Check if given array is almost sorted (elements are at-most one position away)
Last Updated :
29 Nov, 2023
Given an array with n distinct elements. An array is said to be almost sorted (non-decreasing) if any of its elements can occur at a maximum of 1 distance away from their original places in the sorted array. We need to find whether the given array is almost sorted or not.
Examples:
Input : arr[] = {1, 3, 2, 4}
Output : Yes
Explanation : All elements are either
at original place or at most a unit away.
Input : arr[] = {1, 4, 2, 3}
Output : No
Explanation : 4 is 2 unit away from
its original place.
Sorting Approach : With the help of sorting we can predict whether our given array is almost sorted or not. The idea behind that is first sort the input array say A[]and then if array will be almost sorted then each element Ai of the given array must be equal to any of Bi-1, Bi or Bi+1 of sorted array B[].
Time Complexity : O(nlogn)
// suppose B[] is copy of A[]
sort(B, B+n);
// check first element
if ((A[0]!=B[0]) && (A[0]!=B[1]) )
return 0;
// iterate over array
for(int i=1; i<n-1; i++)
{
if (A[i]!=B[i-1]) && (A[i]!=B[i]) && (A[i]!=B[i+1]) )
return false;
}
// check for last element
if ((A[i]!=B[i-1]) && (A[i]!=B[i]) )
return 0;
// finally return true
return true;
Algorithm:
- Sort the copy of input array A to get the sorted array B.
- Check if the first element of A is either the first or second element of B. If not, return false
- Iterate through the array A from the second element to the second-to-last element
- For each element A[i] of A, check if it is equal to A[i-1], A[i], or A[i+1] in B. If not, return false
- Check if the last element of A is either the second-to-last or last element of B. If not, return false
- If all checks pass, return true.
Below is the implementation of the approach:
C++
// CPP program to find whether given array
// almost sorted or not
#include <bits/stdc++.h>
using namespace std;
// function for checking almost sort
bool isAlmostSorted(int A[], int n) {
// Make a copy of A
int B[n];
for (int i = 0; i < n; i++) {
B[i] = A[i];
}
// Sort the copy
sort(B, B+n);
// Check the first element
if ((A[0] != B[0]) && (A[0] != B[1])) {
return false;
}
// Iterate over the array
for (int i = 1; i < n-1; i++) {
if ((A[i] != B[i-1]) && (A[i] != B[i]) && (A[i] != B[i+1])) {
return false;
}
}
// Check the last element
if ((A[n-1] != B[n-1]) && (A[n-1] != B[n-2])) {
return false;
}
// Return true if the array is almost sorted
return true;
}
int main() {
// Input array
int A[] = { 1, 3, 2, 4, 6, 5 };
int n = sizeof(A)/sizeof(A[0]);
if (isAlmostSorted(A, n)) {
cout << "Yes" << endl;
}
else {
cout << "No" << endl;
}
return 0;
}
import java.util.Arrays;
public class Main {
// Function to check if the array is almost sorted
public static boolean isAlmostSorted(int[] A, int n) {
// Make a copy of A
int[] B = Arrays.copyOf(A, n);
// Sort the copy
Arrays.sort(B);
// Check the first element
if ((A[0] != B[0]) && (A[0] != B[1])) {
return false;
}
// Iterate over the array
for (int i = 1; i < n - 1; i++) {
if ((A[i] != B[i - 1]) && (A[i] != B[i]) && (A[i] != B[i + 1])) {
return false;
}
}
// Check the last element
if ((A[n - 1] != B[n - 1]) && (A[n - 1] != B[n - 2])) {
return false;
}
// Return true if the array is almost sorted
return true;
}
public static void main(String[] args) {
// Input array
int[] A = {1, 3, 2, 4, 6, 5};
int n = A.length;
if (isAlmostSorted(A, n)) {
System.out.println("Yes");
} else {
System.out.println("No");
}
}
}
def is_almost_sorted(arr):
# Make a copy of the array
b = arr.copy()
# Sort the copy
b.sort()
