LeetCode-in-All

64. Minimum Path Sum

Medium

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

Note: You can only move either down or right at any point in time.

Example 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]

Output: 7

Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]

Output: 12

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 200
• 0 <= grid[i][j] <= 100

Solution

class Solution {
  int minPathSum(List<List<int>> grid) {
    int m = grid.length;
    int n = grid[0].length;

    List<int> pathSum = List.filled(n, 100000);
    pathSum[0] = 0;

    for (int y = 0; y < m; y++) {
      for (int x = 0; x < n; x++) {
        pathSum[x] =
            (x > 0 ? min(pathSum[x], pathSum[x - 1]) : pathSum[x]) + grid[y][x];
      }
    }
    return pathSum[n - 1];
  }
}

int min(int a, int b) {
  if (a < b) {
    return a;
  }
  return b;
}

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