703159. First 1 in a Sorted Binary Array
First 1 in a Sorted Binary Array
Summary
In this problem, we are given a sorted binary array (i.e., an array containing only 0s and 1s) and asked to find the index of the first 1 in the array. This problem involves searching for an element in a sorted array, which is a basic algorithmic concept.
Detailed Explanation
To solve this problem, we can use binary search, which is a popular algorithm for finding an element in a sorted array. Binary search works by repeatedly dividing the search space in half and eliminating one half until the target element is found. Since our array is sorted, we know that all 1s will be to the right of all 0s.
Here's the step-by-step breakdown of the solution:
- Initialize two pointers,
lowandhigh, to the start and end of the array, respectively. - Calculate the midpoint of the array using
(low + high) / 2. - Check if the element at the midpoint is a 1. If it is, update
highto the midpoint to narrow down the search space. - Repeat steps 2-3 until
highpoints to the first 1 in the array orlowandhighconverge. - Return the index of the first 1 found.
Time complexity: O(log n), where n is the length of the array. This is because we are dividing the search space in half at each step, effectively reducing the number of comparisons needed to find the target element.
Space complexity: O(1), since we only need a few extra variables to perform the binary search.
Optimized Solutions
Here are optimized solutions in various programming languages:
Java
public int findFirstOne(int[] arr) {
int low = 0;
int high = arr.length - 1;
while (low <= high) {
int mid = low + (high - low) / 2;
if (arr[mid] == 1) {
high = mid - 1;
} else {
low = mid + 1;
}
}
return low;
}