Related Articles
Find the index in a circular array from which prefix sum is always non-negative
• Difficulty Level : Hard
• Last Updated : 29 Apr, 2021

Given a circular array arr[] consisting of N integers, the task is to find the starting index of the circular array such that the prefix sum from that index is always non-negative. If there exists no such index, then print “-1”.

Examples:

Input: arr[] = {3, -6, 7, -1, -4, 5, -1}
Output: 2
Explanation:
Consider the index 2 from where the prefix sum of the given circular array is being calculated, then the prefix sum is given by {9, 3, 7, 6, 2, 7, 6}

Input: arr[] = {3, -5, -1}
Output: -1

Approach: The given problem can be solved based on the following observations:

Follow the steps to solve the problem:

• Initialize a variable, say sum as 0, that stores the sum of array elements.
• Initialize a variable, say in as 0 that stores the starting index for the circular traversal.
• Initialize a variable, say min as INT_MAX that stores the minimum prefix sum of the array arr[].
• Traverse the given array and perform the following steps:
• Update the value of sum as the sum of sum and the current element arr[i].
• If the value of sum is less than min, then update the min as sum and in as (i + 1).
• If the sum of the array is negative, then print -1. Otherwise, print the value of (in % N) as the resultant possible index.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function to find the starting index``// of the given circular array s.t.``// prefix sum array is non negative``int` `startingPoint(``int` `A[], ``int` `N)``{``    ``// Stores the sum of the array``    ``int` `sum = 0;` `    ``// Stores the starting index``    ``int` `in = 0;` `    ``// Stores the minimum prefix``    ``// sum of A[0..i]``    ``int` `min = INT_MAX;` `    ``// Traverse the array arr[]``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// Update the value of sum``        ``sum += A[i];` `        ``// If sum is less than min``        ``if` `(sum < min) {` `            ``// Update the min as the``            ``// value of prefix sum``            ``min = sum;` `            ``// Update in``            ``in = i + 1;``        ``}``    ``}` `    ``// Otherwise, no such index is``    ``// possible``    ``if` `(sum < 0) {``        ``return` `-1;``    ``}` `    ``return` `in % N;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 3, -6, 7, -4, -4, 6, -1 };``    ``int` `N = (``sizeof``(arr) / ``sizeof``(arr));``    ``cout << startingPoint(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.io.*;``import` `java.lang.*;``import` `java.util.*;` `class` `GFG{` `// Function to find the starting index``// of the given circular array s.t.``// prefix sum array is non negative``static` `int` `startingPoint(``int` `A[], ``int` `N)``{``    ` `    ``// Stores the sum of the array``    ``int` `sum = ``0``;` `    ``// Stores the starting index``    ``int` `in = ``0``;` `    ``// Stores the minimum prefix``    ``// sum of A[0..i]``    ``int` `min = Integer.MAX_VALUE;` `    ``// Traverse the array arr[]``    ``for``(``int` `i = ``0``; i < N; i++)``    ``{``        ` `        ``// Update the value of sum``        ``sum += A[i];` `        ``// If sum is less than min``        ``if` `(sum < min)``        ``{` `            ``// Update the min as the``            ``// value of prefix sum``            ``min = sum;` `            ``// Update in``            ``in = i + ``1``;``        ``}``    ``}` `    ``// Otherwise, no such index is``    ``// possible``    ``if` `(sum < ``0``)``    ``{``        ``return` `-``1``;``    ``}` `    ``return` `in % N;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``3``, -``6``, ``7``, -``4``, -``4``, ``6``, -``1` `};``    ``int` `N = arr.length;``    ` `    ``System.out.print(startingPoint(arr, N));``}``}` `// This code is contributed by Kingash`

## Python3

 `# Python3 program for the above approach` `# Function to find the starting index``# of the given circular array``# prefix sum array is non negative``import` `sys` `def` `startingPoint(A, N):``    ` `    ``# Stores the sum of the array``    ``sum` `=` `0``    ` `    ``# Stores the starting index``    ``startingindex ``=` `0``    ` `    ``# Stores the minimum prefix``    ``# sum of A[0..i]``    ``min` `=` `sys.maxsize``    ` `    ``# Traverse the array``    ``for` `i ``in` `range``(``0``, N):``        ` `        ``# Update the value of sum``        ``sum` `+``=` `A[i]``        ` `        ``# If sum is less than minimum``        ``if` `(``sum` `< ``min``):``            ` `            ``# Update the min as``            ``# the value of prefix sum``            ``min` `=` `sum``            ` `            ``# Update starting index``            ``startingindex ``=` `i ``+` `1``            ` `    ``# Otherwise no such index is possible``    ``if` `(``sum` `< ``0``):``        ``return` `-``1``        ` `    ``return` `startingindex ``%` `N` `# Driver code``arr ``=` `[ ``3``, ``-``6``, ``7``, ``-``4``, ``-``4``, ``6``, ``-``1` `]``N ``=` `len``(arr)` `print``(startingPoint(arr,N))` `# This code is contributed by Virusbuddah`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{``    ` `// Function to find the starting index``// of the given circular array s.t.``// prefix sum array is non negative``static` `int` `startingPoint(``int``[] A, ``int` `N)``{``    ` `    ``// Stores the sum of the array``    ``int` `sum = 0;` `    ``// Stores the starting index``    ``int` `ind = 0;` `    ``// Stores the minimum prefix``    ``// sum of A[0..i]``    ``int` `min = Int32.MaxValue;` `    ``// Traverse the array arr[]``    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ` `        ``// Update the value of sum``        ``sum += A[i];` `        ``// If sum is less than min``        ``if` `(sum < min)``        ``{``            ` `            ``// Update the min as the``            ``// value of prefix sum``            ``min = sum;` `            ``// Update in``            ``ind = i + 1;``        ``}``    ``}` `    ``// Otherwise, no such index is``    ``// possible``    ``if` `(sum < 0)``    ``{``        ``return` `-1;``    ``}` `    ``return` `ind % N;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int``[] arr = { 3, -6, 7, -4, -4, 6, -1 };``    ``int` `N = arr.Length;``    ` `    ``Console.Write(startingPoint(arr, N));``}``}` `// This code is contributed by ukasp`

## Javascript

 ``
Output:
`5`

Time Complexity: O(N)
Auxiliary Space: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

My Personal Notes arrow_drop_up