Given an array arr[] of size n, the task is to return an equilibrium index (if any) or -1 if no equilibrium index exists. The equilibrium index of an array is an index such that the sum of all elements at lower indexes equals the sum of all elements at higher indexes.
Note: When the index is at the start of the array, the left sum is 0, and when it's at the end, the right sum is 0.
Examples:
Input: arr[] = [1, 2, 0, 3]
Output: 2
Explanation: The sum of left of index 2 is 1 + 2 = 3 and sum on right of index 2 is 3.
Input: arr[] = [1, 1, 1, 1]
Output: -1
Explanation: There is no equilibrium index in the array.
Input: arr[] = [-7, 1, 5, 2, -4, 3, 0]
Output: 3
Explanation: The sum of left of index 3 is -7 + 1 + 5 = -1 and sum on right of index 3 is -4 + 3 + 0 = -1.
[Naive Approach] Using Nested Loop - O(n^2) Time and O(1) Space
The most basic idea is to use nested loops.
- The outer loop iterates through all the indices one by one. Consider it as equilibrium index.
- The inner loop finds out whether index i is equilibrium index or not, by checking if left side sum = right side sum.
C++
// C++ program to find equilibrium index of an array
// using nested loop
#include <iostream>
#include <vector>
using namespace std;
int findEquilibrium(vector<int>& arr) {
// Check for indexes one by one until
// an equilibrium index is found
for (int i = 0; i < arr.size(); ++i) {
// Get left sum
int leftSum = 0;
for (int j = 0; j < i; j++)
leftSum += arr[j];
// Get right sum
int rightSum = 0;
for (int j = i + 1; j < arr.size(); j++)
rightSum += arr[j];
// If leftsum and rightsum are same, then
// index i is an equilibrium index
if (leftSum == rightSum)
return i;
}
// If equilibrium index doesn't exist
return -1;
}
int main() {
vector<int> arr = {-7, 1, 5, 2, -4, 3, 0};
cout << findEquilibrium(arr);
return 0;
}
// C program to find equilibrium index of an array
// using nested loop
#include <stdio.h>
int findEquilibrium(int arr[], int n) {
// Check for indexes one by one until
// an equilibrium index is found
for (int i = 0; i < n; ++i) {
// Get left sum
int leftSum = 0;
for (int j = 0; j < i; j++)
leftSum += arr[j];
// Get right sum
int rightSum = 0;
for (int j = i + 1; j < n; j++)
rightSum += arr[j];
// If leftsum and rightsum are same, then
// index i is an equilibrium index
if (leftSum == rightSum)
return i;
}
// If equilibrium index doesn't exist
return -1;
}
int main() {
int arr[] = {-7, 1, 5, 2, -4, 3, 0};
int n = sizeof(arr) / sizeof(arr[0]);
printf("%d", findEquilibrium(arr, n));
return 0;
}
// Java program to find equilibrium index of an array
// using nested loop
import java.util.*;
class GfG {
static int findEquilibrium(int[] arr) {
// Check for indexes one by one until
// an equilibrium index is found
for (int i = 0; i < arr.length; ++i) {
// Get left sum
int leftSum = 0;
for (int j = 0; j < i; j++)
leftSum += arr[j];
// Get right sum
int rightSum = 0;
for (int j = i + 1; j < arr.length; j++)
rightSum += arr[j];
// If leftsum and rightsum are same, then
// index i is an equilibrium index
if (leftSum == rightSum)
return i;
}
// If equilibrium index doesn't exist
return -1;
}
public static void main(String[] args) {
int[] arr = {-7, 1, 5, 2, -4, 3, 0};
System.out.println(findEquilibrium(arr));
}
}
# Python program to find equilibrium index of an array
# using nested loop
def findEquilibrium(arr):
# Check for indexes one by one until
# an equilibrium index is found
for i in range(len(arr)):
# Get left sum
leftSum = sum(arr[:i])
# Get right sum
rightSum = sum(arr[i + 1:])
# If leftsum and rightsum are same, then
# index i is an equilibrium index
if leftSum == rightSum:
return i
