<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `binary_heap` mod in crate `alloc`."><meta name="keywords" content="rust, rustlang, rust-lang, binary_heap"><title>alloc::binary_heap - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><link rel="shortcut icon" href="https://doc.rust-lang.org/favicon.ico"></head><body class="rustdoc mod"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../alloc/index.html'><img src='https://www.rust-lang.org/logos/rust-logo-128x128-blk-v2.png' alt='logo' width='100'></a><p class='location'>Module binary_heap</p><div class="sidebar-elems"><div class="block items"><ul><li><a href="#structs">Structs</a></li></ul></div><p class='location'><a href='../index.html'>alloc</a></p><script>window.sidebarCurrent = {name: 'binary_heap', ty: 'mod', relpath: '../'};</script><script defer src="../sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><input class="search-input" name="search" autocomplete="off" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='in-band'>Module <a href='../index.html'>alloc</a>::<wbr><a class="mod" href=''>binary_heap</a></span><span class='out-of-band'><span class='since' title='Stable since Rust version 1.0.0'>1.0.0</span><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>−</span>]</a></span><a class='srclink' href='../../src/alloc/binary_heap.rs.html#11-1196' title='goto source code'>[src]</a></span></h1><div class='docblock'><p>A priority queue implemented with a binary heap.</p>
<p>Insertion and popping the largest element have <code>O(log n)</code> time complexity.
Checking the largest element is <code>O(1)</code>. Converting a vector to a binary heap
can be done in-place, and has <code>O(n)</code> complexity. A binary heap can also be
converted to a sorted vector in-place, allowing it to be used for an <code>O(n log n)</code> in-place heapsort.</p>
<h1 id="examples" class="section-header"><a href="#examples">Examples</a></h1>
<p>This is a larger example that implements <a href="http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm">Dijkstra's algorithm</a>
to solve the <a href="http://en.wikipedia.org/wiki/Shortest_path_problem">shortest path problem</a> on a <a href="http://en.wikipedia.org/wiki/Directed_graph">directed graph</a>.
It shows how to use <a href="struct.BinaryHeap.html"><code>BinaryHeap</code></a> with custom types.</p>
<pre class="rust rust-example-rendered">
<span class="kw">use</span> <span class="ident">std</span>::<span class="ident">cmp</span>::<span class="ident">Ordering</span>;
<span class="kw">use</span> <span class="ident">std</span>::<span class="ident">collections</span>::<span class="ident">BinaryHeap</span>;
<span class="kw">use</span> <span class="ident">std</span>::<span class="ident">usize</span>;
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Copy</span>, <span class="ident">Clone</span>, <span class="ident">Eq</span>, <span class="ident">PartialEq</span>)]</span>
<span class="kw">struct</span> <span class="ident">State</span> {
<span class="ident">cost</span>: <span class="ident">usize</span>,
<span class="ident">position</span>: <span class="ident">usize</span>,
}
<span class="comment">// The priority queue depends on `Ord`.</span>
<span class="comment">// Explicitly implement the trait so the queue becomes a min-heap</span>
<span class="comment">// instead of a max-heap.</span>
<span class="kw">impl</span> <span class="ident">Ord</span> <span class="kw">for</span> <span class="ident">State</span> {
<span class="kw">fn</span> <span class="ident">cmp</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">State</span>) <span class="op">-></span> <span class="ident">Ordering</span> {
<span class="comment">// Notice that the we flip the ordering on costs.</span>
<span class="comment">// In case of a tie we compare positions - this step is necessary</span>
<span class="comment">// to make implementations of `PartialEq` and `Ord` consistent.</span>
<span class="ident">other</span>.<span class="ident">cost</span>.<span class="ident">cmp</span>(<span class="kw-2">&</span><span class="self">self</span>.<span class="ident">cost</span>)
.<span class="ident">then_with</span>(<span class="op">||</span> <span class="self">self</span>.<span class="ident">position</span>.<span class="ident">cmp</span>(<span class="kw-2">&</span><span class="ident">other</span>.<span class="ident">position</span>))
}
}
<span class="comment">// `PartialOrd` needs to be implemented as well.</span>
<span class="kw">impl</span> <span class="ident">PartialOrd</span> <span class="kw">for</span> <span class="ident">State</span> {
<span class="kw">fn</span> <span class="ident">partial_cmp</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">other</span>: <span class="kw-2">&</span><span class="ident">State</span>) <span class="op">-></span> <span class="prelude-ty">Option</span><span class="op"><</span><span class="ident">Ordering</span><span class="op">></span> {
<span class="prelude-val">Some</span>(<span class="self">self</span>.<span class="ident">cmp</span>(<span class="ident">other</span>))
}
}
<span class="comment">// Each node is represented as an `usize`, for a shorter implementation.</span>
<span class="kw">struct</span> <span class="ident">Edge</span> {
<span class="ident">node</span>: <span class="ident">usize</span>,