# Check the first element
if (arr[0] != b[0]) and (arr[0] != b[1]):
return False
# Iterate over the array
n = len(arr)
for i in range(1, n - 1):
if (arr[i] != b[i - 1]) and (arr[i] != b[i]) and (arr[i] != b[i + 1]):
return False
# Check the last element
if (arr[n - 1] != b[n - 1]) and (arr[n - 1] != b[n - 2]):
return False
# Return True if the array is almost sorted
return True
# Main function
if __name__ == "__main__":
# Input array
A = [1, 3, 2, 4, 6, 5]
if is_almost_sorted(A):
print("Yes")
else:
print("No")
using System;
using System.Linq;
class Program {
// Function for checking almost sorted
static bool IsAlmostSorted(int[] A, int n)
{
// Make a copy of A
int[] B = new int[n];
Array.Copy(A, B, n);
// Sort the copy
Array.Sort(B);
// Check the first element
if ((A[0] != B[0]) && (A[0] != B[1])) {
return false;
}
// Iterate over the array
for (int i = 1; i < n - 1; i++) {
if ((A[i] != B[i - 1]) && (A[i] != B[i])
&& (A[i] != B[i + 1])) {
return false;
}
}
// Check the last element
if ((A[n - 1] != B[n - 1])
&& (A[n - 1] != B[n - 2])) {
return false;
}
// Return true if the array is almost sorted
return true;
}
static void Main()
{
// Input array
int[] A = { 1, 3, 2, 4, 6, 5 };
int n = A.Length;
if (IsAlmostSorted(A, n)) {
Console.WriteLine("Yes");
}
else {
Console.WriteLine("No");
}
}
}
// function for checking almost sort
function isAlmostSorted(A, n) {
// Make a copy of A
let B = [...A];
// Sort the copy
B.sort((a, b) => a - b);
// Check the first element
if ((A[0] != B[0]) && (A[0] != B[1])) {
return false;
}
// Iterate over the array
for (let i = 1; i < n-1; i++) {
if ((A[i] != B[i-1]) && (A[i] != B[i]) && (A[i] != B[i+1])) {
return false;
}
}
// Check the last element
if ((A[n-1] != B[n-1]) && (A[n-1] != B[n-2])) {
return false;
}
// Return true if the array is almost sorted
return true;
}
// Input array
let A = [1, 3, 2, 4, 6, 5];
let n = A.length;
if (isAlmostSorted(A, n)) {
console.log("Yes");
} else {
console.log("No");
}
Time complexity: O(n Log n)
Auxiliary Space: O(n) as an array B has been created to store copy of input array A. Here, n is size of the input array.
Efficient Approach: The idea is based on Bubble Sort. Like Bubble Sort, we compare adjacent elements and swap them if they are not in order. Here after swapping we move the index one position extra so that bubbling is limited to one place. So after one iteration if the resultant array is sorted then we can say that our input array was almost sorted otherwise not almost sorted.
// perform bubble sort tech once
for (int i=0; i<n-1; i++)
if (A[i+1]<A[i])
swap(A[i], A[i+1]);
i++;
// check whether resultant is sorted or not
for (int i=0; i<n-1; i++)
if (A[i+1]<A[i])
return false;
// If resultant is sorted return true
return true;
C++
// CPP program to find whether given array
// almost sorted or not
#include <bits/stdc++.h>
using namespace std;
// function for checking almost sort
bool almostSort(int A[], int n)
{
// One by one compare adjacents.
for (int i = 0; i < n - 1; i++) {
if (A[i] > A[i + 1]) {
swap(A[i], A[i + 1]);
i++;
}
}
// check whether resultant is sorted or not
for (int i = 0; i < n - 1; i++)
if (A[i] > A[i + 1])
return false;
// is resultant is sorted return true
return true;
}
// driver function
int main()
{
int A[] = { 1, 3, 2, 4, 6, 5 };
int n = sizeof(A) / sizeof(A[0]);
if (almostSort(A, n))
cout << "Yes";
else
cout << "No";
return 0;
}
// JAVA Code to check if given array is almost
// sorted or not
import java.util.*;
class GFG {
// function for checking almost sort
public static boolean almostSort(int A[], int n)
{
// One by one compare adjacents.
