Minimum Path Sum in Grid in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the goal of the Minimum Path Sum problem in a grid?

To find the path from the top-left corner to the bottom-right corner of a grid that has the smallest sum of all numbers along the path, moving only down or right.

beginner

Which moves are allowed when finding the minimum path sum in a grid?

You can only move either one step down or one step right at any point in the grid.

intermediate

How can dynamic programming help solve the Minimum Path Sum problem?

Dynamic programming stores the minimum path sums for each cell based on previously computed cells, avoiding repeated calculations and efficiently finding the overall minimum path sum.

beginner

What is the base case when using dynamic programming for the Minimum Path Sum problem?

The base case is the top-left cell itself, where the minimum path sum is just the value of that cell because it is the starting point.

intermediate

How do you compute the minimum path sum for a cell not in the first row or first column?

Take the minimum of the path sums from the cell above and the cell to the left, then add the current cell's value.

In the Minimum Path Sum problem, which directions can you move?

A Diagonally

B Down or Right

C Up or Left

D Any direction

You can only move down or right to find the minimum path sum.

What is the minimum path sum for the starting cell (top-left corner)?

A The value of the starting cell

B 0

C The sum of all cells

D Infinity

The starting cell's minimum path sum is its own value.

Which technique is commonly used to solve the Minimum Path Sum problem efficiently?

A Dynamic programming

B Brute force recursion

C Greedy algorithm

D Sorting

Dynamic programming avoids repeated calculations by storing intermediate results.

How do you calculate the minimum path sum for a cell in the middle of the grid?

A Only consider the cell above

B Add the current cell value to the maximum of the sums from the cell above and the cell to the left

C Add the current cell value to the sum of the cells diagonally

D Add the current cell value to the minimum of the sums from the cell above and the cell to the left

You take the minimum of the two possible previous paths and add the current cell's value.

What is the time complexity of the dynamic programming solution for Minimum Path Sum in an m x n grid?

A O(m^2 * n^2)

B O(m + n)

C O(m * n)

D O(1)

The solution visits each cell once, so time complexity is proportional to the number of cells.

Explain how to use dynamic programming to find the minimum path sum in a grid.

Think about building the solution step by step from the start.

Describe the base cases and how to fill the first row and first column in the Minimum Path Sum problem.

Consider how you can only move right in the first row and only down in the first column.