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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)
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| − | the overall complexity is O(n) since
| + | Back to [[Chapter 6]] |
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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 00:58, 21 September 2020
