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Minimum Cost Path
Hard Accuracy: 33.51% Submissions: 1917 Points: 8

Given a square grid of size N, each cell of which contains integer cost which represents a cost to traverse through that cell, we need to find a path from top left cell to bottom right cell by which the total cost incurred is minimum.

Note: It is assumed that negative cost cycles do not exist in the input matrix.

Input:
The first line of input will contain the number of test cases T. Then T test cases follow. Each test case contains 2 lines. The first line of each test case contains an integer N denoting the size of the grid. The next line of each test contains a single line containing N*N space separated integers depicting the cost of the respective cells from (0, 0) to (N - 1, N - 1).

Output:
For each testcase, in a new line, print the minimum cost to reach bottom right cell from top left cell.

Your Task:
Complete shortest() function which takes a N*N grid and N as input parameters and returns a single integer depicting the minimum cost to reach the destination.
Expected Time Complexity: O(N * N * log N).
Expected Auxiliary Space: O(N * N).

Constraints:
1 <= T <= 50
1 <= N <= 1000
1 <= cost of cells <= 106

Example:
Input:

2
5
31 100 65 12 18 10 13 47 157 6 100 113 174 11 33 88 124 41 20 140 99 32 111 41 20
2
42 93 7 14

Output:
327
63

Explanation:
Testcase 1:

Grid is:
 31,   100,   65,   12,   18,
 10,    13,    47,  157,   6,
100,  113,  174,   11,   33,
 88,   124,   41,    20,  140,
 99,    32,   111,   41,   20

A cost grid is given in above diagram, minimum
cost to reach bottom right from top left
is 327 (31 + 10 + 13 + 47 + 65 + 12 + 18 + 6 + 33 + 11 + 20 + 41 + 20)
Testcase 2:
Grid is:
42 93
07 14
A cost grid is given in above diagram, minimum
cost to reach bottom right from top left
is 63(42+7+14)

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Minimum Cost Path

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