Module std::collections::binary_heap
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A priority queue implemented with a binary heap.
Insertion and popping the largest element have O(log n) time complexity.
Checking the largest element is O(1). Converting a vector to a binary heap
can be done in-place, and has O(n) complexity. A binary heap can also be
converted to a sorted vector in-place, allowing it to be used for an O(n log n) in-place heapsort.
Examples
This is a larger example that implements Dijkstra's algorithm
to solve the shortest path problem on a directed graph.
It shows how to use BinaryHeap with custom types.
use std::cmp::Ordering; use std::collections::BinaryHeap; use std::usize; #[derive(Copy, Clone, Eq, PartialEq)] struct State { cost: usize, position: usize, } // The priority queue depends on `Ord`. // Explicitly implement the trait so the queue becomes a min-heap // instead of a max-heap. impl Ord for State { fn cmp(&self, other: &State) -> Ordering { // Notice that the we flip the ordering here other.cost.cmp(&self.cost) } } // `PartialOrd` needs to be implemented as well. impl PartialOrd for State { fn partial_cmp(&self, other: &State) -> Option<Ordering> { Some(self.cmp(other)) } } // Each node is represented as an `usize`, for a shorter implementation. struct Edge { node: usize, cost: usize, } // Dijkstra's shortest path algorithm. // Start at `start` and use `dist` to track the current shortest distance // to each node. This implementation isn't memory-efficient as it may leave duplicate // nodes in the queue. It also uses `usize::MAX` as a sentinel value, // for a simpler implementation. fn shortest_path(adj_list: &Vec<Vec<Edge>>, start: usize, goal: usize) -> Option<usize> { // dist[node] = current shortest distance from `start` to `node` let mut dist: Vec<_> = (0..adj_list.len()).map(|_| usize::MAX).collect(); let mut heap = BinaryHeap::new(); // We're at `start`, with a zero cost dist[start] = 0; heap.push(State { cost: 0, position: start }); // Examine the frontier with lower cost nodes first (min-heap) while let Some(State { cost, position }) = heap.pop() { // Alternatively we could have continued to find all shortest paths if position == goal { return Some(cost); } // Important as we may have already found a better way if cost > dist[position] { continue; } // For each node we can reach, see if we can find a way with // a lower cost going through this node for edge in &adj_list[position] { let next = State { cost: cost + edge.cost, position: edge.node }; // If so, add it to the frontier and continue if next.cost < dist[next.position] { heap.push(next); // Relaxation, we have now found a better way dist[next.position] = next.cost; } } } // Goal not reachable None } fn main() { // This is the directed graph we're going to use. // The node numbers correspond to the different states, // and the edge weights symbolize the cost of moving // from one node to another. // Note that the edges are one-way. // // 7 // +-----------------+ // | | // v 1 2 | 2 // 0 -----> 1 -----> 3 ---> 4 // | ^ ^ ^ // | | 1 | | // | | | 3 | 1 // +------> 2 -------+ | // 10 | | // +---------------+ // // The graph is represented as an adjacency list where each index, // corresponding to a node value, has a list of outgoing edges. // Chosen for its efficiency. let graph = vec![ // Node 0 vec![Edge { node: 2, cost: 10 }, Edge { node: 1, cost: 1 }], // Node 1 vec![Edge { node: 3, cost: 2 }], // Node 2 vec![Edge { node: 1, cost: 1 }, Edge { node: 3, cost: 3 }, Edge { node: 4, cost: 1 }], // Node 3 vec![Edge { node: 0, cost: 7 }, Edge { node: 4, cost: 2 }], // Node 4 vec![]]; assert_eq!(shortest_path(&graph, 0, 1), Some(1)); assert_eq!(shortest_path(&graph, 0, 3), Some(3)); assert_eq!(shortest_path(&graph, 3, 0), Some(7)); assert_eq!(shortest_path(&graph, 0, 4), Some(5)); assert_eq!(shortest_path(&graph, 4, 0), None); }
Structs
| BinaryHeap |
A priority queue implemented with a binary heap. |
| Drain |
An iterator that drains a |
| IntoIter |
An iterator that moves out of a |
| Iter |
|