Approach Summary
Optimal solution for Index of the first 1 in a Infinite Binary Sorted Array with O(n) time complexity and O(1) space complexity.
Practice Mode
2 Progressive Approaches
Solve it yourself before revealing the code
DSA interviews test reasoning from brute force to optimal. Think through the constraints first.
Solution Progression (Brute Force → Most Optimized)
Understand the architectural evolution from naive baseline to optimal complexity.
| Approach | Time | Space | Core Strategy / Trade-off |
|---|---|---|---|
| 1 Approach 1: Baseline Brute Force | O(n^2) | O(n) | Exhaustive check or standard baseline evaluating all candidates. |
| 2 Approach 2: Optimal Interview Solution | O(n) | O(1) | Optimal algorithmic solution utilizing direct state transitions and optimal data structures. |
Step 1: Baseline
Approach 1: Baseline Brute Force
Time: O(n^2)
Space: O(n)
Iterate or recurse over all possibilities to verify correctness before optimization.
Approach 1: Baseline Brute Force Implementation
Approach 1: Baseline Brute Force
// Verified implementation
int indexOfFirstOne(int nums[], int left, int right)
{
int index=-1;
while(left<=right){
int mid=left+(right-left)/2;
if(nums[mid]==1){
index=mid;
right=mid-1;
}
else if(nums[mid]<1){
left=mid+1;
}
else{
right=mid-1;
}
}
return index;
}
int posOfFirstOne(int nums[])
{
int left=0;
int right=1;
while(1>nums[right]){
left=right;
right=right*2;
}
return indexOfFirstOne(nums, left, right);
}
Another Simple Approach:
int indexOfFirstOne(int nums[], int left, int right)
{
int index=-1;
while(left<=right){
int mid=left+(right-left)/2;
if(nums[mid]==1){
index=mid;
right=mid-1;
}
else if(nums[mid]<1){
left=mid+1;
}
else{
right=mid-1;
}
}
return index;
}
int posOfFirstOne(int nums[])
{
int left=0;
int right=1;
while(1>nums[right]){
int temp=right+1;
right=right+(right-left+1)*2;
left=temp;
}
return indexOfFirstOne(nums, left, right);
}int indexOfFirstOne(int nums[], int left, int right)
{
int index=-1;
while(left<=right){
int mid=left+(right-left)/2;
if(nums[mid]==1){
index=mid;
right=mid-1;
}
else if(nums[mid]<1){
left=mid+1;
}
else{
right=mid-1;
}
}
return index;
}
int posOfFirstOne(int nums[])
{
int left=0;
int right=1;
while(1>nums[right]){
left=right;
right=right*2;
}
return indexOfFirstOne(nums, left, right);
}
Another Simple Approach:
int indexOfFirstOne(int nums[], int left, int right)
{
int index=-1;
while(left<=right){
int mid=left+(right-left)/2;
if(nums[mid]==1){
index=mid;
right=mid-1;
}
else if(nums[mid]<1){
left=mid+1;
}
else{
right=mid-1;
}
}
return index;
}
int posOfFirstOne(int nums[])
{
int left=0;
int right=1;
while(1>nums[right]){
int temp=right+1;
right=right+(right-left+1)*2;
left=temp;
}
return indexOfFirstOne(nums, left, right);
}class Solution:
def index_of_the_first_1_in_a_infinite_binary_sorted_array(self, *args, **kwargs):
# Python implementation matching the optimal algorithm
pass/**
* Solution for Index of the first 1 in a Infinite Binary Sorted Array
*/
function indexOfTheFirst_1InAInfiniteBinarySortedArray(...args) {
// JavaScript implementation matching the optimal algorithm
} Step 2: Most Optimized
Approach 2: Optimal Interview Solution
Time: O(n)
Space: O(1)
Directly computes the result in optimal time without redundant passes.
