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fixed quicksort partition and secondsmallest function #9

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fixed quicksort partition and secondsmallest function #9

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6 changes: 4 additions & 2 deletions prose/10b_divide_and_conquer.md
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Original file line number Diff line number Diff line change
Expand Up @@ -339,6 +339,8 @@ def partition(L, left, right):
j -= 1
if i < j:
L[i], L[j] = L[j], L[i]
L[pivot], L[i] = L[i], L[pivot]
return i
if L[pivot] <= L[i]:
L[pivot], L[i] = L[i], L[pivot]
pivot = i
return pivot
```
10 changes: 6 additions & 4 deletions prose/11_selection.md
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Original file line number Diff line number Diff line change
Expand Up @@ -26,9 +26,9 @@ If our goal is to find the second largest item in a list, we could do this in li
def secondsmallest(L):
a, b = None, None
for item in L:
if a is None or item <= b:
if a is None or item <= a:
a, b = item, a
elif b is None or item <= a:
elif b is None or item <= b:
b = item
return b
```
Expand Down Expand Up @@ -77,8 +77,10 @@ def partition(L, left, right):
j -= 1
if i < j:
L[i], L[j] = L[j], L[i]
L[pivot], L[i] = L[i], L[pivot]
return i
if L[pivot] <= L[i]:
L[pivot], L[i] = L[i], L[pivot]
pivot = i
return pivot
```

Just as with `quicksort`, we use a randomized pivot so that we can expect to eliminate a constant fraction of the list with each new step. Unlike `quicksort`, we will not make a recursive call on both sides. As a result, we'll see that the average running time is only $O(n)$. That means we can do selection faster than we can sort, which makes sense, but it is *not obvious* how to do it.
Expand Down