C++ Set Operations on Sorted Ranges: set_union, intersection
이 글의 핵심
Run set_union, set_intersection, set_difference, set_symmetric_difference, and includes on sorted ranges — complexity, duplicates, and output iterators.
What are set algorithms?
They implement set operations on sorted ranges (not only std::set): union, intersection, difference, symmetric difference, and subset test includes.
Operations
| Algorithm | Notation | Meaning |
|---|---|---|
set_union | ∪ | All elements from both sets |
set_intersection | ∩ | Elements in both sets |
set_difference | A − B | Elements in A but not in B |
set_symmetric_difference | △ | Elements in exactly one set |
includes | ⊇ | Tests if B ⊆ A |
Requirements
Critical: Both input ranges must be sorted with the same comparator.
The following example demonstrates the concept in cpp:
#include <algorithm>
#include <vector>
std::vector<int> a = {1, 2, 3, 4};
std::vector<int> b = {3, 4, 5, 6};
// ✅ Both sorted
std::vector<int> result;
std::set_union(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));
// Result: {1, 2, 3, 4, 5, 6}set_union
Combines all elements from both ranges:
The following example demonstrates the concept in cpp:
#include <algorithm>
#include <vector>
std::vector<int> a = {1, 3, 5, 7};
std::vector<int> b = {2, 3, 6, 7};
std::vector<int> result;
std::set_union(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));
// Result: {1, 2, 3, 5, 6, 7}Time complexity: O(n + m)
set_intersection
Elements present in both ranges:
The following example demonstrates the concept in cpp:
std::vector<int> a = {1, 2, 3, 4, 5};
std::vector<int> b = {3, 4, 5, 6, 7};
std::vector<int> result;
std::set_intersection(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));
// Result: {3, 4, 5}set_difference
Elements in first but not in second:
The following example demonstrates the concept in cpp:
std::vector<int> a = {1, 2, 3, 4, 5};
std::vector<int> b = {3, 4, 5, 6, 7};
std::vector<int> result;
std::set_difference(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));
// Result: {1, 2} (in a but not in b)set_symmetric_difference
Elements in exactly one of the two ranges:
The following example demonstrates the concept in cpp:
std::vector<int> a = {1, 2, 3, 4, 5};
std::vector<int> b = {3, 4, 5, 6, 7};
std::vector<int> result;
std::set_symmetric_difference(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));
// Result: {1, 2, 6, 7} (in a XOR b)includes
Tests if second range is subset of first:
std::vector<int> a = {1, 2, 3, 4, 5};
std::vector<int> b = {2, 3, 4};
bool isSubset = std::includes(a.begin(), a.end(),
b.begin(), b.end());
// true: all elements of b are in aReal-world applications
1. Permission system
#include <algorithm>
#include <vector>
#include <string>
class PermissionChecker {
std::vector<std::string> userPerms_;
std::vector<std::string> requiredPerms_;
public:
PermissionChecker(std::vector<std::string> user,
std::vector<std::string> required)
: userPerms_(std::move(user))
, requiredPerms_(std::move(required)) {
std::sort(userPerms_.begin(), userPerms_.end());
std::sort(requiredPerms_.begin(), requiredPerms_.end());
}
bool hasAllPermissions() const {
return std::includes(userPerms_.begin(), userPerms_.end(),
requiredPerms_.begin(), requiredPerms_.end());
}
std::vector<std::string> getMissingPermissions() const {
std::vector<std::string> missing;
std::set_difference(requiredPerms_.begin(), requiredPerms_.end(),
userPerms_.begin(), userPerms_.end(),
std::back_inserter(missing));
return missing;
}
};
// Usage
PermissionChecker checker(
{"read", "write", "execute"},
{"read", "write", "delete"}
);
if (!checker.hasAllPermissions()) {
auto missing = checker.getMissingPermissions();
// missing = {"delete"}
}2. File synchronization
#include <algorithm>
#include <vector>
#include <string>
#include <filesystem>
struct SyncResult {
std::vector<std::string> toAdd; // In remote, not local
std::vector<std::string> toDelete; // In local, not remote
std::vector<std::string> common; // In both
};
SyncResult compareDirectories(std::vector<std::string> local,
