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Minimum Cost to cross Grid

MEDIUM

30 mins

4 upvotes

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Dynamic Programming

Greedy

Matrices (2D Arrays)

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Problem

Submissions

Minimum Cost to cross Grid

Contributed by

Yash_5830

Medium

0/80

Avg time to solve 30 mins

Success Rate 70 %

4 upvotes

Problem Statement

You are given a 2 - D grid having ‘N’ rows and ‘M’ columns. Each cell of the grid has an integer value written on it which denotes the cost it takes to pass through that cell. You are currently present at the Top-Left cell (0,0) and you want to reach the Bottom-Right cell (N - 1, M - 1). To do so, you start moving from the Top-Left cell and move through any of the adjacent cells until you reach the Bottom-Right cell. The total cost of the path will be the sum of the costs of all the cells that you have passed through in the path.

Given the cost of each cell in a 2 - D matrix 'MAT', your task is to find the minimum total cost that you need to spend to reach the Bottom-Right cell if you are starting from the Top-Left cell.

Note:

1) From any cell you can move UP, DOWN, LEFT, or RIGHT.

2) You cannot move out of the grid.

Detailed explanation ( Input/output format, Notes, Constraints, Images )

Input Format :

The first line of the input 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', denoting the number of rows and columns in the grid respectively.

Each of the next 'N' lines contains 'M' space-separated integers denoting the cell values of the grid.

Output Format :

For each test case, print a single line containing a single integer denoting the minimum total cost that you need to spend to reach the Bottom-Right cell if you are starting from the Top-Left cell.

The output of each test case will be printed in a separate line.

Note:

You are not required to print the expected output. it has already been taken care of. Just implement the function.

Constraints :

1 <= T <= 10
1 <= N <= 200
1 <= M <= 200
1 <= MAT[i][j] <= 10 ^ 4

Where 'MAT[i][j]' denotes the element present at the 'i'th' row and the 'j'th' column of the matrix 'MAT'.

Time limit: 1 sec.

Sample Input 1 :

Sample output 1 :

8
8

Explanation of Sample output 1 :

For the first test case, the path (0,0) => (0,1) => (0,2) => (1,2) => (2,2) has the minimum total cost, i.e, 8. Hence, the answer is 8 in this case.

For the second test case, the path (0,0) => (0,1) => (1,1)  has the minimum total cost, i.e, 8. Hence, the answer is 8 in this case.

Sample Input 2 :

Sample output 2 :

10
16

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