Floyd s buildheap, Sorting
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- Eleanore Reynolds
- 5 years ago
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1 CSE 7: Data Structures and Algorithms Floyd s buildheap, Sorting Autumn 2018 Shrirang (Shri) Mare shri@cs.washington.edu Thanks to Kasey Champion, Ben Jones, Adam Blank, Michael Lee, Evan McCarty, Robbie Weber, Whitaker Brand, Zora Fung, Stuart Reges, Justin Hsia, Ruth Anderson, and many others for sample slides and materials...
2 Today - Heap review and Array implementation of Heap - Floyd s buildheap algorithm - Intro to Sorting - Insertion sort - Heap sort!2
3 Heap review Heap is a tree-based data structure that satisfies - (a) structure property: it s a complete tree - (b) heap property, which states: - for min-heap: - for max-heap: paren t ch ildren paren t ch ildren - Operations (for min-heap): - removemin() - peekmin() - insert() - Applications: priority queue, sorting,..!
4 <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">aaadvnicbvlbbhmxepumljzws+grf4ukupfqlfsfviaqcrevsewqtlisrv7vjlhqy8oej0srfagv8g/wm8bsltckjlta4nmpbdpmmsvsnx6mvsqtzu7+7dqd29d//bw/r+o/pgopfqku47f5mkafpz6kbcdze5b2fsdrfp1etsv5iad8rzzzjlow/eykqhkgkjgtr/91iykvsipxje4djma9umkss9i1aweyuh4ybwqdl5qfqnfai8quxajn/jyz+lgoulmcxcpqaf72mshohi5cjdw6bayfmrc6bc4ppkepqvrwcg6c+cb1xuu49hu2fj1g9pbfrt11mbrams9snlwjxvmffbvti5ac+mqxsfgmxlz4p95fuvcziascipztdfqap6orhp260c+4xwqkqgshud5ejeirf0cvphipslxzvn+qexgr86t59fvmcvrxtchdazkxkageowrzxk/7ruxofjv1a2jwhwlhmno+boelkapfmejoozasfpcepyorzeskq12cxybsc26txapchqq5nezw8wptizi2zwq/icuxeymb/wttkkzu6bl/ggazuaext7wdfb+ffrm/dh48bpywr4e+wje8oowzu9ykfspttjhsytsl4m5lvlr+vx9wd6u7stzksyh6zdavw/wdtwhqe</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> removemin() Calls: removemin() min-heap function removemin last = last node in the tree minvalue = root swap root with last percolatedown(root) return minvalue end function!5
5 <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">aaadvnicbvlbbhmxepumljzws+grf4ukupfqlfsfviaqcrevsewqtlisrv7vjlhqy8oej0srfagv8g/wm8bsltckjlta4nmpbdpmmsvsnx6mvsqtzu7+7dqd29d//bw/r+o/pgopfqku47f5mkafpz6kbcdze5b2fsdrfp1etsv5iad8rzzzjlow/eykqhkgkjgtr/91iykvsipxje4djma9umkss9i1aweyuh4ybwqdl5qfqnfai8quxajn/jyz+lgoulmcxcpqaf72mshohi5cjdw6bayfmrc6bc4ppkepqvrwcg6c+cb1xuu49hu2fj1g9pbfrt11mbrams9snlwjxvmffbvti5ac+mqxsfgmxlz4p95fuvcziascipztdfqap6orhp260c+4xwqkqgshud5ejeirf0cvphipslxzvn+qexgr86t59fvmcvrxtchdazkxkageowrzxk/7ruxofjv1a2jwhwlhmno+boelkapfmejoozasfpcepyorzeskq12cxybsc26txapchqq5nezw8wptizi2zwq/icuxeymb/wttkkzu6bl/ggazuaext7wdfb+ffrm/dh48bpywr4e+wje8oowzu9ykfspttjhsytsl4m5lvlr+vx9wd6u7stzksyh6zdavw/wdtwhqe</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> removemin() Calls: removemin() Broken heap function removemin last = last node in the tree minvalue = root swap root with last percolatedown(root) return minvalue end function!6
6 removemin() percolatedown(root) node Broken heap smallest Calls: removemin() 1 1: function percolatedown(node) 2: l = left child of node : r = right child of node 4: smallest = smallest in {l, r, node} 5: if smallest 6= node then 6: exchange node with smallest 7: percolate(smallest) 8: end if 9: end function!7
7 removemin() Calls: removemin() node Broken heap smallest percolatedown(smallest) 1: function percolatedown(node) 2: l = left child of node : r = right child of node 4: smallest = smallest in {l, r, node} 5: if smallest 6= node then 6: exchange node with smallest 7: percolate(smallest) 8: end if 9: end function!8
8 removemin() Calls: removemin() Broken heap node smallest 1: function percolatedown(node) 2: l = left child of node : r = right child of node 4: smallest = smallest in {l, r, node} 5: if smallest 6= node then 6: exchange node with smallest 7: percolate(smallest) 8: end if 9: end function!9