# If equilibrium index doesn't exist
return -1
if __name__ == '__main__':
arr = [-7, 1, 5, 2, -4, 3, 0]
print(findEquilibrium(arr))
// C# program to find equilibrium index of an array
// using nested loop
using System;
using System.Collections.Generic;
class GfG {
static int findEquilibrium(int[] arr) {
// Check for indexes one by one until
// an equilibrium index is found
for (int i = 0; i < arr.Length; ++i) {
// Get left sum
int leftSum = 0;
for (int j = 0; j < i; j++)
leftSum += arr[j];
// Get right sum
int rightSum = 0;
for (int j = i + 1; j < arr.Length; j++)
rightSum += arr[j];
// If leftsum and rightsum are same, then
// index i is an equilibrium index
if (leftSum == rightSum)
return i;
}
// If equilibrium index doesn't exist
return -1;
}
static void Main() {
int[] arr = {-7, 1, 5, 2, -4, 3, 0};
Console.WriteLine(findEquilibrium(arr));
}
}
// JavaScript program to find equilibrium index of an array
// using nested loop
function findEquilibrium(arr) {
// Check for indexes one by one until
// an equilibrium index is found
for (let i = 0; i < arr.length; ++i) {
// Get left sum
let leftSum = 0;
for (let j = 0; j < i; j++)
leftSum += arr[j];
// Get right sum
let rightSum = 0;
for (let j = i + 1; j < arr.length; j++)
rightSum += arr[j];
// If leftsum and rightsum are same, then
// index i is an equilibrium index
if (leftSum === rightSum)
return i;
}
// If equilibrium index doesn't exist
return -1;
}
// Driver code
let arr = [-7, 1, 5, 2, -4, 3, 0];
console.log(findEquilibrium(arr));
[Better Approach] Prefix Sum and Suffix Sum Array - O(n) Time and O(n) Space
The idea is to remove the need of inner loop. Instead of calculating the left side sum and right side sum each time, precompute the prefix sum array and suffix sum array, and simply access this in O(1) time.
So for each index i, we can check if prefixSum[i - 1] = suffixSum[i + 1] but to avoid unnecessary boundary checks we can also check if prefixSum[i] = suffixSum[i].
C++
// C++ program to find equilibrium index of an array
// using prefix sum and suffix sum arrays
#include <iostream>
#include <vector>
using namespace std;
int findEquilibrium(vector<int>& arr) {
int n = arr.size();
vector<int> pref(n, 0);
vector<int> suff(n, 0);
// Initialize the ends of prefix and suffix array
pref[0] = arr[0];
suff[n - 1] = arr[n - 1];
// Calculate prefix sum for all indices
for (int i = 1; i < n; i++)
pref[i] = pref[i - 1] + arr[i];
// Calculating suffix sum for all indices
for (int i = n - 2; i >= 0; i--)
suff[i] = suff[i + 1] + arr[i];
// Checking if prefix sum is equal to suffix sum
for (int i = 0; i < n; i++) {
if (pref[i] == suff[i])
return i;
}
// if equilibrium index doesn't exist
return -1;
}
int main() {
vector<int> arr = {-7, 1, 5, 2, -4, 3, 0};
cout << findEquilibrium(arr) << "\n";
return 0;
}
// C program to find equilibrium index of an array
// using prefix sum and suffix sum arrays
#include <stdio.h>
int findEquilibrium(int arr[], int n) {
int pref[n];
int suff[n];
// Initialize the ends of prefix and suffix array
pref[0] = arr[0];
suff[n - 1] = arr[n - 1];
// Calculate prefix sum for all indices
for (int i = 1; i < n; i++)
pref[i] = pref[i - 1] + arr[i];
// Calculating suffix sum for all indices
for (int i = n - 2; i >= 0; i--)
suff[i] = suff[i + 1] + arr[i];
// Checking if prefix sum is equal to suffix sum
for (int i = 0; i < n; i++) {
if (pref[i] == suff[i])
return i;
}
// if equilibrium index doesn't exist
return -1;
}
int main() {
int arr[] = {-7, 1, 5, 2, -4, 3, 0};
int n = sizeof(arr) / sizeof(arr[0]);
printf("%d\n", findEquilibrium(arr, n));
return 0;
}
// Java program to find equilibrium index of an array
