Count Subarrays with Consecutive elements differing by 1
Last Updated :
16 Mar, 2023
Given an array arr[] of N integers. The task is to count the total number of subarrays of the given array such that the difference between the consecutive elements in the subarrays is one. That is, for any index i in the subarrays, arr[i+1] - arr[i] = 1.
Note: Do not consider subarrays with a single element.
Examples:
Input : arr[] = {1, 2, 3}
Output : 3
The subarrays are {1, 2}. {2, 3} and {1, 2, 3}
Input : arr[] = {1, 2, 3, 5, 6, 7}
Output : 6
Naive Approach: A simple approach is to run two nested loops and check every subarray and calculate the count of subarrays with consecutive elements differing by 1.
C++
#include <iostream>
using namespace std;
int countSubarrays(int arr[], int n) {
int count = 0; // Initialize count to 0
// Loop over all subarrays
for (int i = 0; i < n; i++) {
int j = i + 1;
// Check if consecutive elements differ by 1
while (j < n && arr[j] - arr[j-1] == 1) {
j++;
}
// Add the count of subarrays with consecutive elements differing by 1
count += (j - i) * (j - i - 1) / 2;
// Move i to the next position
i = j - 1;
}
// Return the total count of subarrays
return count;
}
int main() {
int arr[] = {1, 2, 3};
int n = sizeof(arr)/sizeof(arr[0]);
int count = countSubarrays(arr, n);
cout << "Total number of subarrays with consecutive elements differing by 1: " << count << endl;
return 0;
}
// This code is contributed by Naveen Gujjar.
import java.util.*;
public class Main {
public static int countSubarrays(int[] arr, int n) {
int count = 0; // Initialize count to 0
// Loop over all subarrays
for (int i = 0; i < n; i++) {
int j = i + 1;
// Check if consecutive elements differ by 1
while (j < n && arr[j] - arr[j-1] == 1) {
j++;
}
// Add the count of subarrays with consecutive elements differing by 1
count += (j - i) * (j - i - 1) / 2;
// Move i to the next position
i = j - 1;
}
// Return the total count of subarrays
return count;
}
public static void main(String[] args) {
int[] arr = {1, 2, 3};
int n = arr.length;
int count = countSubarrays(arr, n);
System.out.println("Total number of subarrays with consecutive elements differing by 1: " + count);
}
}
def countSubarrays(arr, n):
count = 0 # Initialize count to 0
# Loop over all subarrays
i = 0
while i < n:
j = i + 1
# Check if consecutive elements differ by 1
while j < n and arr[j] - arr[j-1] == 1:
j += 1
# Add the count of subarrays with consecutive elements differing by 1
count += (j - i) * (j - i - 1) // 2
# Move i to the next position
i = j
# Return the total count of subarrays
return count
arr = [1, 2, 3]
n = len(arr)
count = countSubarrays(arr, n)
print("Total number of subarrays with consecutive elements differing by 1:", count)
using System;
class Gfg
{
static int countSubarrays(int[] arr, int n)
{
int count = 0; // Initialize count to 0
// Loop over all subarrays
for (int i = 0; i < n; i++) {
int j = i + 1;
// Check if consecutive elements differ by 1
while (j < n && arr[j] - arr[j-1] == 1) {
j++;
}
// Add the count of subarrays with consecutive elements differing by 1
count += (j - i) * (j - i - 1) / 2;
// Move i to the next position
i = j - 1;
}
// Return the total count of subarrays
return count;
}
public static void Main()
{
int[] arr = {1, 2, 3};
int n = arr.Length;
int count = countSubarrays(arr, n);
Console.WriteLine("Total number of subarrays with consecutive elements differing by 1: " + count);
}
}
function countSubarrays(arr, n) {
let count = 0; // Initialize count to 0
// Loop over all subarrays
for (let i = 0; i < n; i++) {
let j = i + 1;
// Check if consecutive elements differ by 1
while (j < n && arr[j] - arr[j - 1] === 1) {
j++;
}
// Add the count of subarrays with consecutive elements differing by 1
count += ((j - i) * (j - i - 1)) / 2;
// Move i to the next position
i = j - 1;
}
// Return the total count of subarrays
return count;
}
const arr = [1, 2, 3];
const n = arr.length;
const count = countSubarrays(arr, n);
console.log(
`Total number of subarrays with consecutive elements differing by 1: ${count}`
);
OutputTotal number of subarrays with consecutive elements differing by 1: 3
Time Complexity: O(N²)
Auxiliary Space: O(1)
Efficient Approach: An efficient approach is to observe that in an array of length say K, the total number of subarrays of size greater than 1 = (K)*(K-1)/2.