<span class="ident">cost</span>: <span class="ident">usize</span>,
}
<span class="comment">// Dijkstra's shortest path algorithm.</span>
<span class="comment">// Start at `start` and use `dist` to track the current shortest distance</span>
<span class="comment">// to each node. This implementation isn't memory-efficient as it may leave duplicate</span>
<span class="comment">// nodes in the queue. It also uses `usize::MAX` as a sentinel value,</span>
<span class="comment">// for a simpler implementation.</span>
<span class="kw">fn</span> <span class="ident">shortest_path</span>(<span class="ident">adj_list</span>: <span class="kw-2">&</span><span class="ident">Vec</span><span class="op"><</span><span class="ident">Vec</span><span class="op"><</span><span class="ident">Edge</span><span class="op">>></span>, <span class="ident">start</span>: <span class="ident">usize</span>, <span class="ident">goal</span>: <span class="ident">usize</span>) <span class="op">-></span> <span class="prelude-ty">Option</span><span class="op"><</span><span class="ident">usize</span><span class="op">></span> {
<span class="comment">// dist[node] = current shortest distance from `start` to `node`</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">dist</span>: <span class="ident">Vec</span><span class="op"><</span><span class="kw">_</span><span class="op">></span> <span class="op">=</span> (<span class="number">0</span>..<span class="ident">adj_list</span>.<span class="ident">len</span>()).<span class="ident">map</span>(<span class="op">|</span><span class="kw">_</span><span class="op">|</span> <span class="ident">usize</span>::<span class="ident">MAX</span>).<span class="ident">collect</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">heap</span> <span class="op">=</span> <span class="ident">BinaryHeap</span>::<span class="ident">new</span>();
<span class="comment">// We're at `start`, with a zero cost</span>
<span class="ident">dist</span>[<span class="ident">start</span>] <span class="op">=</span> <span class="number">0</span>;
<span class="ident">heap</span>.<span class="ident">push</span>(<span class="ident">State</span> { <span class="ident">cost</span>: <span class="number">0</span>, <span class="ident">position</span>: <span class="ident">start</span> });
<span class="comment">// Examine the frontier with lower cost nodes first (min-heap)</span>
<span class="kw">while</span> <span class="kw">let</span> <span class="prelude-val">Some</span>(<span class="ident">State</span> { <span class="ident">cost</span>, <span class="ident">position</span> }) <span class="op">=</span> <span class="ident">heap</span>.<span class="ident">pop</span>() {
<span class="comment">// Alternatively we could have continued to find all shortest paths</span>
<span class="kw">if</span> <span class="ident">position</span> <span class="op">==</span> <span class="ident">goal</span> { <span class="kw">return</span> <span class="prelude-val">Some</span>(<span class="ident">cost</span>); }
<span class="comment">// Important as we may have already found a better way</span>
<span class="kw">if</span> <span class="ident">cost</span> <span class="op">></span> <span class="ident">dist</span>[<span class="ident">position</span>] { <span class="kw">continue</span>; }
<span class="comment">// For each node we can reach, see if we can find a way with</span>
<span class="comment">// a lower cost going through this node</span>
<span class="kw">for</span> <span class="ident">edge</span> <span class="kw">in</span> <span class="kw-2">&</span><span class="ident">adj_list</span>[<span class="ident">position</span>] {
<span class="kw">let</span> <span class="ident">next</span> <span class="op">=</span> <span class="ident">State</span> { <span class="ident">cost</span>: <span class="ident">cost</span> <span class="op">+</span> <span class="ident">edge</span>.<span class="ident">cost</span>, <span class="ident">position</span>: <span class="ident">edge</span>.<span class="ident">node</span> };
<span class="comment">// If so, add it to the frontier and continue</span>
<span class="kw">if</span> <span class="ident">next</span>.<span class="ident">cost</span> <span class="op"><</span> <span class="ident">dist</span>[<span class="ident">next</span>.<span class="ident">position</span>] {
<span class="ident">heap</span>.<span class="ident">push</span>(<span class="ident">next</span>);
<span class="comment">// Relaxation, we have now found a better way</span>
<span class="ident">dist</span>[<span class="ident">next</span>.<span class="ident">position</span>] <span class="op">=</span> <span class="ident">next</span>.<span class="ident">cost</span>;
}
}
}
<span class="comment">// Goal not reachable</span>
<span class="prelude-val">None</span>
}
<span class="kw">fn</span> <span class="ident">main</span>() {
<span class="comment">// This is the directed graph we're going to use.</span>
<span class="comment">// The node numbers correspond to the different states,</span>
<span class="comment">// and the edge weights symbolize the cost of moving</span>
<span class="comment">// from one node to another.</span>
<span class="comment">// Note that the edges are one-way.</span>
<span class="comment">//</span>
<span class="comment">// 7</span>
<span class="comment">// +-----------------+</span>
<span class="comment">// | |</span>
