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发布于 2024-06-17 01:03:33 字数 4422 浏览 0 评论 0 收藏 0

931. Minimum Falling Path Sum

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Description

Given an n x n array of integers matrix, return _the minimum sum of any falling path through_ matrix.

A falling path starts at any element in the first row and chooses the element in the next row that is either directly below or diagonally left/right. Specifically, the next element from position (row, col) will be (row + 1, col - 1), (row + 1, col), or (row + 1, col + 1).

 

Example 1:

Input: matrix = [[2,1,3],[6,5,4],[7,8,9]]
Output: 13
Explanation: There are two falling paths with a minimum sum as shown.

Example 2:

Input: matrix = [[-19,57],[-40,-5]]
Output: -59
Explanation: The falling path with a minimum sum is shown.

 

Constraints:

  • n == matrix.length == matrix[i].length
  • 1 <= n <= 100
  • -100 <= matrix[i][j] <= 100

Solutions

Solution 1

class Solution:
  def minFallingPathSum(self, matrix: List[List[int]]) -> int:
    n = len(matrix)
    f = [0] * n
    for row in matrix:
      g = [0] * n
      for j, x in enumerate(row):
        l, r = max(0, j - 1), min(n, j + 2)
        g[j] = min(f[l:r]) + x
      f = g
    return min(f)
class Solution {
  public int minFallingPathSum(int[][] matrix) {
    int n = matrix.length;
    var f = new int[n];
    for (var row : matrix) {
      var g = f.clone();
      for (int j = 0; j < n; ++j) {
        if (j > 0) {
          g[j] = Math.min(g[j], f[j - 1]);
        }
        if (j + 1 < n) {
          g[j] = Math.min(g[j], f[j + 1]);
        }
        g[j] += row[j];
      }
      f = g;
    }
    // return Arrays.stream(f).min().getAsInt();
    int ans = 1 << 30;
    for (int x : f) {
      ans = Math.min(ans, x);
    }
    return ans;
  }
}
class Solution {
public:
  int minFallingPathSum(vector<vector<int>>& matrix) {
    int n = matrix.size();
    vector<int> f(n);
    for (auto& row : matrix) {
      auto g = f;
      for (int j = 0; j < n; ++j) {
        if (j) {
          g[j] = min(g[j], f[j - 1]);
        }
        if (j + 1 < n) {
          g[j] = min(g[j], f[j + 1]);
        }
        g[j] += row[j];
      }
      f = move(g);
    }
    return *min_element(f.begin(), f.end());
  }
};
func minFallingPathSum(matrix [][]int) int {
  n := len(matrix)
  f := make([]int, n)
  for _, row := range matrix {
    g := make([]int, n)
    copy(g, f)
    for j, x := range row {
      if j > 0 {
        g[j] = min(g[j], f[j-1])
      }
      if j+1 < n {
        g[j] = min(g[j], f[j+1])
      }
      g[j] += x
    }
    f = g
  }
  return slices.Min(f)
}
function minFallingPathSum(matrix: number[][]): number {
  const n = matrix.length;
  const f: number[] = new Array(n).fill(0);
  for (const row of matrix) {
    const g = f.slice();
    for (let j = 0; j < n; ++j) {
      if (j > 0) {
        g[j] = Math.min(g[j], f[j - 1]);
      }
      if (j + 1 < n) {
        g[j] = Math.min(g[j], f[j + 1]);
      }
      g[j] += row[j];
    }
    f.splice(0, n, ...g);
  }
  return Math.min(...f);
}

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