CareerCup

The first method is just to simply go through the array and calculate the sums for all previous elements and all next elements, and compare them.
But is is too inefficient.
More efficient method is:
1). To calculate total sum of all elements.
Growing Sum =0
2). Going through the array, subtract elements from the total sum and add them to growing sum. Compare Growing Sum to the Total Sum. If they are equal - we found our element(s).

Example given in question is wrong. Please rectify that to avoid any confusion.

1+0==1
but -11 +1 +12 !=1

var list = new List<int>() {1, 1, -11, 1, 12};
var getListCount = list.Count;
var isListCountOdd = getListCount % 2 == 0;
var getIntegerIncrement = 3;
int takeFromList;

if (isListCountOdd)
{
	takeFromList = getListCount/2;
}
else
{
	if (getListCount <= 5)
	{
		takeFromList = getListCount - getIntegerIncrement;
	}
	else
	{
		getIntegerIncrement++;
		takeFromList = getListCount - getIntegerIncrement;
	}
}

// Get left and right numbers
var leftNumbers = list.Take(takeFromList);
var rightNumbers = list.Skip(takeFromList).Take(getIntegerIncrement);
// Sum them up
var leftNumbersTotal = leftNumbers.Sum();
var rightNumbersTotal = rightNumbers.Sum();

Console.Write(leftNumbersTotal == rightNumbersTotal ? "Left == Right" : "Left != Right");
Console.ReadKey();

-- This solution is for list contains 4 or more count.
var list = new List<int>() {1, 1, -11, 1, 12};
var getListCount = list.Count;
var isListCountOdd = getListCount % 2 == 0;
var getIntegerIncrement = 3;
int takeFromList;

if (isListCountOdd)
{
	takeFromList = getListCount/2;
}
else
{
	if (getListCount <= 5)
	{
		takeFromList = getListCount - getIntegerIncrement;
	}
	else
	{
		getIntegerIncrement++;
		takeFromList = getListCount - getIntegerIncrement;
	}
}

// Get left and right numbers
var leftNumbers = list.Take(takeFromList);
var rightNumbers = list.Skip(takeFromList).Take(getIntegerIncrement);
// Sum them up
var leftNumbersTotal = leftNumbers.Sum();
var rightNumbersTotal = rightNumbers.Sum();

Console.Write(leftNumbersTotal == rightNumbersTotal ? "Left == Right" : "Left != Right");
Console.ReadKey();

PYTHON::

>>> def sum(l):
a = 0
d = 0
b = len(l)
c = b/2
for i in range(0, c):
a = a + l[i]
for j in range(c, ((c*2)+1)):
d = d + l[j]
if a == d:
print "both sides of sum is equal"
return a
elif a != d:
a = 0
d = 0
for i in range(0, c+1):
a = a + l[i]
for j in range(c+1, ((c*2)+1)):
d = d + l[j]
if a == d:
print "both sides of sum is equal at 2nd level"
return a
else:
print "both sides of sum is not equal"
return False


>>>
>>> sum([1,1,-11,1,12])
both sides of sum is equal
2
>>> sum([-11,1,12,1,1])
both sides of sum is equal at 2nd level
2
>>> sum([-11,1,12,1,0])
both sides of sum is not equal
False
>>>

public static void main(String[] args) {
		int[] a = {1,0,1,12,-2,-8};
		int sum1 = 0, sum2 = 0;
		
		for(int i=1; i<a.length; i++) {
			for(int j = 0; j<=i; j++) {
				sum1 += a[j];
			}
			
			for(int k=i+1; k<a.length; k++) {
				sum2 += a[k];
			}
			if(sum1 == sum2) {
				System.out.println("Sum1: " + sum1);
				for(int l =0; l<=i; l++) {
					System.out.println(a[l]);
				}
				System.out.println("Sum2: " + sum2);
				for(int l =i+1; l<a.length; l++) {
					System.out.println(a[l]);
				}
			}
			sum1 =0; sum2 = 0;
		}
	}

protected void findLeftAndRightSum(){
		//int[] a = {1,0,1,12,-2,-8};
		int[] a = {1, 1, -11, 1, 12};
		int sum1 = 0, sum2 = 0, index = 0;
		
		while(index<a.length){
			sum1 = 0;
			sum2 = 0;
			for(int i=0; i<=index; i++){
				sum1 = sum1+a[i];
			}
			for(int i=index+1; i<a.length; i++){
				sum2 = sum2+a[i];
			}
			if(sum1==sum2){
				break;
			}else{
				index++;
			}
		}
		System.out.println("Common Sum : " + sum1);
	}

protected void findLeftAndRightSum(){
		//int[] a = {1,0,1,12,-2,-8};
		int[] a = {1, 1, -11, 1, 12};
		int sum1 = 0, sum2 = 0, index = 0;
		
		while(index<a.length){
			sum1 = 0;
			sum2 = 0;
			for(int i=0; i<=index; i++){
				sum1 = sum1+a[i];
			}
			for(int i=index+1; i<a.length; i++){
				sum2 = sum2+a[i];
			}
			if(sum1==sum2){
				break;
			}else{
				index++;
			}
		}
		System.out.println("Common Sum : " + sum1);

}

protected void findLeftAndRightSum(){
//int[] a = {1,0,1,12,-2,-8};
int[] a = {1, 1, -11, 1, 12};
int sum1 = 0, sum2 = 0, index = 0;

while(index<a.length){
sum1 = 0;
sum2 = 0;
for(int i=0; i<=index; i++){
sum1 = sum1+a[i];
}
for(int i=index+1; i<a.length; i++){
sum2 = sum2+a[i];
}
if(sum1==sum2){
break;
}else{
index++;
}
}
System.out.println("Common Sum : " + sum1);
}

private static boolean recArray ( int[] nums, int index, int sum1, int sum2 ) {
		  if ( index >= nums.length ) {
		    return sum1 == sum2;
		  }
		  int value = nums[index];
		  return (recArray(nums, index + 1, sum1 + value, sum2) || recArray(nums, index + 1, sum1, sum2 + value));
		}

where index =0 at the beginning