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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

function minPathSum(grid: number[][]): number {
    let [m, n] = [grid.length, grid[0].length]
    let prev = new Array(n + 1).fill(Infinity)
    let cur = new Array(n + 1).fill(0)
    for (let i = 0; i < m; i++) {
        for (let j = 0; j < n; j++) {
            cur[j + 1] = Math.min(prev[j + 1], cur[j]) + grid[i][j]
        }
        prev = cur
        cur = new Array(n + 1)
        cur[0] = Infinity
    }
    return prev[n]
}

export { minPathSum }

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