702894. Smallest subarray with sum greater than x
Here is the detailed Markdown blog post for the problem:
Smallest Subarray with Sum Greater Than x
Summary
Find the smallest subarray (contiguous segment) in an array that has a sum greater than a given integer x. This problem involves arrays and sliding window concepts.
Detailed Explanation
The problem can be solved by using a sliding window approach. The basic idea is to maintain two pointers, start and end, which represent the boundaries of the current subarray being considered. Initialize sum as 0 and min_length as infinity.
- Iterate through the array with the
endpointer. - Calculate the sum of the subarray from the start to the end using a variable
temp_sum. - If
temp_sumis greater thanx, updatemin_lengthif the current subarray length is smaller thanmin_length. - Move the
startpointer one step forward and subtract the element at the previous position fromtemp_sum. Iftemp_sumbecomes negative, reset it to 0. - Repeat steps 2-4 until the end of the array is reached.
Time Complexity Analysis: The time complexity of this algorithm is O(n), where n is the length of the input array. This is because we are performing a single pass through the array.
Space Complexity Analysis: The space complexity is O(1) as we are only using a constant amount of space to store the variables sum, min_length, and the two pointers.
Optimized Solutions
Java
public int findSmallestSubarray(int[] arr, int x) {
int minLength = Integer.MAX_VALUE;
int start = 0;
int end = 0;
int sum = 0;
for (int i = 0; i < arr.length; i++) {
sum += arr[i];
while (sum > x) {
if (i - start + 1 < minLength) {
minLength = i - start + 1;
}
sum -= arr[start++];
}
}
return minLength == Integer.MAX_VALUE ? -1 : minLength;
}