在nxn的二维数组中查找局部最大值

def find_local_maximum(arr, start_row, end_row, start_col, end_col):
    mid_row = (start_row + end_row) // 2
    mid_col = (start_col + end_col) // 2

    max_val = arr[mid_row][mid_col]
    max_row = mid_row
    max_col = mid_col

    # 检查中间元素是否是局部最大值
    if (mid_row == start_row or arr[mid_row][mid_col] > arr[mid_row-1][mid_col]) and \
       (mid_row == end_row or arr[mid_row][mid_col] > arr[mid_row+1][mid_col]) and \
       (mid_col == start_col or arr[mid_row][mid_col] > arr[mid_row][mid_col-1]) and \
       (mid_col == end_col or arr[mid_row][mid_col] > arr[mid_row][mid_col+1]):
        return (max_val, max_row, max_col)

    # 在相应的区域中继续查找局部最大值
    if mid_row > start_row and arr[mid_row][mid_col] < arr[mid_row-1][mid_col]:
        max_val, max_row, max_col = find_local_maximum(arr, start_row, mid_row-1, start_col, end_col)
    elif mid_row < end_row and arr[mid_row][mid_col] < arr[mid_row+1][mid_col]:
        max_val, max_row, max_col = find_local_maximum(arr, mid_row+1, end_row, start_col, end_col)
    elif mid_col > start_col and arr[mid_row][mid_col] < arr[mid_row][mid_col-1]:
        max_val, max_row, max_col = find_local_maximum(arr, start_row, end_row, start_col, mid_col-1)
    elif mid_col < end_col and arr[mid_row][mid_col] < arr[mid_row][mid_col+1]:
        max_val, max_row, max_col = find_local_maximum(arr, start_row, end_row, mid_col+1, end_col)

    return (max_val, max_row, max_col)

# 示例用法
arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
max_val, max_row, max_col = find_local_maximum(arr, 0, len(arr)-1, 0, len(arr[0])-1)
print("局部最大值:", max_val)
print("所在位置: 第", max_row+1, "行, 第", max_col+1, "列")