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<doc-anchor-target id="heapq" class="break-words">
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<h1>
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<doc-anchor-trigger class="header-anchor-trigger" to="#heapq">#</doc-anchor-trigger>
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<span>heapq</span>
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<span><code v-pre>heapq.heappush(heap, item)</code></span>
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</h3>
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</doc-anchor-target>
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<p>Push the value <code v-pre>item</code> onto the heap, maintaining the heap invariant.</p>
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<h3>
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<span><code v-pre>heapq.heappop(heap)</code></span>
|
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</h3>
|
||
</doc-anchor-target>
|
||
<p>Pop and return the smallest item from the heap, maintaining the heap invariant. If the heap is empty, IndexError is raised. To access the smallest item without popping it, use <code v-pre>heap[0]</code>.</p>
|
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<doc-anchor-target id="heapqheapifyx">
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<h3>
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<doc-anchor-trigger class="header-anchor-trigger" to="#heapqheapifyx">#</doc-anchor-trigger>
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<span><code v-pre>heapq.heapify(x)</code></span>
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</h3>
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</doc-anchor-target>
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<p>Transform list <code v-pre>x</code> into a heap, in-place, in linear time.</p>
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<doc-anchor-target id="heapqheappushpopheap-item">
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<h3>
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<doc-anchor-trigger class="header-anchor-trigger" to="#heapqheappushpopheap-item">#</doc-anchor-trigger>
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<span><code v-pre>heapq.heappushpop(heap, item)</code></span>
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</h3>
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</doc-anchor-target>
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<p>Push <code v-pre>item</code> on the heap, then pop and return the smallest item from the heap. The combined action runs more efficiently than <code v-pre>heappush()</code> followed by a separate <code v-pre>heappop()</code>.</p>
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<doc-anchor-trigger class="header-anchor-trigger" to="#heapqheapreplaceheap-item">#</doc-anchor-trigger>
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<span><code v-pre>heapq.heapreplace(heap, item)</code></span>
|
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</h3>
|
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</doc-anchor-target>
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<p>Pop and return the smallest item from the heap, and also push the new item. The heap size doesn’t change. If the heap is empty, IndexError is raised.</p>
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<div class="codeblock-wrapper"><doc-codeblock>
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<pre translate="no" class="language-python"><code v-pre class="language-python"># Heap queue algorithm (a.k.a. priority queue)
|
||
def heappush(heap, item):
|
||
"""Push item onto heap, maintaining the heap invariant."""
|
||
heap.append(item)
|
||
_siftdown(heap, 0, len(heap)-1)
|
||
|
||
def heappop(heap):
|
||
"""Pop the smallest item off the heap, maintaining the heap invariant."""
|
||
lastelt = heap.pop() # raises appropriate IndexError if heap is empty
|
||
if heap:
|
||
returnitem = heap[0]
|
||
heap[0] = lastelt
|
||
_siftup(heap, 0)
|
||
return returnitem
|
||
return lastelt
|
||
|
||
def heapreplace(heap, item):
|
||
"""Pop and return the current smallest value, and add the new item.
|
||
|
||
This is more efficient than heappop() followed by heappush(), and can be
|
||
more appropriate when using a fixed-size heap. Note that the value
|
||
returned may be larger than item! That constrains reasonable uses of
|
||
this routine unless written as part of a conditional replacement:
|
||
|
||
if item > heap[0]:
|
||
item = heapreplace(heap, item)
|
||
"""
|
||
returnitem = heap[0] # raises appropriate IndexError if heap is empty
|
||
heap[0] = item
|
||
_siftup(heap, 0)
|
||
return returnitem
|
||
|
||
def heappushpop(heap, item):
|
||
"""Fast version of a heappush followed by a heappop."""
|
||
if heap and heap[0] < item:
|
||
item, heap[0] = heap[0], item
|
||
_siftup(heap, 0)
|
||
return item
|
||
|
||
def heapify(x):
|
||
"""Transform list into a heap, in-place, in O(len(x)) time."""
|
||
n = len(x)
|
||
# Transform bottom-up. The largest index there's any point to looking at
|
||
# is the largest with a child index in-range, so must have 2*i + 1 < n,
|
||
# or i < (n-1)/2. If n is even = 2*j, this is (2*j-1)/2 = j-1/2 so
|
||
# j-1 is the largest, which is n//2 - 1. If n is odd = 2*j+1, this is
|
||
# (2*j+1-1)/2 = j so j-1 is the largest, and that's again n//2-1.
|
||
for i in reversed(range(n//2)):
|
||
_siftup(x, i)
|
||
|
||
# 'heap' is a heap at all indices >= startpos, except possibly for pos. pos
|
||
# is the index of a leaf with a possibly out-of-order value. Restore the
|
||
# heap invariant.
|
||
def _siftdown(heap, startpos, pos):
|
||
newitem = heap[pos]
|
||
# Follow the path to the root, moving parents down until finding a place
|
||
# newitem fits.
|
||
while pos > startpos:
|
||
parentpos = (pos - 1) >> 1
|
||
parent = heap[parentpos]
|
||
if newitem < parent:
|
||
heap[pos] = parent
|
||
pos = parentpos
|
||
continue
|
||
break
|
||
heap[pos] = newitem
|
||
|
||
def _siftup(heap, pos):
|
||
endpos = len(heap)
|
||
startpos = pos
|
||
newitem = heap[pos]
|
||
# Bubble up the smaller child until hitting a leaf.
|
||
childpos = 2*pos + 1 # leftmost child position
|
||
while childpos < endpos:
|
||
# Set childpos to index of smaller child.
|
||
rightpos = childpos + 1
|
||
if rightpos < endpos and not heap[childpos] < heap[rightpos]:
|
||
childpos = rightpos
|
||
# Move the smaller child up.
|
||
heap[pos] = heap[childpos]
|
||
pos = childpos
|
||
childpos = 2*pos + 1
|
||
# The leaf at pos is empty now. Put newitem there, and bubble it up
|
||
# to its final resting place (by sifting its parents down).
|
||
heap[pos] = newitem
|
||
_siftdown(heap, startpos, pos)</code></pre>
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</doc-codeblock></div>
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