## Amazon Interview Question

Interns**Country:**India

**Interview Type:**In-Person

But the binary search stops when it finds the element... how would you guarantee that it would be the first instance of the element????

```
Let k be the given number then code would be similar to the following
int starting_index(int *a,int start,int end)
{
int mid=(start+end)/2;
if(end!=mid)
{
if(a[mid-1]<k && a[mid]==k)
return mid;
else if(a[mid]<k)
starting_index(a,mid+1,end);
else
starting_index(a,start,mid-1);
}
else
{
if(a[mid]==k)
return mid;
else
return -1;
}
}
-1 is returned when there is no occurence of given number.
```

Binary Search to find an instance of the given number, then scan backward to find the first instance of the given number, as the array is sorted.

Time complexity is O(n).

Then why don't you just scan forward without Binary Search to find the first instance with the same time complexity?

O(n) is worse-case complexity here for a edge case when entire array consists of the same number.

Therefore I think it's safe to assume that average complexity will be O(log n).

Perform binary search.

```
int findFirstOccurrence(int* arr,int l,int h,int tofind)
{
int mid;
if(l>h) return INT_MIN;
if(l==h)
return arr[l]==tofind?l:-1;
mid=(l+h)>>1;
if(arr[mid]==tofind && (mid==l || arr[mid]>arr[mid-1]))
return mid;
if(tofind<=arr[mid])
return findFirstOccurrence(arr,l,mid-1,tofind);
return findFirstOccurrence(arr,mid+1,h,tofind);
}
```

Complete code here: ideone.com/8q91s

```
public class BinarySearch {
//both from and to are inclusive.
static int minOccurance(int[] array, int from, int to, int v) {
if(from == to) {
if(v == array[from]) {
return from;
} else {
return -1;
}
}
int middle = (from + to) >> 1;
if(v < array[middle]) {
return minOccurance(array, from, middle-1, v);
} else if (v > array[middle]) {
return minOccurance(array, middle + 1, to, v);
} else {
int left = minOccurance(array, from, middle-1, v);
if(left == -1 ) {
return middle;
} else {
return left;
}
}
}
public static void main(String[] args) {
int[] arr = new int[] {1,1,1,1,1,1,1,1,1, 2, 2,2, 4,4,5,5,5,5,5,5,5};
System.out.println(minOccurance(arr, 0, arr.length - 1, 1));
System.out.println(minOccurance(arr, 0, arr.length - 1, 2));
System.out.println(minOccurance(arr, 0, arr.length - 1, 3));
System.out.println(minOccurance(arr, 0, arr.length - 1, 4));
System.out.println(minOccurance(arr, 0, arr.length - 1, 5));
}
}
```

```
//using binary search
int findIndex(int *arr, int low, int high, int data)
{
int mid = (low+high)/2;
if(arr[low] == data)
return low;
else if(arr[mid] >= data)
return findIndex(arr, low , mid, data);
else
return findIndex(arr, mid+1, high, data);
}
//assumed that number is present in array
```

```
public static int findFirstNum(int[] input,int start,int end,int target)
{
if(start>end)
return -1;
else
{
int middle=(start+end)/2;
if(target<=input[middle])
{
int index=findFirstNum(input,start,middle-1,target);
if(index==-1)
{
if(input[middle]==target)
{
return middle;
}
else
return -1;
}
else
return index;
}
else
{
return findFirstNum(input,middle+1,end,target);
}
}
}
```

public class Find_First_Instance_In_Sorted_Array {

public static int find_first(int[] test,int aim){

int result_index=find(test,aim,0,test.length-1);

return result_index;

}

public static int find(int[] test,int aim,int begin,int end){

if(begin==end){

if(test[begin]==aim){

return begin;

}

else{

return -1;

}

}

if(begin==end-1){

if((test[begin]==aim)||(test[end]==aim)){

if(test[begin]==aim){

return begin;

}

if(test[end]==aim){

return end;

}

}

else{

return -1;

}

}

int mid=(begin+end)/2;

if(test[mid]>aim){

return find(test,aim,begin,mid-1);

}

if(test[mid]<aim){

return find(test,aim,mid+1,end);

}

if(test[mid]==aim){

return find(test,aim,begin,mid-1)!=-1?find(test,aim,begin,mid-1):mid;

}

return -1;

}

public static void main(String[] args) {

int[] test=new int[]{1,2,3,3,3,3,4,5,6,7,7,8};

int aim=3;

int result_index=find_first(test,aim);

System.out.println(result_index);

}

}

The complexity can be 2*logn first to find the number then next binary search to find the first instance

Time Complexity: O(log n)

int First_Instance(int A[], int min, int max, int k){

int mid = (min+ max)/2;

int index, temp;

if(min<=max){

if(k< A[mid])

index= First_Instance(A, min, mid- 1, k);

else if(k> A[mid])

index= First_Instance(A, min, mid- 1, k);

else

while(A[mid]!= k){

temp= mid;

mid++;

}

return temp;

}

return -1;

}

i1 = 0, i2= arr_end

Loop till (mod(i1 - i2) != 1)

1. Binary search from i1 to i2, ill the number is found: - store the index - i2

2. Continue the binary search on the left, till the next lower number is found- if no number is lower, return 0.

else store index - i1

return i2;

P.S : Not a very clear algo but hope its explanatory.

Complexity will be log(n)

int find_first(int arr[], int start, int end, int num)

{

static int count;

count++;

int low, large;

int mid = (start+end)/2;

while(arr[mid] > num)

{

if(mid == start)

return -1;

mid = (start + mid)/2;

}

if(arr[mid] == num)

{

large = mid;

while(arr[mid] >= num)

{

if(mid == start)

return start;

mid = (start + mid)/2;

}

low = mid;

}

else

{

large = end;

low = mid;

}

if(large - low == 1)

{

if(arr[large] == num)

return large;

else

return -1;

}

return find_first(arr, low, large, num);

}

int main()

{

int arr[]={1,1,1,5,5,5,5,5,5,7,7,7,8,9,12,13,15,16,17,17};

int val = find_first(arr,0,19,8);

return 0;

}

I'm not sure if I'm missing anything or misunderstood the question. If you just do a Binary Search, this will only find the "target", i.e., the value it's looking for, but it is not guarantee the first occurance. As someone mentioned up there that we still have to do a backward scan to make sure that is the first occurance, why can't we just do a forward scan at the first place and return the first one it sees. This way we don't have to do a Binary Search and the run time will be O(n), which is equals to O(logn)+O(n).

Please let me know if I'm wrong, maybe I misread this problem.

Here is the code with complexity log(n)

```
#include <stdio.h>
/*
* Find the first occurence of the given number in index.
*/
void main()
{
int nums[] = {1,1,3,5,8,8,8,10,12,23,23,55};
int len = sizeof(nums)/sizeof(int);
int start = 0, end = len-1, search = 8;
int found_right = -1;
while ((end - start) > 1)
{
if (found_right != -1)
{
if (nums[end] != search)
{
break;
}
found_right = end;
end -= 1;
continue;
}
int mid = (end + start)/2;
int val = nums[mid];
if (val == search)
{
end = mid-1;
found_right = mid;
}
else if(val < search)
{
start = mid;
}
else
{
end = mid;
}
}
if (found_right != -1)
{
printf("found at %d", found_right);
}
else
{
printf("Sorry!");
}
}
```

logn

- Anonymous August 05, 2012perform binary search