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7<title>Tree Order Statistics Timing Test</title>
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12<h1>Tree Order-Statistics Timing Test</h1>
13<h2><a name="description" id="description">Description</a></h2>
14<p>This test creates a container, inserts random integers into
15    the the container, and then checks the order-statistics of the
16    container's values. (If the container is one of <tt>pb_ds</tt>
17    's trees, it does this with the <tt>order_of_key</tt> method of
18    <a href="tree_order_statistics_node_update.html"><tt>tree_order_statistics_node_update</tt></a>
19    ; otherwise, it uses the <tt>find</tt> method and
20    <tt>std::distance</tt> .) It measures the average time for such
21    queries as a function of the number of values inserted.</p>
22<p>(The test was executed with <a href="http://gcc.gnu.org/viewcvs/*checkout*/trunk/libstdc%2B%2B-v3/testsuite/performance/ext/pb_ds/tree_order_statistics_timing.cc"><tt>tree_order_statistics_timing_test</tt></a>
23    200 200 2100)</p>
24<h2><a name="purpose" id="purpose">Purpose</a></h2>
25<p>The test checks the performance difference of policies based
26    on node-invariant as opposed to a external functions. (see
27    <a href="tree_based_containers.html#invariants">Design::Associative
28    Containers::Tree-Based Containers::Node Invariants</a> .)</p>
29<h2><a name="results" id="results">Results</a></h2>
30<p>Figures <a href="#NTG">NTG</a>, <a href="#NTM">NTM</a>, and
31    <a href="#NTL">NTL</a> show the results for the native and
32    tree-based containers in <a href="assoc_performance_tests.html#gcc"><u>g++</u></a>, <a href="assoc_performance_tests.html#msvc"><u>msvc++</u></a>, and
33    <a href="assoc_performance_tests.html#local"><u>local</u></a>,
34    respectively.</p>
35<div id="NTG_res_div">
36<div id="NTG_gcc">
37<div id="NTG_tree_order_statistics_timing_test">
38<div id="NTG_assoc">
39<div id="NTG_Native_and_tree-based_container_order-statistics_queries"><div style="border-style: dotted; border-width: 1px; border-color: lightgray"><h6 class="c1"><a name="NTG" id="NTG"><img src="tree_order_statistics_timing_test_gcc.png" alt="no image" /></a></h6>NTG: Native and tree-based container order-statistics queries - <a href="assoc_performance_tests.html#gcc">g++</a><p>In the above figure, the names in the legends have the following meaning:</p>
40<ol>
41<li>
42n_set-
43<tt>std::set</tt></li>
44<li>
45splay_tree_ost_set-
46<a href="tree.html"><tt>tree</tt></a>
47 with <tt>Tag</tt> = <a href="splay_tree_tag.html"><tt>splay_tree_tag</tt></a>
48, and <tt>Node_Update</tt> = <a href="tree_order_statistics_node_update.html"><tt>tree_order_statistics_node_update</tt></a>
49</li>
50<li>
51rb_tree_ost_set-
52<a href="tree.html"><tt>tree</tt></a>
53 with <tt>Tag</tt> = <a href="rb_tree_tag.html"><tt>rb_tree_tag</tt></a>
54, and <tt>Node_Update</tt> = <a href="tree_order_statistics_node_update.html"><tt>tree_order_statistics_node_update</tt></a>
55</li>
56</ol>
57</div><div style="width: 100%; height: 20px"></div></div>
58</div>
59</div>
60</div>
61</div>
62<div id="NTM_res_div">
63<div id="NTM_msvc">
64<div id="NTM_tree_order_statistics_timing_test">
65<div id="NTM_assoc">
66<div id="NTM_Native_and_tree-based_container_order-statistics_queries"><div style="border-style: dotted; border-width: 1px; border-color: lightgray"><h6 class="c1"><a name="NTM" id="NTM"><img src="tree_order_statistics_timing_test_msvc.png" alt="no image" /></a></h6>NTM: Native and tree-based container order-statistics queries - <a href="assoc_performance_tests.html#msvc">msvc++</a><p>In the above figure, the names in the legends have the following meaning:</p>
67<ol>
68<li>
69n_set-
70<tt>std::set</tt></li>
71<li>
72splay_tree_ost_set-
73<a href="tree.html"><tt>tree</tt></a>
74 with <tt>Tag</tt> = <a href="splay_tree_tag.html"><tt>splay_tree_tag</tt></a>
75, and <tt>Node_Update</tt> = <a href="tree_order_statistics_node_update.html"><tt>tree_order_statistics_node_update</tt></a>
76</li>
77<li>
78rb_tree_ost_set-
79<a href="tree.html"><tt>tree</tt></a>
80 with <tt>Tag</tt> = <a href="rb_tree_tag.html"><tt>rb_tree_tag</tt></a>
81, and <tt>Node_Update</tt> = <a href="tree_order_statistics_node_update.html"><tt>tree_order_statistics_node_update</tt></a>
82</li>
83</ol>
84</div><div style="width: 100%; height: 20px"></div></div>
85</div>
86</div>
87</div>
88</div>
89<div id="NTL_res_div">
90<div id="NTL_local">
91<div id="NTL_tree_order_statistics_timing_test">
92<div id="NTL_assoc">
93<div id="NTL_Native_and_tree-based_container_order-statistics_queries"><div style = "border-style: dotted; border-width: 1px; border-color: lightgray"><h6 class="c1"><a name="NTL" id= "NTL"><img src="tree_order_statistics_timing_test_local.png" alt="no image" /></a></h6>NTL: Native and tree-based container order-statistics queries - <a href = "assoc_performance_tests.html#local">local</a></div><div style = "width: 100%; height: 20px"></div></div>
94</div>
95</div>
96</div>
97</div>
98<h2><a name="observations" id="observations">Observations</a></h2>
99<p>In this test, the native red-black tree can support
100    order-statistics queries only externally, by performing a
101    <tt>find</tt> (alternatively, <tt>lower_bound</tt> or
102    <tt>upper_bound</tt> ) and then using <tt>std::distance</tt> .
103    This is clearly linear, and it is not that surprising that the
104    cost is high.</p>
105<p><tt>pb_ds</tt> 's tree-based containers use in this test the
106    <tt>order_of_key</tt> method of <a href="tree_order_statistics_node_update.html"><tt>tree_order_statistics_node_update</tt></a>.
107    This method has only linear complexity in the length of the
108    root-node path. Unfortunately, the average path of a splay tree
109    (<a href="tree.html"><tt>tree</tt></a>
110    with <tt>Tag =</tt> <a href="splay_tree_tag.html"><tt>splay_tree_tag</tt></a> ) can
111    be higher than logarithmic; the longest path of a red-black
112    tree (<a href="tree.html"><tt>tree</tt></a>
113    with <tt>Tag =</tt> <a href="rb_tree_tag.html"><tt>rb_tree_tag</tt></a> ) is
114    logarithmic in the number of elements. Consequently, the splay
115    tree has worse performance than the red-black tree.</p>
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