C++ – Elegant way to find closest value in a vector from above

algorithmcstl

I need a function that takes a vector (assumed to be sorted), and a value, and returns the closest number that's [edit] ~~greater than~~ less than or equal to that number, preferably using an algorithm from the STL. I have come up with a solution using std::lower_bound(), but it seems kludgy and ugly:

struct ClosestCmp {
    bool operator()(const int & x, const int & y) { return x > y; }
};

// vec is assumed to be sorted
int closest(const std::vector<int> & vec, int value)
{
    std::vector<int>::const_reverse_iterator cri =
        std::lower_bound(vec.rbegin(), vec.rend(), value, ClosestCmp());
    if (cri != vec.rend()) {
        return *cri;
    }
    return -1;
}

// ...
vec.push_back(1);
vec.push_back(2);
vec.push_back(4);
vec.push_back(5);
std::cout << closest(vec, 2) << "\n"; // Should ouput "2"
std::cout << closest(vec, 3) << "\n"; // Should ouput "2"
std::cout << closest(vec, 4) << "\n"; // Should ouput "4"

Can anyone suggest a way that's more elegant, maybe using an STL algorithm without needing a comparison function or a reverse iterator? I have looked in the STL, but haven't been able to find a better solution than this.

Best Answer

For reminder:

std::lower_bound: returns the first value that does not compare less
std::upper_bound: returns the first value that compares strictly greater

From your description, std::lower_bound already looks like the perfect fit, what is wrong with:

int closest(std::vector<int> const& vec, int value) {
    auto const it = std::lower_bound(vec.begin(), vec.end(), value);
    if (it == vec.end()) { return -1; }

    return *it;
}

Which is used as:

int main() {
    std::vector<int> vec;
    vec.push_back(2);
    vec.push_back(4);

    std::cout << closest(vec, 2) << "\n";
    std::cout << closest(vec, 3) << "\n";
    std::cout << closest(vec, 4) << "\n";
}

Output:

2
4
4

Related Solutions

Sql – the most efficient/elegant way to parse a flat table into a tree

Now that MySQL 8.0 supports recursive queries, we can say that all popular SQL databases support recursive queries in standard syntax.

WITH RECURSIVE MyTree AS (
    SELECT * FROM MyTable WHERE ParentId IS NULL
    UNION ALL
    SELECT m.* FROM MyTABLE AS m JOIN MyTree AS t ON m.ParentId = t.Id
)
SELECT * FROM MyTree;

I tested recursive queries in MySQL 8.0 in my presentation Recursive Query Throwdown in 2017.

Below is my original answer from 2008:

There are several ways to store tree-structured data in a relational database. What you show in your example uses two methods:

Adjacency List (the "parent" column) and
Path Enumeration (the dotted-numbers in your name column).

Another solution is called Nested Sets, and it can be stored in the same table too. Read "Trees and Hierarchies in SQL for Smarties" by Joe Celko for a lot more information on these designs.

I usually prefer a design called Closure Table (aka "Adjacency Relation") for storing tree-structured data. It requires another table, but then querying trees is pretty easy.

I cover Closure Table in my presentation Models for Hierarchical Data with SQL and PHP and in my book SQL Antipatterns: Avoiding the Pitfalls of Database Programming.

CREATE TABLE ClosureTable (
  ancestor_id   INT NOT NULL REFERENCES FlatTable(id),
  descendant_id INT NOT NULL REFERENCES FlatTable(id),
  PRIMARY KEY (ancestor_id, descendant_id)
);

Store all paths in the Closure Table, where there is a direct ancestry from one node to another. Include a row for each node to reference itself. For example, using the data set you showed in your question:

INSERT INTO ClosureTable (ancestor_id, descendant_id) VALUES
  (1,1), (1,2), (1,4), (1,6),
  (2,2), (2,4),
  (3,3), (3,5),
  (4,4),
  (5,5),
  (6,6);

Now you can get a tree starting at node 1 like this:

SELECT f.* 
FROM FlatTable f 
  JOIN ClosureTable a ON (f.id = a.descendant_id)
WHERE a.ancestor_id = 1;

The output (in MySQL client) looks like the following:

+----+
| id |
+----+
|  1 | 
|  2 | 
|  4 | 
|  6 | 
+----+

In other words, nodes 3 and 5 are excluded, because they're part of a separate hierarchy, not descending from node 1.

Re: comment from e-satis about immediate children (or immediate parent). You can add a "path_length" column to the ClosureTable to make it easier to query specifically for an immediate child or parent (or any other distance).

INSERT INTO ClosureTable (ancestor_id, descendant_id, path_length) VALUES
  (1,1,0), (1,2,1), (1,4,2), (1,6,1),
  (2,2,0), (2,4,1),
  (3,3,0), (3,5,1),
  (4,4,0),
  (5,5,0),
  (6,6,0);

Then you can add a term in your search for querying the immediate children of a given node. These are descendants whose path_length is 1.

SELECT f.* 
FROM FlatTable f 
  JOIN ClosureTable a ON (f.id = a.descendant_id)
WHERE a.ancestor_id = 1
  AND path_length = 1;

+----+
| id |
+----+
|  2 | 
|  6 | 
+----+

Re comment from @ashraf: "How about sorting the whole tree [by name]?"

Here's an example query to return all nodes that are descendants of node 1, join them to the FlatTable that contains other node attributes such as name, and sort by the name.

SELECT f.name
FROM FlatTable f 
JOIN ClosureTable a ON (f.id = a.descendant_id)
WHERE a.ancestor_id = 1
ORDER BY f.name;

Re comment from @Nate:

SELECT f.name, GROUP_CONCAT(b.ancestor_id order by b.path_length desc) AS breadcrumbs
FROM FlatTable f 
JOIN ClosureTable a ON (f.id = a.descendant_id) 
JOIN ClosureTable b ON (b.descendant_id = a.descendant_id) 
WHERE a.ancestor_id = 1 
GROUP BY a.descendant_id 
ORDER BY f.name

+------------+-------------+
| name       | breadcrumbs |
+------------+-------------+
| Node 1     | 1           |
| Node 1.1   | 1,2         |
| Node 1.1.1 | 1,2,4       |
| Node 1.2   | 1,6         |
+------------+-------------+

A user suggested an edit today. SO moderators approved the edit, but I am reversing it.

The edit suggested that the ORDER BY in the last query above should be ORDER BY b.path_length, f.name, presumably to make sure the ordering matches the hierarchy. But this doesn't work, because it would order "Node 1.1.1" after "Node 1.2".

If you want the ordering to match the hierarchy in a sensible way, that is possible, but not simply by ordering by the path length. For example, see my answer to MySQL Closure Table hierarchical database - How to pull information out in the correct order.

C++ – Best way to extract a subvector from a vector

vector<T>::const_iterator first = myVec.begin() + 100000;
vector<T>::const_iterator last = myVec.begin() + 101000;
vector<T> newVec(first, last);

It's an O(N) operation to construct the new vector, but there isn't really a better way.

Best Answer

Related Solutions

Sql – the most efficient/elegant way to parse a flat table into a tree

C++ – Best way to extract a subvector from a vector

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