Largest element
Given an integer array nums and an integer k, return the kth largest element in the array.
Note that it is the kth largest element in the sorted order, not the kth distinct element.
Can you solve it without sorting?
Example 1:
Input: nums = [3,2,1,5,6,4], k = 2
Output: 5
Example 2:
Input: nums = [3,2,3,1,2,4,5,5,6], k = 4
Output: 4
Constraints:
1 <= k <= nums.lenght <= 10^5
-10^4 <= nums[i] <= 10^4
Sample input:
3,2,1,5,6,4
2
Sample output:
5
Program:
def findKthLargest(nums, k):
# Convert the problem to find kth smallest
return quickSelect(nums, 0, len(nums) - 1, len(nums) - k)
def quickSelect(nums, low, high, k):
if low == high:
return nums[low]
# Choose a pivot
pivotIndex = partition(nums, low, high)
# If the pivot is in its final sorted position
if k == pivotIndex:
return nums[k]
# If k is less than the pivot index
elif k < pivotIndex:
return quickSelect(nums, low, pivotIndex - 1, k)
# If k is more than the pivot index
else:
return quickSelect(nums, pivotIndex + 1, high, k)
def partition(nums, low, high):
pivot = nums[high]
i = low
for j in range(low, high):
if nums[j] <= pivot:
nums[i], nums[j] = nums[j], nums[i]
i += 1
nums[i], nums[high] = nums[high], nums[i]
return i
# Input from user
nums = list(map(int, input().split(',')))
k = int(input())
# Output the result
print(findKthLargest(nums, k))
Explanation:
Objective:
1)We aim to find the kth largest element in a given integer array without sorting the entire array. This saves computational effort, especially when dealing with large arrays.
QuickSelect Algorithm:
1)The primary technique used here is the QuickSelect algorithm, which is derived from the popular QuickSort algorithm. QuickSelect is designed to work in O(n) average time complexity, making it much more efficient than sorting the whole array to find the kth largest element.
Function Definitions:
1)findKthLargest(nums, k): This is the main function. It kicks off the QuickSelect process. Notice that it translates the problem of finding the kth largest element into finding the (length of array - k)th smallest element.
2)quickSelect(nums, low, high, k): A recursive function that partitions the array and checks if we've found the kth smallest element.
3)partition(nums, low, high): This function chooses a pivot and arranges elements in the array such that elements lesser than the pivot are on the left and those greater are on the right.
Choosing a Pivot:
1)The pivot chosen in our partition function is the last element in the current segment of the array. This is a simple and common pivot choice, but there are other strategies available.
Partitioning:
1)The core idea of the partition function is to rearrange the elements of the array so that:
1)Every element less than or equal to the pivot comes before the pivot.
2)Every element greater than the pivot comes after it.
2)At the end of the partitioning process, the pivot is essentially in its final sorted position.
Recursive Process:
1)Once the array is partitioned using the pivot, we have three potential scenarios:
1)If the pivot’s position matches k, then we've found our element.
2)If k is less than the pivot's position, we need to search on the left side of the pivot.
3)If k is more than the pivot's position, our search continues on the right side.
2)This recursive nature ensures we only traverse parts of the array necessary to find our kth largest element, avoiding unnecessary computations.
Input & Output:
1)The code prompts the user to input an array of integers separated by commas, followed by the integer value of k.
2)After processing, it then prints the kth largest element in the array.
Advantages:
1)Since we're not sorting the entire array but only partitioning specific sections, we save on computation, making this method efficient especially for larger arrays.
Conclusion:
1)The QuickSelect algorithm provides an elegant and efficient method for finding the kth largest (or smallest) element in an array without the need for full sorting. It’s a powerful tool to have in one's algorithmic toolkit, especially when handling data that doesn't require full organization.
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