给定一个包含非负整数的 m x n 网格 grid ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。说明：每次只能向下或者向右移动一步。
示例 1：
输入：grid = [[1,3,1],[1,5,1],[4,2,1]]
输出：7示例 2：
输入：grid = [[1,2,3],[4,5,6]]
输出：12动态规划解法：
1
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53object MinPathSum {
def main(args: Array[String]): Unit = {
println(minPathSum(
Array[Array[Int]](
Array(1, 3, 1),
Array(1, 5, 1),
Array(4, 2, 1)
)))
println(minPathSum(
Array[Array[Int]](
Array(1)
)))
println(minPathSum(
Array[Array[Int]](
Array(1, 2)
)))
println(minPathSum(
Array[Array[Int]](
Array(2),
Array(1)
)))
}
def minPathSum(grid: Array[Array[Int]]): Int = {
val m = grid.length
val n = grid(0).length
val dp = new Array[Array[Int]](m)
for (i <- 0 until m) {
dp(i) = new Array[Int](n)
}
dp(0)(0) = grid(0)(0)
for (i <- 1 until m) {
dp(i)(0) = dp(i - 1)(0) + grid(i)(0)
}
for (i <- 1 until n) {
dp(0)(i) = dp(0)(i - 1) + grid(0)(i)
}
for (i <- 1 until m) {
for (j <- 1 until n) {
dp(i)(j) = Math.min(dp(i - 1)(j), dp(i)(j - 1)) + grid(i)(j)
}
}
dp(m - 1)(n - 1)
}
}