// using prefix sum and suffix sum arrays
import java.util.*;
class GfG {
static int findEquilibrium(int[] arr) {
int n = arr.length;
int[] pref = new int[n];
int[] suff = new int[n];
// Initialize the ends of prefix and suffix array
pref[0] = arr[0];
suff[n - 1] = arr[n - 1];
// Calculate prefix sum for all indices
for (int i = 1; i < n; i++)
pref[i] = pref[i - 1] + arr[i];
// Calculating suffix sum for all indices
for (int i = n - 2; i >= 0; i--)
suff[i] = suff[i + 1] + arr[i];
// Checking if prefix sum is equal to suffix sum
for (int i = 0; i < n; i++) {
if (pref[i] == suff[i])
return i;
}
// if equilibrium index doesn't exist
return -1;
}
public static void main(String[] args) {
int[] arr = {-7, 1, 5, 2, -4, 3, 0};
System.out.println(findEquilibrium(arr));
}
}
# Python program to find equilibrium index of an array
# using prefix sum and suffix sum arrays
def findEquilibrium(arr):
n = len(arr)
pref = [0] * n
suff = [0] * n
# Initialize the ends of prefix and suffix array
pref[0] = arr[0]
suff[n - 1] = arr[n - 1]
# Calculate prefix sum for all indices
for i in range(1, n):
pref[i] = pref[i - 1] + arr[i]
# Calculating suffix sum for all indices
for i in range(n - 2, -1, -1):
suff[i] = suff[i + 1] + arr[i]
# Checking if prefix sum is equal to suffix sum
for i in range(n):
if pref[i] == suff[i]:
return i
# if equilibrium index doesn't exist
return -1
if __name__ == "__main__":
arr = [-7, 1, 5, 2, -4, 3, 0]
print(findEquilibrium(arr))
// C# program to find equilibrium index of an array
// using prefix sum and suffix sum arrays
using System;
class GfG {
static int findEquilibrium(int[] arr) {
int n = arr.Length;
int[] pref = new int[n];
int[] suff = new int[n];
// Initialize the ends of prefix and suffix array
pref[0] = arr[0];
suff[n - 1] = arr[n - 1];
// Calculate prefix sum for all indices
for (int i = 1; i < n; i++)
pref[i] = pref[i - 1] + arr[i];
// Calculating suffix sum for all indices
for (int i = n - 2; i >= 0; i--)
suff[i] = suff[i + 1] + arr[i];
// Checking if prefix sum is equal to suffix sum
for (int i = 0; i < n; i++) {
if (pref[i] == suff[i])
return i;
}
// if equilibrium index doesn't exist
return -1;
}
static void Main() {
int[] arr = {-7, 1, 5, 2, -4, 3, 0};
Console.WriteLine(findEquilibrium(arr));
}
}
// JavaScript program to find equilibrium index of an array
// using prefix sum and suffix sum arrays
function findEquilibrium(arr) {
const n = arr.length;
const pref = new Array(n).fill(0);
const suff = new Array(n).fill(0);
// Initialize the ends of prefix and suffix array
pref[0] = arr[0];
suff[n - 1] = arr[n - 1];
// Calculate prefix sum for all indices
for (let i = 1; i < n; i++)
pref[i] = pref[i - 1] + arr[i];
// Calculating suffix sum for all indices
for (let i = n - 2; i >= 0; i--)
suff[i] = suff[i + 1] + arr[i];
// Checking if prefix sum is equal to suffix sum
for (let i = 0; i < n; i++) {
if (pref[i] === suff[i])
return i;
}
// if equilibrium index doesn't exist
return -1;
}
// Driver Code
const arr = [-7, 1, 5, 2, -4, 3, 0];
console.log(findEquilibrium(arr));
[Expected Approach] Running Prefix Sum and Suffix Sum - O(n) Time and O(1) Space
Now the above prefix sum array and suffix sum array approach can be further optimized in terms of space, by using prefix sum and suffix sum variables. The idea is that instead of storing the prefix sum and suffix sum for each element in an array, we can simply use the fact that
PrefixSum(arr[0 : pivot - 1]) + arr[pivot] + SuffixSum[pivot + 1: n - 1] = ArraySum
so, SuffixSum[pivot + 1: n - 1] = ArraySum - PrefixSum(arr[0 : pivot - 1])
Here, pivot refers to the index that we are currently checking for the equilibrium index.
