703302. Decreasing Sequence
Easy
Decreasing Sequence
Summary
The problem is to find the longest decreasing sequence in an array. This problem involves basic algorithmic concepts such as arrays and mathematical operations.
Detailed Explanation
Given an integer array, we need to find the longest decreasing sequence (LDS) in it. A decreasing sequence is a subarray where each element is smaller than its previous element. We'll iterate through the array, keeping track of the length of the LDS we've found so far and updating our result if we find a longer one.
Here's a step-by-step breakdown of the solution:
- Initialize the maximum length of the LDS (
maxLen) to 1. - Iterate through the array from left to right.
- For each element, check if it's smaller than the previous element (if this is the first element or we just moved from a larger one). If so, increment the current length of the LDS (
currLen). - Update
maxLenifcurrLenis greater thanmaxLen. - After iterating through the entire array, return
maxLen, which represents the length of the longest decreasing sequence.
Time complexity: O(n), where n is the size of the input array. We only need to iterate through the array once. Space complexity: O(1), as we only use a constant amount of space to store our variables.
Optimized Solutions
Java
public int findLongestDecreasingSequence(int[] arr) {
int maxLen = 1;
int currLen = 1;
for (int i = 1; i < arr.length; i++) {
if (arr[i] < arr[i - 1]) {
currLen++;
maxLen = Math.max(maxLen, currLen);
} else {
currLen = 1;
}
}
return maxLen;
}