9 removemin() Calls: removemin() Broken heap node smallest percolatedown(smallest) 1: function percolatedown(node) 2: l = left child of node : r = right child of node 4: smallest = smallest in {l, r, node} 5: if smallest 6= node then 6: exchange node with smallest 7: percolate(smallest) 8: end if 9: end function!10
10 removemin() Calls: removemin() Broken heap node smallest 1: function percolatedown(node) 2: l = left child of node : r = right child of node 4: smallest = smallest in {l, r, node} 5: if smallest 6= node then 6: exchange node with smallest 7: percolate(smallest) 8: end if 9: end function!11
11 removemin() Calls: removemin() min-heap node smallest percolatedown(smallest) 1: function percolatedown(node) 2: l = left child of node : r = right child of node 4: smallest = smallest in {l, r, node} 5: if smallest 6= node then 6: exchange node with smallest 7: percolate(smallest) 8: end if 9: end function!12
12 <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">aaadvnicbvlbbhmxepumljzws+grf4ukupfqlfsfviaqcrevsewqtlisrv7vjlhqy8oej0srfagv8g/wm8bsltckjlta4nmpbdpmmsvsnx6mvsqtzu7+7dqd29d//bw/r+o/pgopfqku47f5mkafpz6kbcdze5b2fsdrfp1etsv5iad8rzzzjlow/eykqhkgkjgtr/91iykvsipxje4djma9umkss9i1aweyuh4ybwqdl5qfqnfai8quxajn/jyz+lgoulmcxcpqaf72mshohi5cjdw6bayfmrc6bc4ppkepqvrwcg6c+cb1xuu49hu2fj1g9pbfrt11mbrams9snlwjxvmffbvti5ac+mqxsfgmxlz4p95fuvcziascipztdfqap6orhp260c+4xwqkqgshud5ejeirf0cvphipslxzvn+qexgr86t59fvmcvrxtchdazkxkageowrzxk/7ruxofjv1a2jwhwlhmno+boelkapfmejoozasfpcepyorzeskq12cxybsc26txapchqq5nezw8wptizi2zwq/icuxeymb/wttkkzu6bl/ggazuaext7wdfb+ffrm/dh48bpywr4e+wje8oowzu9ykfspttjhsytsl4m5lvlr+vx9wd6u7stzksyh6zdavw/wdtwhqe</latexit> <latexit sha1_base64="0ozphwbxcd26cpwzmvf2mmwbehw=">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</latexit> removemin() 11 function removemin last = last node in the tree minvalue = root swap root with last percolatedown(root) return minvalue end function node Runtime of removemin(): smallest O(n ) + c 1 + O(n log n ) = O(n ) min-heap percolatedown(smallest) How can we do better?
13 Binary heap: Array implementation Indices !14
14 Binary heap: Array implementation Indices !15
15 Binary heap: Array implementation Indices !16
16 Binary heap: Array implementation Indices !17
17 Binary heap: Array implementation Indices !18
18 Binary heap: Array implementation leftch ild(i) = 2i rig h tch ild(i) = 2i + 1 i paren t(i) = With array starting at index Indices !19
19 Binary heap: Array implementation leftch ild(i) = 2i + 1 rig h tch ild(i) = 2i + 2 i 1 paren t(i) = With array starting at index Indices !20
20 Sorting!21
21 Sorting - - Problem: Arrange items in a collection in a specified order. - - Lots of applications: - lookup / search - merging sequences - data processing -Lots of sorting algorithms out there -Why study sorting?!22
22 Types of sorting algorithms 1. Comparison Sorts - Order of elements determined by comparing them - Fastest comparison sort: - Elements should support compareto() O(n log n ) 2. Non-comparison Sorts - Order of elements determined by leveraging properties of input - Typical runtime: - Also called as Niche Sorts aka linear sorts O(n ) In this class we ll focus on comparison sorts!2
23 Insertion sort
24 <latexit sha1_base64="vz+khmrgcgpgdbfgoexbcawjade=">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</latexit> <latexit sha1_base64="vz+khmrgcgpgdbfgoexbcawjade=">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</latexit> <latexit sha1_base64="vz+khmrgcgpgdbfgoexbcawjade=">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</latexit> <latexit sha1_base64="vz+khmrgcgpgdbfgoexbcawjade=">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</latexit> Insertion sort Runtime: -Stable: -In-place: for i=0tondo current = A[i] j = findnewindex(current, i) shift elements from j to i 1by1 A[j] =current end for!25
25 Heap sort - 1. Run Floyd s buildheap - 2. removemin() n times!26
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