C++
// C++ program to find equilibrium index of an array
// using prefix sum and suffix sum variables
#include <iostream>
#include <vector>
using namespace std;
int equilibriumPoint(vector<int>& arr) {
int prefSum = 0, total = 0;
// Calculate the array sum
for (int ele: arr) {
total += ele;
}
// Iterate pivot over all the elements of the array and
// till left != right
for (int pivot = 0; pivot < arr.size(); pivot++) {
int suffSum = total - prefSum - arr[pivot];
if (prefSum == suffSum) {
return pivot;
}
prefSum += arr[pivot];
}
// there is no equilibrium point
return -1;
}
int main() {
vector<int> arr = { 1, 7, 3, 6, 5, 6 };
cout << equilibriumPoint(arr) << endl;
return 0;
}
// C program to find equilibrium index of an array
// using prefix sum and suffix sum variables
#include <stdio.h>
int equilibriumPoint(int arr[], int n) {
int prefSum = 0, total = 0;
// Calculate the array sum
for (int i = 0; i < n; i++) {
total += arr[i];
}
// Iterate pivot over all the elements of the array
for (int pivot = 0; pivot < n; pivot++) {
int suffSum = total - prefSum - arr[pivot];
if (prefSum == suffSum) {
return pivot;
}
prefSum += arr[pivot];
}
// There is no equilibrium point
return -1;
}
int main() {
int arr[] = {1, 7, 3, 6, 5, 6};
int n = sizeof(arr) / sizeof(arr[0]);
printf("%d\n", equilibriumPoint(arr, n));
return 0;
}
// Java program to find equilibrium index of an array
// using prefix sum and suffix sum variables
import java.util.*;
class GfG {
static int equilibriumPoint(int[] arr) {
int prefSum = 0, total = 0;
// Calculate the array sum
for (int ele : arr) {
total += ele;
}
// Iterate pivot over all the elements of the array
for (int pivot = 0; pivot < arr.length; pivot++) {
int suffSum = total - prefSum - arr[pivot];
if (prefSum == suffSum) {
return pivot;
}
prefSum += arr[pivot];
}
// There is no equilibrium point
return -1;
}
public static void main(String[] args) {
int[] arr = {1, 7, 3, 6, 5, 6};
System.out.println(equilibriumPoint(arr));
}
}
# Python program to find equilibrium index of an array
# using prefix sum and suffix sum variables
def equilibriumPoint(arr):
prefSum = 0
total = sum(arr)
# Iterate pivot over all the elements of the array
for pivot in range(len(arr)):
suffSum = total - prefSum - arr[pivot]
if prefSum == suffSum:
return pivot
prefSum += arr[pivot]
# There is no equilibrium point
return -1
if __name__ == "__main__":
arr = [1, 7, 3, 6, 5, 6]
result = equilibriumPoint(arr)
print(result)
// C# program to find equilibrium index of an array
// using prefix sum and suffix sum variables
using System;
class GfG {
static int equilibriumPoint(int[] arr) {
int prefSum = 0, total = 0;
// Calculate the array sum
foreach (int ele in arr) {
total += ele;
}
// Iterate pivot over all the elements of the array
for (int pivot = 0; pivot < arr.Length; pivot++) {
int suffSum = total - prefSum - arr[pivot];
if (prefSum == suffSum) {
return pivot;
}
prefSum += arr[pivot];
}
// There is no equilibrium point
return -1;
}
static void Main(string[] args) {
int[] arr = {1, 7, 3, 6, 5, 6};
Console.WriteLine(equilibriumPoint(arr));
}
}
// JavaScript program to find equilibrium index of an array
// using prefix sum and suffix sum variables
function equilibriumPoint(arr) {
let prefSum = 0;
let total = arr.reduce((sum, ele) => sum + ele, 0);
// Iterate pivot over all the elements of the array
for (let pivot = 0; pivot < arr.length; pivot++) {
let suffSum = total - prefSum - arr[pivot];
if (prefSum === suffSum) {
return pivot;
}
prefSum += arr[pivot];
}
// There is no equilibrium point
return -1;
}
// Driver code
const arr = [1, 7, 3, 6, 5, 6];
console.log(equilibriumPoint(arr));
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