So, the idea is to traverse the array by using two pointers to calculate subarrays with consecutive elements in a window of maximum length and then calculate all subarrays in that window using the above formula.
Below is the step-by-step algorithm:
- Take two pointers to say fast and slow, for maintaining a window of consecutive elements.
- Start traversing the array.
- If elements differ by 1 increment only the fast pointer.
- Else, calculate the length of the current window between the indexes fast and slow.
Below is the implementation of the given approach:
C++
// C++ program to count Subarrays with
// Consecutive elements differing by 1
#include <iostream>
using namespace std;
// Function to count Subarrays with
// Consecutive elements differing by 1
int subarrayCount(int arr[], int n)
{
// Variable to store count of subarrays
// whose consecutive elements differ by 1
int result = 0;
// Take two pointers for maintaining a
// window of consecutive elements
int fast = 0, slow = 0;
// Traverse the array
for (int i = 1; i < n; i++) {
// If elements differ by 1
// increment only the fast pointer
if (arr[i] - arr[i - 1] == 1) {
fast++;
}
else {
// Calculate length of subarray
int len = fast - slow + 1;
// Calculate total subarrays except
// Subarrays with single element
result += len * (len - 1) / 2;
// Update fast and slow
fast = i;
slow = i;
}
}
// For last iteration. That is if array is
// traversed and fast > slow
if (fast != slow) {
int len = fast - slow + 1;
result += len * (len - 1) / 2;
}
return result;
}
// Driver Code
int main()
{
int arr[] = { 1, 2, 3, 5, 6, 7 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << subarrayCount(arr, n);
return 0;
}
// Java program to count Subarrays with
// Consecutive elements differing by 1
class cfg
{
// Function to count Subarrays with
// Consecutive elements differing by 1
static int subarrayCount(int arr[], int n)
{
// Variable to store count of subarrays
// whose consecutive elements differ by 1
int result = 0;
// Take two pointers for maintaining a
// window of consecutive elements
int fast = 0, slow = 0;
// Traverse the array
for (int i = 1; i < n; i++) {
// If elements differ by 1
// increment only the fast pointer
if (arr[i] - arr[i - 1] == 1) {
fast++;
}
else {
// Calculate length of subarray
int len = fast - slow + 1;
// Calculate total subarrays except
// Subarrays with single element
result += len * (len - 1) / 2;
// Update fast and slow
fast = i;
slow = i;
}
}
// For last iteration. That is if array is
// traversed and fast > slow
if (fast != slow) {
int len = fast - slow + 1;
result += len * (len - 1) / 2;
}
return result;
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 1, 2, 3, 5, 6, 7 };
int n = arr.length;
System.out.println(subarrayCount(arr, n));
}
}
//This code is contributed by Mukul Singh
# Python3 program to count Subarrays with
# Consecutive elements differing by 1
# Function to count Subarrays with
# Consecutive elements differing by 1
def subarrayCount(arr, n) :
# Variable to store count of subarrays
# whose consecutive elements differ by 1
result = 0
# Take two pointers for maintaining a
# window of consecutive elements
fast, slow = 0, 0
# Traverse the array
for i in range(1, n) :
# If elements differ by 1
# increment only the fast pointer
if (arr[i] - arr[i - 1] == 1) :
fast += 1
else :
# Calculate length of subarray
length = fast - slow + 1
# Calculate total subarrays except
# Subarrays with single element
result += length * (length - 1) // 2;
# Update fast and slow
fast = i
slow = i
# For last iteration. That is if array is
# traversed and fast > slow
if (fast != slow) :
length = fast - slow + 1
result += length * (length - 1) // 2;