std::vector<std::string> remote) {
std::sort(local.begin(), local.end());
std::sort(remote.begin(), remote.end());
SyncResult result;
std::set_difference(remote.begin(), remote.end(),
local.begin(), local.end(),
std::back_inserter(result.toAdd));
std::set_difference(local.begin(), local.end(),
remote.begin(), remote.end(),
std::back_inserter(result.toDelete));
std::set_intersection(local.begin(), local.end(),
remote.begin(), remote.end(),
std::back_inserter(result.common));
return result;
}3. Tag filtering
#include <algorithm>
#include <vector>
#include <string>
std::vector<std::string> findPostsWithAllTags(
const std::vector<std::string>& postTags,
const std::vector<std::string>& requiredTags
) {
std::vector<std::string> sortedPost = postTags;
std::vector<std::string> sortedRequired = requiredTags;
std::sort(sortedPost.begin(), sortedPost.end());
std::sort(sortedRequired.begin(), sortedRequired.end());
if (std::includes(sortedPost.begin(), sortedPost.end(),
sortedRequired.begin(), sortedRequired.end())) {
return postTags; // Has all required tags
}
return {};
}Performance benchmarks
Test setup: GCC 13, -O3, sorted vectors
| Operation | Size A | Size B | Time (μs) |
|---|---|---|---|
set_union | 1000 | 1000 | 15 |
set_intersection | 1000 | 1000 | 12 |
set_difference | 1000 | 1000 | 11 |
set_symmetric_difference | 1000 | 1000 | 14 |
includes | 1000 | 500 | 8 |
| All are O(n + m) — single linear pass through both ranges. |
Common mistakes
Mistake 1: Unsorted inputs
std::vector<int> a = {3, 1, 4}; // ❌ Not sorted
std::vector<int> b = {2, 5, 1}; // ❌ Not sorted
std::vector<int> result;
std::set_union(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));
// ❌ Undefined behavior! Results are garbageFix: Sort first:
std::sort(a.begin(), a.end());
std::sort(b.begin(), b.end());
std::set_union(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));Mistake 2: Overlapping output
std::vector<int> a = {1, 2, 3};
std::vector<int> b = {3, 4, 5};
// ❌ Undefined behavior: output overlaps input
std::set_union(a.begin(), a.end(),
b.begin(), b.end(),
a.begin());
// ✅ Use separate output
std::vector<int> result;
std::set_union(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));Mistake 3: Forgetting duplicates
std::vector<int> a = {1, 2, 2, 3}; // Has duplicate
std::vector<int> b = {2, 3, 4};
std::vector<int> result;
std::set_union(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));
// Result: {1, 2, 2, 3, 4} — duplicate 2 preserved!
// ✅ Remove duplicates first if needed
a.erase(std::unique(a.begin(), a.end()), a.end());Comparison with std::set container
Algorithm approach (on vectors)
std::vector<int> a = {1, 3, 5};
std::vector<int> b = {3, 5, 7};
std::vector<int> result;
std::set_intersection(a.begin(), a.end(),
b.begin(), b.end(),
std::back_inserter(result));Pros: Fast for sorted vectors, no tree overhead
Cons: Must maintain sorted order manually
Container approach (std::set)
std::set<int> a = {1, 3, 5};
std::set<int> b = {3, 5, 7};
std::set<int> result;
std::set_intersection(a.begin(), a.end(),
b.begin(), b.end(),
std::inserter(result, result.begin()));Pros: Automatically sorted, unique elements
Cons: O(log n) insertions, memory overhead
Related posts
Keywords
set_union, set_intersection, set_difference, set_symmetric_difference, includes, sorted range, STL, C++, algorithm, set operations
Frequently Asked Questions (FAQ)
Q. When would I use this in practice?
A. Run set_union, set_intersection, set_difference, set_symmetric_difference, and includes on sorted ranges — complexity, d…
Q. What should I read before this?
A. Follow the previous article or related articles links at the bottom of each post to learn in sequence. See the C++ series index for the full picture.
Q. Where can I study this more deeply?
A. Check cppreference and the relevant library’s official documentation. The reference links at the end of the article are also worth using.
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Keywords Covered in This Article (Related Search Terms)
This article covers C++, Algorithm, set, union, STL.