Difference between pages "3.23" and "4.21"

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(Created page with "the general form of this problem is to find the kth largest value. finding the median is when k = n/2. to find the kth largest value, * select a partition element and split...")
 
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the general form of this problem is to find the kth largest value.  finding the median is when k = n/2.
  
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to find the kth largest value,
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* select a partition element and split the array into 2 sub-arrays - one with the elements smaller than the partition and one with the elements larger than the partition. '''O(n)'''
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* if the array with the elements larger than the partition has k - 1 elements, the partition is the kth largest element
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* if the array with the elements larger than the partition has >= k elements, recurse with the same value of k using the larger elements as the new array. '''O(n/2)''' (average case)
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* else the median is in the array with elements smaller than the partition so adjust k to account for the large elements being discarded and recurse using the smaller elements as the new array '''O(n/2)''' (average case)
  
Back to [[Chapter 3]]
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the overall complexity is O(n) since
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O(n) + O(n/2) + O(n/4) + ... approaches O(2n) which is just O(n) since 2 is a constant.
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Back to [[Chapter 4]]

Latest revision as of 18:27, 20 September 2020

the general form of this problem is to find the kth largest value. finding the median is when k = n/2.

to find the kth largest value,

  • select a partition element and split the array into 2 sub-arrays - one with the elements smaller than the partition and one with the elements larger than the partition. O(n)
  • if the array with the elements larger than the partition has k - 1 elements, the partition is the kth largest element
  • if the array with the elements larger than the partition has >= k elements, recurse with the same value of k using the larger elements as the new array. O(n/2) (average case)
  • else the median is in the array with elements smaller than the partition so adjust k to account for the large elements being discarded and recurse using the smaller elements as the new array O(n/2) (average case)

the overall complexity is O(n) since

O(n) + O(n/2) + O(n/4) + ... approaches O(2n) which is just O(n) since 2 is a constant.


Back to Chapter 4