Minimum Path Sum Problem Statement

Consider a 2-dimensional grid 'GRID' with 'N' rows and 'M' columns in Ninjaland. Each cell in the grid has an associated cost. The goal is to determine the minimum path sum from the top-left to the bottom-right, moving only down or right.

Explanation:

Find a path from top-left (0, 0) to bottom-right ('N'-1, 'M'-1) that minimizes the sum of costs along the path.

Input:

The first line contains an integer 'T' denoting the number of test cases. 
The first line of each test case contains two space-separated integers 'N' and 'M', indicating the grid's dimensions.
The next 'N' lines each contain 'M' space-separated integers, representing the costs for that row.

Output:

For each test case, output the minimum path sum from the top-left to the bottom-right corner of the grid.

Example:

Example input and output have been omitted for brevity. Please refer to test cases to validate functionality.

Constraints:

  • 1 <= T <= 100
  • 1 <= N, M <= 102
  • 1 <= GRID[i][j] <= 105
  • Time limit: 1 sec

Note:

You need to implement the function to compute the result, printing is managed internally.

Follow Up:

Can you solve this problem with an O(1) space complexity solution?
AnswerBot
4mo

The Minimum Path Sum Problem involves finding the minimum sum of costs along a path from the top-left to the bottom-right of a grid.

  • Use dynamic programming to calculate the minimum path sum by conside...read more

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