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The algorithm pattern we'll learn today appears in countless other problems. Master it here, and you'll unlock solutions to many more challenges.

Today we will cover:

• Minimum Path Sum

• Data Compaction in LSM Trees

Read time: under 4 minutes

CODING CHALLENGE

Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output: 7
Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]
Output: 12

Solve the problem here before reading the solution.

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SOLUTION

To solve this problem, we'll use dynamic programming. We'll create a 2D array to store the minimum path sum for each cell. The solution works as follows:

1. Create a DP table with the same dimensions as the input grid.

2. Initialize the first cell, first row, and first column.

3. For each cell, calculate the minimum path sum by adding the current cell's value to the minimum of the paths from above or left.

4. The bottom-right cell will contain the minimum path sum from top-left to bottom-right.

Time complexity is O(m*n), where m and n are the dimensions of the grid. Space complexity is also O(m*n).

SYSTEM DESIGN

Data Compaction in LSM Trees

NOTE: If you don’t know what an LSM Tree is, please read the System Design topic here before moving forward.

When databases use LSM Trees to write data, they create multiple small files called SSTables. Over time, these files accumulate and slow down read operations because the database needs to check many files to find data. This is where compaction comes in.

Compaction is the process of combining multiple SSTables into a single, larger SSTable. During compaction, the database merges these files while removing duplicates and deleted entries.

There are two main compaction strategies: Size-tiered and Leveled compaction.

Size-tiered compaction groups SSTables of similar sizes together. When enough SSTables of a similar size exist, they're merged into a larger SSTable. This process continues, creating increasingly larger SSTables. This strategy works well for write-heavy workloads because it minimizes write amplification (how many times data is rewritten).

Leveled compaction organizes SSTables into levels, with each level being larger than the previous one. Level 0 contains the newest data, and when it gets full, some data is merged into Level 1. This continues through multiple levels, with each level being about 10 times larger than the previous one. This approach provides better read performance because there's less overlap between SSTables.

Here's how both strategies compare:

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