Generate Array whose difference of each element with its left yields the given Array

Given an integer N and an arr1[], of (N – 1) integers, the task is to find the sequence arr2[] of N integers in the range [1, N] such that arr1[i] = arr2[i+1] – arr2[i]. The integers in sequence arr1[] lies in range [-N, N].
Examples:

Input: N = 3, arr1[] = {-2, 1} 
Output: arr2[] = {3, 1, 2} 
Explanation: 
arr2[1] – arr2[0] = (1 – 3) = -2 = arr1[0] 
arr2[2] – arr2[1] = (2 – 1) = 1 = arr1[1]
Input: N = 5, arr1 = {1, 1, 1, 1, 1} 
Output: arr2 = {1, 2, 3, 4, 5} 
Explanation: 
arr2[1] – arr2[0] = (2 – 1) = 1 = arr1[0] 
arr2[2] – arr2[1] = (3 – 2) = 1 = arr1[1] 
arr2[3] – arr2[2] = (4 – 3) = 1 = arr1[2] 
arr2[4] – arr2[3] = (5 – 4) = 1 = arr1[3] 

Approach:
Follow the steps to solve the problem: 

1. Assume the first element of arr2[] to be X.
2. The next element will be X + arr1[0].
3. The rest of the elements of arr2[] can be represented, w.r.t X.
4. It is known that the sequence arr2[] can contain integers in the range [1, N]. So the minimum possible integer would be 1.
5. The minimum number of the arr2[] can be found out in terms of X, and equate it with 1 to find the value of X.
6. Finally using the values of X, all the other numbers in arr2[] can be found out.

Below is the implementation of the above approach: 

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the sequence
void find_seq(int arr[],
              int m, int n) {
    int b[n];
    int x = 0;

    // initializing 1st element
    b[0] = x;

    // Creating sequence in
    // terms of x
    for (int i = 0;
         i < n - 1; i++) {

        b[i + 1] = x +
                   arr[i] + b[i];
    }

    int mn = n;

    // Finding min element
    for (int i = 0; i < n; i++)
    {
        mn = min(mn, b[i]);
    }

    // Finding value of x
    x = 1 - mn;

    // Creating original sequence
    for (int i = 0; i < n; i++) {
        b[i] += x;
    }

    // Output original sequence
    for (int i = 0; i < n; i++) {
        cout << b[i] << " ";
    }
    cout << endl;
}

// Driver function
int main()
{
    int N = 3;
    int arr[] = { -2, 1 };

    int M = sizeof(arr) / sizeof(int);
    find_seq(arr, M, N);

    return 0;
}

Java

// Java implementation of the above approach
class GFG{

// Function to find the sequence
static void find_seq(int arr[], int m,
                                int n)
{
    int b[] = new int[n];
    int x = 0;

    // Initializing 1st element
    b[0] = x;

    // Creating sequence in
    // terms of x
    for(int i = 0; i < n - 1; i++)
    {
       b[i + 1] = x + arr[i] + b[i];
    }

    int mn = n;

    // Finding min element
    for(int i = 0; i < n; i++)
    {
       mn = Math.min(mn, b[i]);
    }

    // Finding value of x
    x = 1 - mn;

    // Creating original sequence
    for(int i = 0; i < n; i++)
    {
       b[i] += x;
    }

    // Output original sequence
    for(int i = 0; i < n; i++)
    {
        System.out.print(b[i] + " ");
    }
    System.out.println();
}

// Driver code
public static void main (String[] args)
{
    int N = 3;
    int arr[] = new int[]{ -2, 1 };
    int M = arr.length;

    find_seq(arr, M, N);
}
}

// This code is contributed by Pratima Pandey

Python3

# Python3 program for the above approach

# Function to find the sequence
def find_seq(arr, m, n):

    b = []
    x = 0

    # Initializing 1st element
    b.append(x)

    # Creating sequence in
    # terms of x
    for i in range(n - 1):
        b.append(x + arr[i] + b[i])

    mn = n

    # Finding min element
    for i in range(n):
        mn = min(mn, b[i])

    # Finding value of x
    x = 1 - mn

    # Creating original sequence
    for i in range(n):
        b[i] += x

    # Output original sequence
    for i in range(n):
        print(b[i], end = ' ')

    print()

# Driver code
if __name__=='__main__':

    N = 3
    arr = [ -2, 1 ]
    M = len(arr)

    find_seq(arr, M, N)

# This code is contributed by rutvik_56

C#

// C# implementation of the above approach
using System;

class GFG{

// Function to find the sequence
static void find_seq(int []arr, int m,
                                int n)
{
    int []b = new int[n];
    int x = 0;

    // Initializing 1st element
    b[0] = x;

    // Creating sequence in
    // terms of x
    for(int i = 0; i < n - 1; i++)
    {
       b[i + 1] = x + arr[i] + b[i];
    }

    int mn = n;

    // Finding min element
    for(int i = 0; i < n; i++)
    {
       mn = Math.Min(mn, b[i]);
    }

    // Finding value of x
    x = 1 - mn;

    // Creating original sequence
    for(int i = 0; i < n; i++)
    {
       b[i] += x;
    }

    // Output original sequence
    for(int i = 0; i < n; i++)
    {
       Console.Write(b[i] + " ");
    }
    Console.WriteLine();
}

// Driver code
public static void Main(String[] args)
{
    int N = 3;
    int []arr = new int[]{ -2, 1 };
    int M = arr.Length;

    find_seq(arr, M, N);
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript program for the above approach

// Function to find the sequence
function find_seq(arr,m, n) {
    let b = new Array(n);
    let x = 0;

    // initializing 1st element
    b[0] = x;

    // Creating sequence in
    // terms of x
    for (let i = 0;
         i < n - 1; i++) {

        b[i + 1] = x +
                   arr[i] + b[i];
    }

    let mn = n;

    // Finding min element
    for (let i = 0; i < n; i++)
    {
        mn = Math.min(mn, b[i]);
    }

    // Finding value of x
    x = 1 - mn;

    // Creating original sequence
    for (let i = 0; i < n; i++) {
        b[i] += x;
    }

    // Output original sequence
    for (let i = 0; i < n; i++) {
        document.write(b[i] + " ");
    }
    document.write("<br>");
}

// Driver function

    let N = 3;
    let arr = [ -2, 1 ];

    let M = arr.length;
    find_seq(arr, M, N);


// This code is contributed by Mayank Tyagi

</script>

Output:

3 1 2

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