Is Sum of Increasing Product Blocks easy or hard?

The problem is typically classified as Medium because the logic is simple but requires recognizing the increasing block pattern. Once the simulation strategy is clear, the implementation becomes straightforward with linear time and constant space.

Sum of Increasing Product Blocks Python/Java solution

Most implementations follow the same structure: iterate through the array while increasing the block size after each segment, compute the product of elements inside the block, and accumulate the result. This logic translates directly across Python, Java, C++, Go, and TypeScript with identical O(n) complexity.

How to solve Sum of Increasing Product Blocks in O(n)?

Maintain a pointer to the current index and a variable representing the current block size. Multiply the next k elements to form the block product, add it to the result, move the pointer forward, and increase k. Because the pointer only moves forward and never revisits elements, the total runtime stays linear.

What is the best approach for Sum of Increasing Product Blocks?

The most efficient solution uses direct simulation. Iterate through the elements while increasing the block size from 1 upward. For each block, compute the product of its elements and add it to the total. This processes every element once, giving O(n) time complexity and O(1) extra space.

Is Sum of Increasing Product Blocks asked at Google/Amazon/Meta?

Problems based on increasing patterns, block processing, and arithmetic simulation frequently appear in interviews at large companies like Amazon, Google, and Meta. While the exact title may vary, the underlying technique—simulating structured sequences efficiently—is a common interview theme.

What data structure is used in Sum of Increasing Product Blocks?

The solution primarily relies on simple variables and sequential traversal rather than complex data structures. A pointer or index tracks the current position, and integers track the block size and running product. The focus is on simulation and arithmetic reasoning rather than specialized containers.

What is the time complexity of Sum of Increasing Product Blocks?

The optimal simulation approach runs in O(n) time because each element is visited exactly once while forming the increasing blocks. Only a few counters and a running product are stored, so the space complexity is O(1). A naive implementation that repeatedly recomputes products can degrade to O(n^2).

3792. Sum of Increasing Product Blocks - Practice Online

You are given an integer n.

A sequence is formed as follows:

The 1^st block contains 1.
The 2^nd block contains 2 * 3.
The i^th block is the product of the next i consecutive integers.

Let F(n) be the sum of the first n blocks.

Return an integer denoting F(n) modulo 10⁹ + 7.

Example 1:

Input: n = 3

Output: 127

Explanation:

Block 1: 1
Block 2: 2 * 3 = 6
Block 3: 4 * 5 * 6 = 120

F(3) = 1 + 6 + 120 = 127

Example 2:

Input: n = 7

Output: 6997165

Explanation:

Block 1: 1
Block 2: 2 * 3 = 6
Block 3: 4 * 5 * 6 = 120
Block 4: 7 * 8 * 9 * 10 = 5040
Block 5: 11 * 12 * 13 * 14 * 15 = 360360
Block 6: 16 * 17 * 18 * 19 * 20 * 21 = 39070080
Block 7: 22 * 23 * 24 * 25 * 26 * 27 * 28 = 5967561600

F(7) = 6006997207 % (10⁹ + 7) = 6997165

Constraints:

1 <= n <= 1000