Minimum increments by index value required to obtain at least two equal Array elements
Last Updated :
22 Jun, 2021
Given a strictly decreasing array arr[] consisting of N integers, the task is to find the minimum number of operations required to make at least two array elements equal, where each operation involves increasing every array element by its index value.
Examples:
Input: arr[] = {6, 5, 1}
Output: 1
Explanation:
{6 + 1, 5 + 2, 1 + 3} = {7, 7, 4}
Input: arr[] = {12, 8, 4}
Output: 4
Explanation:
Step 1 : {12 + 1, 8 + 2, 4 + 3} = {13, 10, 7}
Step 2 : {13 + 1, 10 + 2, 7 + 3} = {14, 12, 10}
Step 3 : {15, 14, 13}
Step 4 : {16, 16, 16}
Naive approach: Follow the below steps to solve the problem:
- Check if the array already has at least two equal elements or not. If found to be true, print 0.
- Otherwise, keep updating the array by increasing each array element by its index value and increase count. Check if array has two equal elements or not.
- Print count once the array is found to be containing at least two equal elements.
Below is the implementation of the above approach:
C++
// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to update every element
// adding to it its index value
void update(int arr[], int N)
{
for (int i = 0; i < N; i++) {
arr[i] += (i + 1);
}
}
// Function to check if at least
// two elements are equal or not
bool check(int arr[], int N)
{
bool f = 0;
for (int i = 0; i < N; i++) {
// Count the frequency of arr[i]
int count = 0;
for (int j = 0; j < N; j++) {
if (arr[i] == arr[j]) {
count++;
}
}
if (count >= 2) {
f = 1;
break;
}
}
if (f == 1)
return true;
else
return false;
}
// Function to calculate the number
// of increment operations required
void incrementCount(int arr[], int N)
{
// Stores the minimum number of steps
int min = 0;
while (check(arr, N) != true) {
update(arr, N);
min++;
}
cout << min;
}
// Driver Code
int main()
{
int N = 3;
int arr[N] = { 12, 8, 4 };
incrementCount(arr, N);
return 0;
}
// Java program to implement
// the above approach
import java.util.*;
class GFG{
// Function to update every element
// adding to it its index value
static void update(int arr[], int N)
{
for(int i = 0; i < N; i++)
{
arr[i] += (i + 1);
}
}
// Function to check if at least
// two elements are equal or not
static boolean check(int arr[], int N)
{
int f = 0;
for(int i = 0; i < N; i++)
{
// Count the frequency of arr[i]
int count = 0;
for(int j = 0; j < N; j++)
{
if (arr[i] == arr[j])
{
count++;
}
}
if (count >= 2)
{
f = 1;
break;
}
}
if (f == 1)
return true;
else
return false;
}
// Function to calculate the number
// of increment operations required
static void incrementCount(int arr[], int N)
{
// Stores the minimum number of steps
int min = 0;
while (check(arr, N) != true)
{
update(arr, N);
min++;
}
System.out.println(min);
}
// Driver code
public static void main (String[] args)
{
int N = 3;
int arr[] = { 12, 8, 4 };
incrementCount(arr, N);
}
}
// This code is contributed by offbeat
# Python3 program to implement
# the above approach
# Function to update every element
# adding to it its index value
def update(arr, N):
for i in range(N):
arr[i] += (i + 1);
# Function to check if at least
# two elements are equal or not
def check(arr, N):
f = 0;
for i in range(N):
# Count the frequency of arr[i]
count = 0;
for j in range(N):
if (arr[i] == arr[j]):
count += 1;
if (count >= 2):
f = 1;
break;
if (f == 1):
return True;
else:
return False;
# Function to calculate the number
# of increment operations required
def incrementCount(arr, N):
# Stores the minimum number of steps
min = 0;
while (check(arr, N) != True):
update(arr, N);
min += 1;
print(min);
# Driver code
if __name__ == '__main__':
N = 3;
arr = [ 12, 8, 4 ];
incrementCount(arr, N);
# This code is contributed by 29AjayKumar
// C# program to implement
// the above approach
using System;
class GFG{
// Function to update every element
// adding to it its index value
static void update(int []arr, int N)
{
for(int i = 0; i < N; i++)
{
arr[i] += (i + 1);
}
}
// Function to check if at least
// two elements are equal or not
static bool check(int []arr, int N)
{
int f = 0;
for(int i = 0; i < N; i++)
{
// Count the frequency of arr[i]
int count = 0;
for(int j = 0; j < N; j++)
{
if (arr[i] == arr[j])
{
count++;
}
}
if (count >= 2)
{
f = 1;
break;
}
}
if (f == 1)
return true;
else
return false;
}
// Function to calculate the number
// of increment operations required
static void incrementCount(int []arr, int N)
{
// Stores the minimum number of steps
int min = 0;
while (check(arr, N) != true)
{
update(arr, N);
min++;
}
Console.WriteLine(min);
}
// Driver code
public static void Main(String[] args)
{
int N = 3;
int []arr = { 12, 8, 4 };
incrementCount(arr, N);
}
}
// This code is contributed by Amit Katiyar
<script>
// Java Script program to implement
// the above approach
// Function to update every element
// adding to it its index value
function update(arr,N)
{
for(let i = 0; i < N; i++)
{
arr[i] += (i + 1);
}
}
// Function to check if at least
// two elements are equal or not
function check(arr,N)
{
let f = 0;
for(let i = 0; i < N; i++)
{
// Count the frequency of arr[i]
let count = 0;
for(let j = 0; j < N; j++)
{
if (arr[i] == arr[j])
{
count++;
}
}
if (count >= 2)
{
f = 1;
break;
}
}
if (f == 1)
return true;
else
return false;
}
// Function to calculate the number
// of increment operations required
function incrementCount(arr,N)
{
// Stores the minimum number of steps
let min = 0;
while (check(arr, N) != true)
{
update(arr, N);
min++;
}
document.write(min);
}
// Driver code
let N = 3;
let arr= [12, 8, 4 ];
incrementCount(arr, N);
//contributed by 171fa07058
</script>
Time Complexity: O(N2)
Auxiliary Space: O(1)
Efficient Approach: The above approach can be optimized by observing that by the given operation, the difference between any two adjacent elements reduces by 1 as the array is decreasing. Therefore, the minimum number of operations required is equal to the minimum difference between any two adjacent elements.
Below is the implementation of the above approach:
C++
// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to calculate the minimum
// number of steps required
void incrementCount(int arr[], int N)
{
// Stores minimum difference
int mini = arr[0] - arr[1];
for (int i = 2; i < N; i++) {
mini
= min(mini, arr[i - 1] - arr[i]);
}
cout << mini;
}
// Driver Code
int main()
{
int N = 3;
int arr[N] = { 12, 8, 4 };
incrementCount(arr, N);
return 0;
}
// Java program to implement
// the above approach
import java.util.*;
class GFG{
// Function to calculate the minimum
// number of steps required
static void incrementCount(int arr[], int N)
{
// Stores minimum difference
int mini = arr[0] - arr[1];
for(int i = 2; i < N; i++)
{
mini = Math.min(mini,
arr[i - 1] - arr[i]);
}
System.out.println(mini);
}
// Driver code
public static void main (String[] args)
{
int N = 3;
int arr[] = { 12, 8, 4 };
incrementCount(arr, N);
}
}
// This code is contributed by offbeat
# Python3 program to implement
# the above approach
# Function to calculate the minimum
# number of steps required
def incrementCount(arr, N):
# Stores minimum difference
mini = arr[0] - arr[1]
for i in range(2, N):
mini = min(mini,
arr[i - 1] - arr[i])
print(mini)
# Driver Code
N = 3
arr = [ 12, 8, 4 ]
# Function call
incrementCount(arr, N)
# This code is contributed by Shivam Singh
// C# program to implement
// the above approach
using System;
class GFG{
// Function to calculate the minimum
// number of steps required
static void incrementCount(int []arr, int N)
{
// Stores minimum difference
int mini = arr[0] - arr[1];
for(int i = 2; i < N; i++)
{
mini = Math.Min(mini,
arr[i - 1] - arr[i]);
}
Console.WriteLine(mini);
}
// Driver code
public static void Main(String[] args)
{
int N = 3;
int []arr = { 12, 8, 4 };
incrementCount(arr, N);
}
}
// This code is contributed by 29AjayKumar
<script>
// JavaScript program for the above approach
// Function to calculate the minimum
// number of steps required
function incrementCount(arr, N)
{
// Stores minimum difference
let mini = arr[0] - arr[1];
for(let i = 2; i < N; i++)
{
mini = Math.min(mini,
arr[i - 1] - arr[i]);
}
document.write(mini);
}
// Driver Code
let N = 3;
let arr = [ 12, 8, 4 ];
incrementCount(arr, N);
</script>
Time Complexity: O(N)
Auxiliary Space: O(1)
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