return result
# Driver Code
if __name__ == "__main__" :
arr = [ 1, 2, 3, 5, 6, 7 ]
n = len(arr)
print(subarrayCount(arr, n))
# This code is contributed by Ryuga
// C# program to count Subarrays with
// Consecutive elements differing by 1
using System;
class cfg
{
// Function to count Subarrays with
// Consecutive elements differing by 1
static int subarrayCount(int []arr, int n)
{
// Variable to store count of subarrays
// whose consecutive elements differ by 1
int result = 0;
// Take two pointers for maintaining a
// window of consecutive elements
int fast = 0, slow = 0;
// Traverse the array
for (int i = 1; i < n; i++) {
// If elements differ by 1
// increment only the fast pointer
if (arr[i] - arr[i - 1] == 1) {
fast++;
}
else {
// Calculate length of subarray
int len = fast - slow + 1;
// Calculate total subarrays except
// Subarrays with single element
result += len * (len - 1) / 2;
// Update fast and slow
fast = i;
slow = i;
}
}
// For last iteration. That is if array is
// traversed and fast > slow
if (fast != slow) {
int len = fast - slow + 1;
result += len * (len - 1) / 2;
}
return result;
}
// Driver Code
public static void Main()
{
int []arr = { 1, 2, 3, 5, 6, 7 };
int n = arr.Length;
Console.WriteLine(subarrayCount(arr, n));
}
}
//This code is contributed by inder_verma..
<?php
// PHP program to count Subarrays with
// Consecutive elements differing by 1
// Function to count Subarrays with
// Consecutive elements differing by 1
function subarrayCount($arr, $n)
{
// Variable to store count of subarrays
// whose consecutive elements differ by 1
$result = 0;
// Take two pointers for maintaining a
// window of consecutive elements
$fast = 0; $slow = 0;
// Traverse the array
for ($i = 1; $i < $n; $i++)
{
// If elements differ by 1
// increment only the fast pointer
if ($arr[$i] - $arr[$i - 1] == 1)
{
$fast++;
}
else
{
// Calculate length of subarray
$len = $fast - $slow + 1;
// Calculate total subarrays except
// Subarrays with single element
$result += $len * ($len - 1) / 2;
// Update fast and slow
$fast = $i;
$slow = $i;
}
}
// For last iteration. That is if array
// is traversed and fast > slow
if ($fast != $slow)
{
$len = $fast - $slow + 1;
$result += $len * ($len - 1) / 2;
}
return $result;
}
// Driver Code
$arr = array(1, 2, 3, 5, 6, 7);
$n = sizeof($arr);
echo subarrayCount($arr, $n);
// This code is contributed
// by Akanksha Rai
?>
<script>
// Javascript program to count Subarrays with
// Consecutive elements differing by 1
// Function to count Subarrays with
// Consecutive elements differing by 1
function subarrayCount(arr , n) {
// Variable to store count of subarrays
// whose consecutive elements differ by 1
var result = 0;
// Take two pointers for maintaining a
// window of consecutive elements
var fast = 0, slow = 0;
// Traverse the array
for (i = 1; i < n; i++) {
// If elements differ by 1
// increment only the fast pointer
if (arr[i] - arr[i - 1] == 1) {
fast++;
} else {
// Calculate length of subarray
var len = fast - slow + 1;
// Calculate total subarrays except
// Subarrays with single element
result += len * (len - 1) / 2;
// Update fast and slow
fast = i;
slow = i;
}
}
// For last iteration. That is if array is
// traversed and fast > slow
if (fast != slow) {
var len = fast - slow + 1;
result += len * (len - 1) / 2;
}
return result;
}
// Driver Code
var arr = [ 1, 2, 3, 5, 6, 7 ];
var n = arr.length;
document.write(subarrayCount(arr, n));
// This code contributed by aashish1995
</script>
Complexity Analysis:
- Time Complexity: O(N), as we are using a loop to traverse N times so the complexity for the program will be O(N).
- 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