<span class="comment">// v 1 2 | 2</span>
<span class="comment">// 0 -----> 1 -----> 3 ---> 4</span>
<span class="comment">// | ^ ^ ^</span>
<span class="comment">// | | 1 | |</span>
<span class="comment">// | | | 3 | 1</span>
<span class="comment">// +------> 2 -------+ |</span>
<span class="comment">// 10 | |</span>
<span class="comment">// +---------------+</span>
<span class="comment">//</span>
<span class="comment">// The graph is represented as an adjacency list where each index,</span>
<span class="comment">// corresponding to a node value, has a list of outgoing edges.</span>
<span class="comment">// Chosen for its efficiency.</span>
<span class="kw">let</span> <span class="ident">graph</span> <span class="op">=</span> <span class="macro">vec</span><span class="macro">!</span>[
<span class="comment">// Node 0</span>
<span class="macro">vec</span><span class="macro">!</span>[<span class="ident">Edge</span> { <span class="ident">node</span>: <span class="number">2</span>, <span class="ident">cost</span>: <span class="number">10</span> },
<span class="ident">Edge</span> { <span class="ident">node</span>: <span class="number">1</span>, <span class="ident">cost</span>: <span class="number">1</span> }],
<span class="comment">// Node 1</span>
<span class="macro">vec</span><span class="macro">!</span>[<span class="ident">Edge</span> { <span class="ident">node</span>: <span class="number">3</span>, <span class="ident">cost</span>: <span class="number">2</span> }],
<span class="comment">// Node 2</span>
<span class="macro">vec</span><span class="macro">!</span>[<span class="ident">Edge</span> { <span class="ident">node</span>: <span class="number">1</span>, <span class="ident">cost</span>: <span class="number">1</span> },
<span class="ident">Edge</span> { <span class="ident">node</span>: <span class="number">3</span>, <span class="ident">cost</span>: <span class="number">3</span> },
<span class="ident">Edge</span> { <span class="ident">node</span>: <span class="number">4</span>, <span class="ident">cost</span>: <span class="number">1</span> }],
<span class="comment">// Node 3</span>
<span class="macro">vec</span><span class="macro">!</span>[<span class="ident">Edge</span> { <span class="ident">node</span>: <span class="number">0</span>, <span class="ident">cost</span>: <span class="number">7</span> },
<span class="ident">Edge</span> { <span class="ident">node</span>: <span class="number">4</span>, <span class="ident">cost</span>: <span class="number">2</span> }],
<span class="comment">// Node 4</span>
<span class="macro">vec</span><span class="macro">!</span>[]];
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">shortest_path</span>(<span class="kw-2">&</span><span class="ident">graph</span>, <span class="number">0</span>, <span class="number">1</span>), <span class="prelude-val">Some</span>(<span class="number">1</span>));
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">shortest_path</span>(<span class="kw-2">&</span><span class="ident">graph</span>, <span class="number">0</span>, <span class="number">3</span>), <span class="prelude-val">Some</span>(<span class="number">3</span>));
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">shortest_path</span>(<span class="kw-2">&</span><span class="ident">graph</span>, <span class="number">3</span>, <span class="number">0</span>), <span class="prelude-val">Some</span>(<span class="number">7</span>));
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">shortest_path</span>(<span class="kw-2">&</span><span class="ident">graph</span>, <span class="number">0</span>, <span class="number">4</span>), <span class="prelude-val">Some</span>(<span class="number">5</span>));
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">shortest_path</span>(<span class="kw-2">&</span><span class="ident">graph</span>, <span class="number">4</span>, <span class="number">0</span>), <span class="prelude-val">None</span>);
}</pre>
</div><h2 id='structs' class='section-header'><a href="#structs">Structs</a></h2>
<table>
<tr class=' module-item'>
<td><a class="struct" href="struct.BinaryHeap.html"
title='struct alloc::binary_heap::BinaryHeap'>BinaryHeap</a></td>
<td class='docblock-short'>
<p>A priority queue implemented with a binary heap.</p>
</td>
</tr>
<tr class=' module-item'>
<td><a class="struct" href="struct.Drain.html"
title='struct alloc::binary_heap::Drain'>Drain</a></td>
<td class='docblock-short'>
<p>A draining iterator over the elements of a <code>BinaryHeap</code>.</p>
</td>
</tr>
<tr class=' module-item'>
<td><a class="struct" href="struct.IntoIter.html"
title='struct alloc::binary_heap::IntoIter'>IntoIter</a></td>
<td class='docblock-short'>
<p>An owning iterator over the elements of a <code>BinaryHeap</code>.</p>
</td>
</tr>
<tr class=' module-item'>
<td><a class="struct" href="struct.Iter.html"
title='struct alloc::binary_heap::Iter'>Iter</a></td>
<td class='docblock-short'>
<p>An iterator over the elements of a <code>BinaryHeap</code>.</p>
</td>
</tr>
<tr class=' module-item'>
<td><a class="struct" href="struct.PeekMut.html"
title='struct alloc::binary_heap::PeekMut'>PeekMut</a></td>
<td class='docblock-short'>
<p>Structure wrapping a mutable reference to the greatest item on a
<code>BinaryHeap</code>.</p>
</td>
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