How do you solve Range Sum of Sorted Subarray Sums on LeetCode?

Range Sum of Sorted Subarray Sums (LeetCode #1508) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n² log n) time complexity and O(n²) space complexity. Key insight: Using prefix sums can significantly reduce the time taken to compute subarray sums.

What is the time complexity of Range Sum of Sorted Subarray Sums?

The optimal solution for Range Sum of Sorted Subarray Sums runs in O(n² log n) time and uses O(n²) space. The time complexity is O(n² log n) due to the sorting of subarray sums, while the space complexity remains O(n²) for storing these sums.

What is the brute force solution for Range Sum of Sorted Subarray Sums?

The brute force approach for Range Sum of Sorted Subarray Sums is Brute Force, with O(n²) time complexity and O(n²) space complexity. We can generate all possible subarrays, compute their sums, and then sort these sums to find the desired range. This approach is straightforward but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n² log n).

What algorithm or data structure is used to solve Range Sum of Sorted Subarray Sums?

Range Sum of Sorted Subarray Sums uses the following concepts: Array, Two Pointers, Binary Search, Sorting, Prefix Sum. The recommended patterns to study are: Prefix Sum, Heap.

What are the interview tips for Range Sum of Sorted Subarray Sums?

Always clarify the constraints and expected output format. Discuss your thought process aloud to showcase your problem-solving skills. Consider edge cases, such as the smallest and largest possible inputs.

What are common mistakes when solving Range Sum of Sorted Subarray Sums?

Not considering the modulo operation when summing up results. Overlooking the need to sort the subarray sums before accessing them.

#1508

Range Sum of Sorted Subarray Sums

Medium

ArrayTwo PointersBinary SearchSortingPrefix SumPrefix SumHeap

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n² log n)Space O(n²)

Instead of generating all subarrays and sorting, we can use a prefix sum array to efficiently compute subarray sums and then use a min-heap to maintain the smallest sums in sorted order.

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Algorithm

4 steps

1Step 1: Create a prefix sum array to store cumulative sums of the original array.
2Step 2: Use a min-heap to keep track of the smallest subarray sums as we iterate through the prefix sums.
3Step 3: For each prefix sum, compute all possible subarray sums ending at that index and add them to the heap.
4Step 4: Extract the smallest sums from the heap until we reach the right index, summing them as we go.

solution.py18 lines

1import heapq
2
3def rangeSum(nums, left, right):
4    n = len(nums)
5    prefix_sum = [0] * (n + 1)
6    for i in range(n):
7        prefix_sum[i + 1] = prefix_sum[i] + nums[i]
8    min_heap = []
9    for i in range(n):
10        for j in range(i + 1, n + 1):
11            subarray_sum = prefix_sum[j] - prefix_sum[i]
12            heapq.heappush(min_heap, subarray_sum)
13    result = 0
14    for _ in range(left - 1):
15        heapq.heappop(min_heap)
16    for _ in range(right - left + 1):
17        result = (result + heapq.heappop(min_heap)) % (10**9 + 7)
18    return result

ℹ

Complexity note: The time complexity is O(n² log n) due to the sorting of subarray sums, while the space complexity remains O(n²) for storing these sums.

1Using prefix sums can significantly reduce the time taken to compute subarray sums.
2Sorting the sums allows for efficient retrieval of the desired range.

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