In this matrix-based problem, you are given a 2D grid of integers. Your task is to make each column strictly increasing from top to bottom. In one operation, you can increment any element of the grid by 1. The goal is to find the minimum number of increments needed to satisfy the strictly increasing condition for all columns independently.
IBM and other enterprise companies ask this to evaluate basic matrix traversal skills and a candidate's understanding of Greedy algorithms. It's an "Easy" level problem that checks if you can correctly navigate rows and columns and apply a simple constraint: each element must be at least one greater than the element directly above it.
The pattern is a simple Greedy approach. Since we want the minimum operations, for each element grid[r][c], we should only increment it if it is not already greater than grid[r-1][c]. If it's smaller or equal, we must increase it to exactly grid[r-1][c] + 1. This greedy choice at each step ensures we use the fewest increments possible to satisfy the condition for the current element without affecting future elements more than necessary.
Matrix:
[[3, 2]
[1, 3]]
Column 0: [3, 1]. Element 1 must be > 3. Target = 4. Operations = 4 - 1 = 3.
Column 1: [2, 3]. 3 is already > 2. Operations = 0.
Total operations = 3 + 0 = 3.
Candidates sometimes try to compare elements across rows or diagonals, forgetting that the condition only applies to columns. Another mistake is failing to update the element in the grid after calculating the operations; if you don't update grid[r][c] to its new value, the calculation for grid[r+1][c] will be wrong. Using an extra matrix for tracking is also a common unnecessary overhead.
Practice nested loops for matrix traversal. Make sure you are comfortable switching between row-major and column-major orders. For "minimum increment" problems, always remember the greedy rule: "Just enough to satisfy the condition." This logic applies to many array problems where you need to make elements non-decreasing or strictly increasing.
| Title | Difficulty | Topics | LeetCode |
|---|---|---|---|
| Find Valid Matrix Given Row and Column Sums | Medium | Solve | |
| Max Increase to Keep City Skyline | Medium | Solve | |
| Maximum Matrix Sum | Medium | Solve | |
| Reconstruct a 2-Row Binary Matrix | Medium | Solve | |
| Largest Submatrix With Rearrangements | Medium | Solve |
