Find Array formed by adding each element of given array with largest element in new array to its left

Given an array A of size N, the task is to find the resultant array formed by adding each element of the given array with the largest element in the new array to its left.
Examples:

Input: arr[] = {5, 1, 6, -3, 2} 
Output: {5, 6, 12, 9, 14} 
Element A₀: No element if present at its left. Hence the element at 0th index of the resultant array = 5 
Element A₁: Largest element to its left in the resultant array = 5. Hence the element at 1th index of the resultant array = 1 + 5 = 6 
Element A₂: Largest element to its left in the resultant array = 6. Hence the element at 2nd index of the resultant array = 6 + 6 = 12 
Element A₃: Largest element to its left in the resultant array = 12. Hence the element at 3rd index of the result array = -3 + 12 = 9 
Element A₄: Largest element to its left in the resultant array = 12. Hence the element at 4th index of the result array = 2 + 12 = 14 
Therefore the resultant array = {5, 6, 12, 9, 14}
Input: arr[] = {40, 12, 62} 
Output: {40, 52, 114} 

Approach:
In order to find such an array, each element of the new array will be computed one by one for each index in the range [0, N-1], according to the following rules: 

1. For the starting index, i.e. 0, the new array will be empty. Hence there won’t be any largest element. In this case, the element at 0th index in the given array is copied down in the new array, i.e. 
   

B0 = A0

where A is the given array and 
      B is the new array

       2.For every other index in the range [1, N-1], first the largest element is found out to its left in the new array and then it is            added to the corresponding element of the original array, i.e., 

Bi = Ai + max(B0, B1, ..., Bi-1)

where A is the given array, 
      B is the new array, and
      i is the current index

Below is the implementation of the above approach: 

C++

// C++ program to find Array formed by adding
// each element of given array with largest
// element in new array to its left

#include <bits/stdc++.h>
using namespace std;

// Function to find array B from array
// A such that Ai = Bi – max(B0…Bi-1)
void find_array(int a[], int n)
{
    // Initialising as 0 as first
    // element will remain same
    int x = 0;

    for (int i = 0; i < n; i++) {

        // restoring values of B
        a[i] += x;

        cout << a[i] << ' ';

        // Find max value
        x = max(x, a[i]);
    }
}

// Driver code
int main()
{
    int a[] = {40, 12, 62};
    int n = sizeof(a) / sizeof(a[0]);

    // Function call
    find_array(a, n);

    return 0;
}

Java

// Java program to find Array formed by adding
// each element of given array with largest
// element in new array to its left

public class GFG
{

// Function to find array B from array
// A such that Ai = Bi – max(B0…Bi-1)
static void find_array(int []a, int n)
{
    // Initialising as 0 as first
    // element will remain same
    int x = 0;

    for (int i = 0; i < n; i++) {

        // restoring values of B
        a[i] += x;

        System.out.print(a[i] + " ");

        // Find max value
        x = Math.max(x, a[i]);
    }
}

// Driver code
public static void main(String []args)
{
    int []a = {40, 12, 62};
    int n = a.length ;

    // Function call
    find_array(a, n);
}
}

// This code is contributed by Yash_R

Python3

# Python3 program to find Array formed by adding
# each element of given array with largest
# element in new array to its left

# Function to find array B from array
# A such that Ai = Bi – max(B0…Bi-1)
def find_array(a,  n) :

    # Initialising as 0 as first
    # element will remain same
    x = 0;

    for i in range(n) :

        # restoring values of B
        a[i] += x;

        print(a[i],end= ' ');

        # Find max value
        x = max(x, a[i]);

# Driver code
if __name__ == "__main__" :

    a = [40, 12, 62];
    n = len(a);

    # Function call
    find_array(a, n);

# This code is contributed by Yash_R

C#

// C# program to find Array formed by adding
// each element of given array with largest
// element in new array to its left
using System;

class gfg
{

// Function to find array B from array
// A such that Ai = Bi – max(B0…Bi-1)
static void find_array(int []a, int n)
{
    // Initialising as 0 as first
    // element will remain same
    int x = 0;

    for (int i = 0; i < n; i++) {

        // restoring values of B
        a[i] += x;

        Console.Write(a[i] + " ");

        // Find max value
        x = Math.Max(x, a[i]);
    }
}

// Driver code
public static void Main(string []args)
{
    int []a = {40, 12, 62};
    int n = a.Length ;

    // Function call
    find_array(a, n);
}
}

// This code is contributed by Yash_R

Javascript

<script>

// Javascript program to find Array formed by adding
// each element of given array with largest
// element in new array to its left

// Function to find array B from array
// A such that Ai = Bi – max(B0…Bi-1)
function find_array(a, n)
{
    // Initialising as 0 as first
    // element will remain same
    let x = 0;

    for (let i = 0; i < n; i++) {

        // restoring values of B
        a[i] += x;

        document.write(a[i] + ' ');

        // Find max value
        x = Math.max(x, a[i]);
    }
}

// Driver code

    let a = [40, 12, 62];
    let n = a.length;

    // Function call
    find_array(a, n);


// This code is contributed by Mayank Tyagi

</script>

Output:

40 52 114

Time Complexity:  O(N)

Auxiliary Space: O(1)