Algorithm

4 steps

1Step 1: Initialize min_sum and max_sum to 0, which will track the cumulative sum of differences.
2Step 2: Iterate through the differences array, updating min_sum and max_sum based on the current difference.
3Step 3: Calculate the range of valid starting values as [lower - min_sum, upper - max_sum].
4Step 4: The count of valid starting values is the maximum of 0 and the difference between the upper and lower bounds of valid starting values.

solution.py13 lines

1# Full working Python code
2
3def count_hidden_sequences(differences, lower, upper):
4    min_sum = 0
5    max_sum = 0
6    current_sum = 0
7    for diff in differences:
8        current_sum += diff
9        min_sum = min(min_sum, current_sum)
10        max_sum = max(max_sum, current_sum)
11    valid_lower = lower - min_sum
12    valid_upper = upper - max_sum
13    return max(0, valid_upper - valid_lower + 1)

ℹ

Complexity note: The time complexity is O(n) because we only make a single pass through the differences array to compute min_sum and max_sum.

1The differences array allows us to derive the entire hidden sequence from any starting point.
2The range of possible starting points can be calculated directly from the minimum and maximum sums of the differences.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.