Introduction to Sorting
Authors: Darren Yao, Benjamin Qi, Allen Li, Andrew Wang
Arranging collections in increasing order.
Sorting refers to arranging items in some particular order.
Sorting Methods
Focus Problem – try your best to solve this problem before continuing!
Resources | ||||
---|---|---|---|---|
CPH | bubble sort, merge sort, counting sort | |||
CSA | selection sort, insertion sort, bubble sort, merge sort |
Library Sorting
Although you usually do not need to know how sorting is implemented, you should know how to use built-in methods.
C++
Resources | ||||
---|---|---|---|---|
CPH | can stop before user-defined structs, which are covered in silver | |||
CPP | reference | |||
CF | first two related to sorting |
Java
Resources | ||||
---|---|---|---|---|
tutorialspoint | Covers sorting arrays | |||
Oracle | API for sorting static arrays | |||
Oracle | API for sorting dynamic arrays |
Python
Resources | ||||
---|---|---|---|---|
PY | reference |
C++
Static Arrays
To sort static arrays, use sort(arr, arr + N)
where is the number of
elements to be sorted. The range can also be specified by replacing arr
and
arr + N
with the intended range. For example, sort(arr + 1, arr + 4)
sorts
indices .
#include <bits/stdc++.h>using namespace std;int main() {int arr[] = {5, 1, 3, 2, 4};int N = 5;sort(arr, arr + N);for (int i = 0; i < N; i++) cout << arr[i] << " "; // 1 2 3 4 5cout << endl;int arr2[] = {5, 1, 3, 2, 4};sort(arr2 + 1, arr2 + 4);for (int i = 0; i < N; i++) cout << arr2[i] << " "; // 5 1 2 3 4}
Java
Static Arrays
To sort a static array, use Arrays.sort(arr)
.
import java.util.*;class Main {public static void main(String[] args) {int arr[] = {5, 1, 3, 2, 4};Arrays.sort(arr);for (int i = 0; i < arr.length; i++)System.out.print(arr[i] + " "); // 1 2 3 4 5}}
Warning!
The Arrays.sort()
function uses quicksort on primitive data types such as
long
s. This is fine for USACO, but in other contests such as Codeforces, it
may time out on test cases specifically engineered to trigger worst-case
behavior in quicksort. See here
for an example of a solution that was hacked on Codeforces.
There are two ways to avoid this:
- Declare the underlying array as an array of objects, for example
Long
instead oflong
. This forces theArrays.sort()
function to use mergesort, which is always . - Shuffle the array beforehand.
Note: The generator for the hack above works for OpenJDK 13 and below. In OpenJDK 14, heapsort is used if quicksort takes too long (source).
Dynamic Arrays
C++
In order to sort a dynamic array, use sort(v.begin(), v.end())
(or
sort(begin(v),end(v))
). The default sort function sorts the array in ascending
order. Similarly, we can specify the range. For example,
sort(v.begin() + 1, v.begin() + 4)
sorts indices .
#include <bits/stdc++.h>using namespace std;int main() {vector<int> v{5, 1, 3, 2, 4};sort(v.begin(), v.end());// Outputs 1 2 3 4 5for (int i : v) { cout << i << " "; }cout << endl;
Java
In order to sort a dynamic array, use Collections.sort(list)
. This function
sorts the array in ascending order by default.
import java.util.*;class Main {public static void main(String[] args) {List<Integer> arr =new ArrayList<Integer>(Arrays.asList(5, 1, 3, 2, 4));Collections.sort(arr);System.out.println(arr); // Outputs [1, 2, 3, 4, 5]}}
Python
There's two main ways to sort a list in Python.
You can use sorted(arr)
, which returns a new list and doesn't modify the old
one, or arr.sort()
, which sorts the list in place.
arr = [5, 1, 3, 2, 4]print(sorted(arr)) # Outputs [1, 2, 3, 4, 5]print(arr) # Outputs the original arrayarr.sort()print(arr) # Outputs [1, 2, 3, 4, 5]
For more on sorting in Python, see this link.
(Dynamic) Arrays of Pairs & Tuples
C++
By default, C++ pairs are sorted by first element and then second element in case of a tie.
#include <bits/stdc++.h>using namespace std;int main() {vector<pair<int, int>> v{{1, 5}, {2, 3}, {1, 2}};sort(v.begin(), v.end());/** Outputs:* 1 2* 1 5* 2 3*/for (pair<int, int> p : v) { cout << p.first << " " << p.second << endl; }}
Tuples are sorted similarly.
Java
You'll need to define your own custom comparator. This is covered in Silver.
Python
By default, Python tuples sort by first element, then second element, and so on in case of repeated ties.
arr = [(1, 5), (2, 3), (1, 2)]arr = sorted(arr)print(arr) # Outputs [(1, 2), (1, 5), (2, 3)]
Problems
Warning!
Bronze problems are designed so that you shouldn't need a time sort (repeatedly extracting the minimum in time will always suffice).
Status | Source | Problem Name | Difficulty | Tags | |
---|---|---|---|---|---|
CSES | Easy | Show TagsSorting | |||
CF | Easy | Show TagsSorting | |||
CF | Normal | Show TagsGreedy, Sorting | |||
Bronze | Normal | Show TagsSimulation, Sorting | |||
Bronze | Hard | Show TagsSimulation, Sorting |
Note: There are some more sorting problems in the Intro to Sets module.
Check Your Understanding
What would the array be after 1 pass of bubble sort?
Module Progress:
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