# Introduction :

In this tutorial, we will learn how to find all elements in an integer array which are bigger than all other elements present to the right. For example :

`[1,2,5,3,1,0]`

In this array, *5,3,1* and *0* are elements greater than all right elements.

We will learn three different ways to solve this problem.

## Approach 1 : Using brute force :

Using *brute force*, we can solve this problem. Use two *for loops* one inside another. The outer loop will iterate through the elements one by one. The inner loop will iterate through all *right* elements to the element that is iterate by the *outer* loop. The inner loop will check if any element is greater than the current element or not. If no elements are found, it will print the current element pointed by the outer loop.

### C program :

The C program using brute force method is as below :

```
#include <stdio.h>
#include <stdlib.h>
#define SIZE 6
int main()
{
//1
int numArray[SIZE] = {1, 2, 5, 3, 1, 0};
//2
int i, j;
//3
for (i = 0; i < SIZE; i++)
{
//4
for (j = i + 1; j < SIZE; j++) { //5 if (numArray[j] > numArray[i])
{
break;
}
//6
if (j == SIZE - 1)
{
printf("%d ", numArray[i]);
}
}
//7
if (i == SIZE - 1)
{
printf("%d\n", numArray[i]);
}
}
return 0;
}
```

### Explanation :

*The commented numbers in the above program denote the step numbers below :*

*numArray*is the given array. You can change these values to anything you want.*i*and*j*are two variables initialized to use in the loops.- The outer loops iterates through the array values one by one.
- For each value pointed by the outer loop, the inner loop iterate others to its right.
- If any larger number is found, exit from the inner loop.
- If no larger number is found, print the current value pointed by the outer loop.
- This
*if*statement is for printing the last element of the array. The last element will always be there because we don’t have any element to the right of it.

The time complexity of this method is *O(n^2)* and it is not a recommended way to solve.

## Approach 2 : O(n) with extra space :

We can also solve this problem in *O(n)* time complexity and with an extra space. Below algorithm we will use for that :

- Create one extra array of same size as the original array holding numbers. Create one index pointer variable to point to the current index in the second array.
- Iterate through the elements one by one.
- For each element, check in the second array if any larger value is exists. If yes, remove it and check the element to its left. If not, add this element to the array.
- Finally, the second array will hold the required numbers.

### C program :

```
#include <stdio.h>
#define SIZE 6
int main()
{
//1
int numArray[SIZE] = {1, 2, 5, 3, 1, 0};
int resultArray[SIZE] = {0};
//2
int resultArrayIndex = 0;
int i;
//3
resultArray[0] = numArray[0];
//4
for (i = 1; i < SIZE; i++) { //5 while (resultArrayIndex >= 0)
{
//6
if (resultArray[resultArrayIndex] < numArray[i])
{
resultArrayIndex--;
}
else
{
break;
}
}
//7
resultArray[resultArrayIndex + 1] = numArray[i];
resultArrayIndex++;
}
//8
for (i = 0; i < resultArrayIndex + 1; i++)
{
printf("%d ", resultArray[i]);
}
return 0;
}
```

### Explanation :

*The commented numbers in the above program denote the step numbers below :*

*numArray*is the array holding the numbers.*resultArray*is the array to hold the final result.*resultArrayIndex*is assigned to*0*. This variable will point to the current index position of the array*resultArray*.- Add the first element of the array
*numArray*to the*resultArray*. - Run one
*for loop*starting from the second element and iterate through each element one by one. - Check for each element in the
*resultArray*. - If it is smaller than the number pointed by the loop, decrement the value of
*resultArrayIndex*i.e. decrement the pointer variable. If not, exit from the loop. - Add the current element to the array
*resultArray*. - Finally, print out the contents of the
*resultArray*.

The complexity of this program is *O(n)* for both space and time. This is an optimized solution than the previous one but we have one more way to solve it. Let me show you how :

## Approach 3: Using one for loop and without using extra space :

This is the most efficient solution and easiest to solve it. The following algorithm is used for that :

- Scan the items of the array from
*right to left*. - Create one variable to assign the current largest number. Initialize it as
*-1*. - For each element, check if it is bigger than the largest number or not. If yes, print its value and update the largest number variable. If not, move to the next value.

That’s it.

### C program :

```
#include <stdio.h>
#define SIZE 6
int main()
{
//1
int numArray[SIZE] = {1, 2, 5, 3, 1, 0};
//2
int i;
int largestNumber = -1;
//3
for (i = SIZE - 1; i >= 0; i--)
{
//4
if (numArray[i] > largestNumber)
{
printf("%d ", numArray[i]);
largestNumber = numArray[i];
}
}
return 0;
}
```

### Explanation :

*The commented numbers in the above program denote the step numbers below :*

*numArray*is the given array.- Create one integer variable
*i*to use in the*loop*for iteration and one variable*largestNumber*to store the current largest number. Initialize it to*-1*. - Run one
*for loop*to scan all items from right to left. - If the current item is bigger than
*largestNumber*, print it and assign its value to*largestNumber*.

The time complexity of this solution is *O(n)*.

### Conclusion :

In this tutorial, we have learned how to find all elements in an array bigger than its right elements. We have learned three different ways to solve it. Try to execute these solutions with different array and drop one comment below if you have any queries.