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3546. Equal Sum Grid Partition I 👍

  • Time: $O(mn)$
  • Space: $O(mn)$
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class Solution {
 public:
  bool canPartitionGrid(vector<vector<int>>& grid) {
    const long totalSum = accumulate(grid.begin(), grid.end(), 0L,
                                     [](long acc, const vector<int>& row) {
      return acc + accumulate(row.begin(), row.end(), 0L);
    });
    return canPartition(grid, totalSum) ||
           canPartition(transposed(grid), totalSum);
  }

 private:
  bool canPartition(const vector<vector<int>>& lines, long totalSum) {
    long runningSum = 0;
    for (const vector<int>& line : lines) {
      runningSum += accumulate(line.begin(), line.end(), 0L);
      if (runningSum * 2 == totalSum)
        return true;
    }
    return false;
  }

  vector<vector<int>> transposed(const vector<vector<int>>& grid) {
    vector<vector<int>> res(grid[0].size(), vector<int>(grid.size()));
    for (int i = 0; i < grid.size(); ++i)
      for (int j = 0; j < grid[0].size(); ++j)
        res[j][i] = grid[i][j];
    return res;
  }
};

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class Solution {
  public boolean canPartitionGrid(int[][] grid) {
    final long totalSum = Arrays.stream(grid).flatMapToInt(Arrays::stream).asLongStream().sum();
    return canPartition(grid, totalSum) || canPartition(transposed(grid), totalSum);
  }

  private boolean canPartition(int[][] lines, long totalSum) {
    long runningSum = 0;
    for (int[] line : lines) {
      runningSum += Arrays.stream(line).asLongStream().sum();
      if (runningSum * 2 == totalSum)
        return true;
    }
    return false;
  }

  private int[][] transposed(int[][] grid) {
    int[][] res = new int[grid[0].length][grid.length];
    for (int i = 0; i < grid.length; ++i)
      for (int j = 0; j < grid[0].length; ++j)
        res[j][i] = grid[i][j];
    return res;
  }
}

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class Solution:
  def canPartitionGrid(self, grid: list[list[int]]) -> bool:
    totalSum = sum(map(sum, grid))

    def canPartition(grid: list[list[int]]) -> bool:
      runningSum = 0
      for row in grid:
        runningSum += sum(row)
        if runningSum * 2 == totalSum:
          return True
      return False

    return canPartition(grid) or canPartition(zip(*grid))