Minimum Path Sum in Grid in DSA Typescript - 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 possible 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?

Only moves to the right or moves down are allowed at each step.

intermediate

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

By storing the minimum path sums to each cell, we avoid recalculating paths multiple times, building the solution from the top-left to the bottom-right efficiently.

beginner

What is the base case when using dynamic programming for Minimum Path Sum in a grid?

The top-left cell's minimum path sum is its own value because it's the starting point.

intermediate

In the Minimum Path Sum problem, how do you calculate the minimum sum for a cell not in the first row or column?

Take the minimum of the 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 Left and Down

B Left and Up

C Right and Up

D Right and Down

Only moves to the right or down are allowed to find the minimum path sum.

What is the minimum path sum for the starting cell in the grid?

A Zero

B The value of the starting cell

C The sum of all cells in the first row

D The sum of all cells in the first column

The starting cell's minimum path sum is its own value because it is the starting point.

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

A Add the current cell's value to the minimum of the sums from the cell above and the cell to the left

B Add the current cell's value to the sum from the cell above only

C Add the current cell's value to the sum from the cell to the left only

D Add the current cell's value to the maximum of the sums from the cell above and the cell to the left

We choose the smaller sum between the cell above and the cell to the left, then add the current cell's value.

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

A Dynamic Programming

B Brute Force

C Greedy Algorithm

D Divide and Conquer

Dynamic Programming stores intermediate results to avoid repeated calculations.

If the grid is [[1,3,1],[1,5,1],[4,2,1]], what is the minimum path sum?

A 8

B 9

C 7

D 10

The path 1→3→1→1→1 sums to 7, which is the minimum.

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 movement restrictions and why they matter in the Minimum Path Sum problem.

Consider how allowed moves affect possible paths.