How do you solve Range Sum Query - Immutable on LeetCode?

Range Sum Query - Immutable (LeetCode #303) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using a prefix sum array drastically reduces the time complexity for multiple queries.

What is the time complexity of Range Sum Query - Immutable?

The optimal solution for Range Sum Query - Immutable runs in O(n) time and uses O(n) space. The time complexity for building the prefix sum array is O(n), and each query is O(1), making it efficient for multiple queries.

What is the brute force solution for Range Sum Query - Immutable?

The brute force approach for Range Sum Query - Immutable is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves calculating the sum for each query by iterating through the specified range in the array. This is straightforward but inefficient for large arrays or many queries. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Range Sum Query - Immutable?

Range Sum Query - Immutable uses the following concepts: Array, Design, Prefix Sum. The recommended patterns to study are: Prefix Sum, Array.

What are the interview tips for Range Sum Query - Immutable?

Always consider the constraints and the number of queries when choosing an approach. Explain your thought process clearly to the interviewer. Practice implementing both brute force and optimized solutions.

What are common mistakes when solving Range Sum Query - Immutable?

Not initializing the prefix sum array correctly. Confusing the indices when calculating the sum using the prefix array.

#303

Range Sum Query - Immutable

Easy

ArrayDesignPrefix SumPrefix SumArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

Using a prefix sum array allows us to compute the sum of any subarray in constant time after an initial setup phase. This is efficient for handling multiple queries.

⚙️

Algorithm

3 steps

1Step 1: Create a prefix sum array where each element at index i contains the sum of the elements from the start of the array to index i.
2Step 2: For each sumRange query, compute the sum using the prefix sums: sum = prefix[right + 1] - prefix[left].
3Step 3: Return the computed sum.

solution.py7 lines

1class NumArray:
2    def __init__(self, nums):
3        self.prefix = [0] * (len(nums) + 1)
4        for i in range(len(nums)):
5            self.prefix[i + 1] = self.prefix[i] + nums[i]
6    def sumRange(self, left: int, right: int) -> int:
7        return self.prefix[right + 1] - self.prefix[left]

ℹ

Complexity note: The time complexity for building the prefix sum array is O(n), and each query is O(1), making it efficient for multiple queries.

1Using a prefix sum array drastically reduces the time complexity for multiple queries.
2Understanding the difference between a brute force and an optimized approach is crucial.

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