for (int i = 0; i < n - 1; i++) {
if (A[i] > A[i + 1]) {
int temp = A[i];
A[i] = A[i+1];
A[i+1] = temp;
i++;
}
}
// check whether resultant is sorted or not
for (int i = 0; i < n - 1; i++)
if (A[i] > A[i + 1])
return false;
// is resultant is sorted return true
return true;
}
/* Driver program to test above function */
public static void main(String[] args)
{
int A[] = { 1, 3, 2, 4, 6, 5 };
int n = A.length;
if (almostSort(A, n))
System.out.print("Yes");
else
System.out.print("No");
}
}
// This code is contributed by Arnav Kr. Mandal.
# Python3 program to find whether given
# array almost sorted or not
# Function for checking almost sort
def almostSort(A, n):
# One by one compare adjacents.
i = 0
while i < n - 1:
if A[i] > A[i + 1]:
A[i], A[i + 1] = A[i + 1], A[i]
i += 1
i += 1
# check whether resultant is sorted or not
for i in range(0, n - 1):
if A[i] > A[i + 1]:
return False
# Is resultant is sorted return true
return True
# Driver Code
if __name__ == "__main__":
A = [1, 3, 2, 4, 6, 5]
n = len(A)
if almostSort(A, n):
print("Yes")
else:
print("No")
# This code is contributed
# by Rituraj Jain
// C# Code to check if given array
// is almost sorted or not
using System;
class GFG {
// function for checking almost sort
public static bool almostSort(int []A, int n)
{
// One by one compare adjacents.
for (int i = 0; i < n - 1; i++)
{
if (A[i] > A[i + 1])
{
int temp = A[i];
A[i] = A[i + 1];
A[i + 1] = temp;
i++;
}
}
// Check whether resultant is
// sorted or not
for (int i = 0; i < n - 1; i++)
if (A[i] > A[i + 1])
return false;
// is resultant is sorted return true
return true;
}
// Driver Code
public static void Main()
{
int []A = {1, 3, 2, 4, 6, 5};
int n = A.Length;
if (almostSort(A, n))
Console.Write("Yes");
else
Console.Write("No");
}
}
// This code is contributed by Nitin Mittal.
<script>
// Javascript Code to check if given array
// is almost sorted or not
// function for checking almost sort
function almostSort(A, n)
{
// One by one compare adjacents.
for (let i = 0; i < n - 1; i++)
{
if (A[i] > A[i + 1])
{
let temp = A[i];
A[i] = A[i + 1];
A[i + 1] = temp;
i++;
}
}
// Check whether resultant is
// sorted or not
for (let i = 0; i < n - 1; i++)
if (A[i] > A[i + 1])
return false;
// is resultant is sorted return true
return true;
}
let A = [1, 3, 2, 4, 6, 5];
let n = A.length;
if (almostSort(A, n))
document.write("Yes");
else
document.write("No");
</script>
<?php
// PHP program to find
// whether given array
// almost sorted or not
// function for checking
// almost sort
function almostSort($A, $n)
{
// One by one compare adjacents.
for ($i = 0; $i < $n - 1; $i++)
{
if ($A[$i] > $A[$i + 1])
{
list($A[$i],
$A[$i + 1]) = array($A[$i + 1],
$A[$i] );
$i++;
}
}
// check whether resultant
// is sorted or not
for ($i = 0; $i <$n - 1; $i++)
if ($A[$i] > $A[$i + 1])
return false;
// is resultant is
// sorted return true
return true;
}
// Driver Code
$A = array (1, 3, 2,
4, 6, 5);
$n = sizeof($A) ;
if (almostSort($A, $n))
echo "Yes", "\n";
else
echo "Yes", "\n";
// This code is contributed by ajit
?>
Output:
Yes
Time Complexity: O(N), as we are using any loops for traversing.
Auxiliary Space: O(1), as we are not using any extra space.
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem