Smallest index that splits an array into two subarrays with equal product
Last Updated :
23 Jul, 2025
Given an array(1-based indexing) arr[] consisting of N non zero integers, the task is to find the leftmost index i such that the product of all the elements of the subarrays arr[1, i] and arr[i + 1, N] is the same.
Examples:
Input: arr[] = {1, 2, 3, 3, 2, 1}
Output: 3
Explanation: Index 3 generates subarray {arr[1], arr[3]} with product 6 (= 1 * 2 * 3) and {arr[4], arr[6]} with product 6 ( = 3 * 2 * 1).
Input: arr = {3, 2, 6}
Output: 2
Brute Force Approach:
To solve this problem is to iterate through the array and keep track of the product of the elements from the beginning of the array to the current index and from the current index to the end of the array. For each index i, if the product of the two subarrays is equal, return i. If no such index is found, return -1.
Implementation of the above approach:
C++
#include <iostream>
using namespace std;
// Function to find the smallest index that splits the array
// into two subarrays with equal product
void prodEquilibrium(int arr[], int N)
{
int leftProduct = 1;
int rightProduct = 1;
for (int i = 0; i < N; i++) {
// calculate product of elements from 0 to i
leftProduct *= arr[i];
// calculate product of elements from i+1 to N-1
for (int j = i + 1; j < N; j++) {
rightProduct *= arr[j];
}
// if the product of the two subarrays is equal,
// return i
if (leftProduct == rightProduct) {
cout << i + 1 << endl;
return;
}
// reset rightProduct for the next iteration
rightProduct = 1;
}
// if no such index is found, return -1
cout << -1 << endl;
}
// Driver Code
int main()
{
int arr[] = { 1, 2, 3, 3, 2, 1 };
int N = sizeof(arr) / sizeof(arr[0]);
prodEquilibrium(arr, N);
return 0;
}
import java.util.*;
public class Main {
// Function to find the smallest index that splits the
// array into two subarrays with equal product
static void prodEquilibrium(int[] arr, int N)
{
int leftProduct = 1;
int rightProduct = 1;
for (int i = 0; i < N; i++) {
// calculate product of elements from 0 to i
leftProduct *= arr[i];
// calculate product of elements from i+1 to N-1
for (int j = i + 1; j < N; j++) {
rightProduct *= arr[j];
}
// if the product of the two subarrays is equal,
// return i
if (leftProduct == rightProduct) {
System.out.println(i + 1);
return;
}
// reset rightProduct for the next iteration
rightProduct = 1;
}
// if no such index is found, return -1
System.out.println(-1);
}
// Driver Code
public static void main(String[] args)
{
int[] arr = { 1, 2, 3, 3, 2, 1 };
int N = arr.length;
prodEquilibrium(arr, N);
}
}
// This code is contributed by Prajwal Kandekar
def prodEquilibrium(arr, N):
leftProduct = 1
rightProduct = 1
for i in range(N):
# calculate product of elements from 0 to i
leftProduct *= arr[i]
# calculate product of elements from i+1 to N-1
for j in range(i+1, N):
rightProduct *= arr[j]
# if the product of the two subarrays is equal, return i
if leftProduct == rightProduct:
print(i+1)
return
# reset rightProduct for the next iteration
rightProduct = 1
# if no such index is found, return -1
print(-1)
# Driver Code
arr = [1, 2, 3, 3, 2, 1]
N = len(arr)
prodEquilibrium(arr, N)
# This code is contributed by Prajwal Kandekar
using System;
public class Program
{
// Function to find the smallest index that splits the array
// into two subarrays with equal product
public static void ProdEquilibrium(int[] arr, int N)
{
int leftProduct = 1;
int rightProduct = 1;
for (int i = 0; i < N; i++)
{
// calculate product of elements from 0 to i
leftProduct *= arr[i];
// calculate product of elements from i+1 to N-1
for (int j = i + 1; j < N; j++)
{
rightProduct *= arr[j];
}
// if the product of the two subarrays is equal,
// return i
if (leftProduct == rightProduct)
{
Console.WriteLine(i + 1);
return;
}
// reset rightProduct for the next iteration
rightProduct = 1;
}
// if no such index is found, return -1
Console.WriteLine("-1");
}
// Driver Code
public static void Main()
{
int[] arr = { 1, 2, 3, 3, 2, 1 };
int N = arr.Length;
ProdEquilibrium(arr, N);
}
}
// Javascript code for the above approach
// Function to find the smallest index that splits the array into
// two subarrays with equal product
function prodEquilibrium(arr, N) {
let leftProduct = 1;
let rightProduct = 1;
for (let i = 0; i < N; i++) {
// calculate product of elements from 0 to i
leftProduct *= arr[i];
// calculate product of elements from i+1 to N-1
for (let j = i + 1; j < N; j++) {
rightProduct *= arr[j];
}
// if the product of the two subarrays is equal, return i
if (leftProduct === rightProduct) {
console.log(i + 1);
return;
}
// reset rightProduct for the next iteration
rightProduct = 1;
}
// if no such index is found, return -1
console.log(-1);
}
// Driver Code
let arr = [1, 2, 3, 3, 2, 1];
let N = arr.length;
prodEquilibrium(arr, N);
Time Complexity: O(N^2)
Space Complexity: O(1)
Approach: Follow the steps below to solve the problem:
- Initialize a variable, say product, > that stores the product of all the array elements.
- Traverse the given array and find the product of all the array elements store it in the product.
- Initialize two variables left and right to 1 that stores the product of the left and the right subarray
- Traverse the given array and perform the following steps:
- Multiply the value of left by arr[i].
- Divide the value of right by arr[i].
- If the value of left is equal to right, then print the value of the current index i as the resultant index and break out of the loop.
- After completing the above steps, if any such index doesn't exist, then print "-1" as the result.
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include <iostream>
using namespace std;
// Function to find the smallest
// index that splits the array into
// two subarrays with equal product
void prodEquilibrium(int arr[], int N)
{
// Stores the product of the array
int product = 1;
// Traverse the given array
for (int i = 0; i < N; i++) {
product *= arr[i];
}
// Stores the product of left
// and the right subarrays
int left = 1;
int right = product;
// Traverse the given array
for (int i = 0; i < N; i++) {
// Update the products
left = left * arr[i];
right = right / arr[i];
// Check if product is equal
if (left == right) {
// Print resultant index
cout << i + 1 << endl;
return;
}
}
// If no partition exists, then
// print -1.
cout << -1 << endl;
}
// Driver Code
int main()
{
int arr[] = { 1, 2, 3, 3, 2, 1 };
int N = sizeof(arr) / sizeof(arr[0]);
prodEquilibrium(arr, N);
return 0;
}
// Java program for the above approach
import java.util.*;
class GFG{
// Function to find the smallest
// index that splits the array into
// two subarrays with equal product
static void prodEquilibrium(int arr[], int N)
{
// Stores the product of the array
int product = 1;
// Traverse the given array
for(int i = 0; i < N; i++)
{
product *= arr[i];
}
// Stores the product of left
// and the right subarrays
int left = 1;
int right = product;
// Traverse the given array
for(int i = 0; i < N; i++)
{
// Update the products
left = left * arr[i];
right = right / arr[i];
// Check if product is equal
if (left == right)
{
// Print resultant index
System.out.print(i + 1 + "\n");
return;
}
}
// If no partition exists, then
// print -1.
System.out.print(-1 + "\n");
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 1, 2, 3, 3, 2, 1 };
int N = arr.length;
prodEquilibrium(arr, N);
}
}
// This code is contributed by 29AjayKumar
# Python 3 program for the above approach
# Function to find the smallest
# index that splits the array into
# two subarrays with equal product
def prodEquilibrium(arr, N):
# Stores the product of the array
product = 1
# Traverse the given array
for i in range(N):
product *= arr[i]
# Stores the product of left
# and the right subarrays
left = 1
right = product
# Traverse the given array
for i in range(N):
# Update the products
left = left * arr[i]
right = right // arr[i]
# Check if product is equal
if (left == right):
# Print resultant index
print(i + 1)
return
# If no partition exists, then
# print -1.
print(-1)
# Driver Code
if __name__ == '__main__':
arr = [1, 2, 3, 3, 2, 1]
N = len(arr)
prodEquilibrium(arr, N)
# This code is contributed by ipg2016107.
// C# program for the above approach
using System;
class GFG {
// Function to find the smallest
// index that splits the array into
// two subarrays with equal product
static void prodEquilibrium(int[] arr, int N)
{
// Stores the product of the array
int product = 1;
// Traverse the given array
for (int i = 0; i < N; i++) {
product *= arr[i];
}
// Stores the product of left
// and the right subarrays
int left = 1;
int right = product;
// Traverse the given array
for (int i = 0; i < N; i++) {
// Update the products
left = left * arr[i];
right = right / arr[i];
// Check if product is equal
if (left == right) {
// Print resultant index
Console.WriteLine(i + 1 + "\n");
return;
}
}
// If no partition exists, then
// print -1.
Console.WriteLine(-1 + "\n");
}
// Driver Code
public static void Main(string[] args)
{
int[] arr = { 1, 2, 3, 3, 2, 1 };
int N = arr.Length;
prodEquilibrium(arr, N);
}
}
// This code is contributed by ukasp.
<script>
// JavaScript program for the above approach
// Function to find the smallest
// index that splits the array into
// two subarrays with equal product
function prodEquilibrium(arr, N)
{
// Stores the product of the array
let product = 1;
// Traverse the given array
for (let i = 0; i < N; i++) {
product *= arr[i];
}
// Stores the product of left
// and the right subarrays
let left = 1;
let right = product;
// Traverse the given array
for (let i = 0; i < N; i++) {
// Update the products
left = left * arr[i];
right = right / arr[i];
// Check if product is equal
if (left == right) {
// Print resultant index
document.write((i + 1) + "<br>");
return;
}
}
// If no partition exists, then
// print -1.
document.write((-1) + "<br>");
}
// Driver Code
let arr = [ 1, 2, 3, 3, 2, 1 ];
let N = arr.length;
prodEquilibrium(arr, N);
// This code is contributed by Dharanendra L V.
</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