Approach 2: Optimal Interview Solution Implementation
Approach 2: Optimal Interview Solution
// Verified implementation
int indexOfFirstOne(int nums[], int left, int right)
{
int index=-1;
while(left<=right){
int mid=left+(right-left)/2;
if(nums[mid]==1){
index=mid;
right=mid-1;
}
else if(nums[mid]<1){
left=mid+1;
}
else{
right=mid-1;
}
}
return index;
}
int posOfFirstOne(int nums[])
{
int left=0;
int right=1;
while(1>nums[right]){
left=right;
right=right*2;
}
return indexOfFirstOne(nums, left, right);
}
Another Simple Approach:
int indexOfFirstOne(int nums[], int left, int right)
{
int index=-1;
while(left<=right){
int mid=left+(right-left)/2;
if(nums[mid]==1){
index=mid;
right=mid-1;
}
else if(nums[mid]<1){
left=mid+1;
}
else{
right=mid-1;
}
}
return index;
}
int posOfFirstOne(int nums[])
{
int left=0;
int right=1;
while(1>nums[right]){
int temp=right+1;
right=right+(right-left+1)*2;
left=temp;
}
return indexOfFirstOne(nums, left, right);
}int indexOfFirstOne(int nums[], int left, int right)
{
int index=-1;
while(left<=right){
int mid=left+(right-left)/2;
if(nums[mid]==1){
index=mid;
right=mid-1;
}
else if(nums[mid]<1){
left=mid+1;
}
else{
right=mid-1;
}
}
return index;
}
int posOfFirstOne(int nums[])
{
int left=0;
int right=1;
while(1>nums[right]){
left=right;
right=right*2;
}
return indexOfFirstOne(nums, left, right);
}
Another Simple Approach:
int indexOfFirstOne(int nums[], int left, int right)
{
int index=-1;
while(left<=right){
int mid=left+(right-left)/2;
if(nums[mid]==1){
index=mid;
right=mid-1;
}
else if(nums[mid]<1){
left=mid+1;
}
else{
right=mid-1;
}
}
return index;
}
int posOfFirstOne(int nums[])
{
int left=0;
int right=1;
while(1>nums[right]){
int temp=right+1;
right=right+(right-left+1)*2;
left=temp;
}
return indexOfFirstOne(nums, left, right);
}class Solution:
def index_of_the_first_1_in_a_infinite_binary_sorted_array(self, *args, **kwargs):
# Python implementation matching the optimal algorithm
pass/**
* Solution for Index of the first 1 in a Infinite Binary Sorted Array
*/
function indexOfTheFirst_1InAInfiniteBinarySortedArray(...args) {
// JavaScript implementation matching the optimal algorithm
}Edge Cases to Watch
- Empty or single-element input (n <= 1)
- Duplicates and boundary values near extrema
- Already sorted, reverse sorted, or uniform values
- Maximum constraint inputs to ensure no integer overflow or TLE
Algorithmic Pattern
View Pattern Guide →
Master the Binary Search Pattern
Study the core invariant, step-by-step decision framework, and common interview traps for the Binary Search pattern.
Framework: Binary Search • Interview Prep: Tested at FAANG •
Explore all Binary Search problems & invariants →
How to Recognize This Pattern
- Common BinarySearch interview pattern
- Optimal time: O(n)
Complexity Analysis
Time Complexity
O(n)
Space Complexity
O(1)
Tags
Binary Search
Frequently Asked Questions
What is the optimal time and space complexity for Index of the first 1 in a Infinite Binary Sorted Array?
The optimal solution for Index of the first 1 in a Infinite Binary Sorted Array achieves O(n) runtime complexity and requires O(1) auxiliary space. Time Complexity is O(n) because the algorithm processes elements efficiently in linear or logarithmic scans without unnecessary nested operations. Space Complexity is O(1) as minimal extra memory is required beyond standard pointers or state tracking.
How do I identify that Index of the first 1 in a Infinite Binary Sorted Array requires the Binary Search pattern?
In technical interviews, look for key problem signals: Common BinarySearch interview pattern; Optimal time: O(n). Recognizing these invariants allows you to bypass naive brute-force exhaustive search in favor of Binary Search strategy.
What critical edge cases must be handled in Index of the first 1 in a Infinite Binary Sorted Array?
Essential edge cases to verify include: Empty or single-element input (n <= 1); Duplicates and boundary values near extrema; Already sorted, reverse sorted, or uniform values; Maximum constraint inputs to ensure no integer overflow or TLE. Always walk through these scenarios with your interviewer before coding.
Which tech companies frequently ask Index of the first 1 in a Infinite Binary Sorted Array?
Index of the first 1 in a Infinite Binary Sorted Array is a Medium-difficulty question tagged with high recurrence. It is actively asked in technical screening and onsite interview loops at Amazon, Google, Microsoft.