Math for coding interviews/DP tables - filling a grid
DP Tables: Filling the Grid, Step by Step
Bottom-up DP builds a table where each cell depends only on cells you have already filled. You fill the table from small subproblems to large ones. The answer is usually in the last cell. The table size determines the space and time complexity.
See it for yourself
A grid with rows and columns. Cells fill in from top-left to bottom-right. Arrows show which earlier cells each new cell depends on. The bottom-right corner holds the final answer.
DP tables - filling a grid
Bottom-up DP builds a table where each cell depends only on cells you have already filled. You fill the table from small subproblems to large ones. The answer is usually in the last cell. The table size determines the space and time complexity.
Think of it this way: Building a staircase from the ground up. You cannot place the 10th step until the 9th is stable. Each step depends on the ones below it.
For algorithms: The DP table makes the recurrence relation (the mathematical relationship between subproblems) visible and concrete. Seeing it as a grid helps spot the pattern.
Real-world analogy
Building a staircase from the ground up. You cannot place the 10th step until the 9th is stable. Each step depends on the ones below it.
Why it matters in interviews
The DP table makes the recurrence relation (the mathematical relationship between subproblems) visible and concrete. Seeing it as a grid helps spot the pattern.