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Minimum Path Sum

Easy

Given a m x n grid filled with non-negative integers, find a path from the top-left corner to the bottom-right corner that minimizes the sum of all numbers along its path.

You can only move:

  • Right
  • Down

Return the minimum path sum.

Example 1

Input

m = 3
n = 3
grid =
[
    [1, 3, 1],
    [1, 5, 1],
    [4, 2, 1]
]

Output

7

Explanation

The minimum path is:

1 → 3 → 1 → 1 → 1

 

Therefore:

1 + 3 + 1 + 1 + 1 = 7

Example 2

Input

m = 2
n = 3
grid =
[
    [1, 2, 3],
    [4, 5, 6]
]

Output

12

Explanation

The minimum path is:

1 → 2 → 3 → 6

 

Therefore:

1 + 2 + 3 + 6 = 12

Constraints

1 <= m
n <= 200
0 <= grid[i][j] <= 200
You can only move right or down.

Hints:

Hint 1

For each cell, the minimum path to reach it comes from either:

  • The cell above
  • The cell to the left
Hint 2

Use:

dp[i][j] = grid[i][j] + min(dp[i-1][j], dp[i][j-1])

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Input

Expected Output