From e7ada660adfc18d6df0145668b6cad0b212f6366 Mon Sep 17 00:00:00 2001
From: ga63cit <jakob.schulz@tum.de>
Date: Fri, 12 Aug 2022 15:34:35 +0200
Subject: [PATCH] initial commit implementing functionality of iterating over
 all partitions of a vector

---
 src/lib.rs        |  1 +
 src/partitions.rs | 74 +++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 75 insertions(+)
 create mode 100644 src/partitions.rs

diff --git a/src/lib.rs b/src/lib.rs
index 5cca5d99f..ede7a6893 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -218,6 +218,7 @@ mod minmax;
 #[cfg(feature = "use_alloc")]
 mod multipeek_impl;
 mod pad_tail;
+mod partitions;
 #[cfg(feature = "use_alloc")]
 mod peek_nth;
 mod peeking_take_while;
diff --git a/src/partitions.rs b/src/partitions.rs
new file mode 100644
index 000000000..55416ed23
--- /dev/null
+++ b/src/partitions.rs
@@ -0,0 +1,74 @@
+/// Based on https://stackoverflow.com/a/30898130/4322240.
+
+/// Representation of a state in which the iterator can be.
+/// elements: contains the elements to be partitioned. All elements are treated
+///     as distinct.
+/// index_map: in terms of the linked post, index_map[i] = p_i (but 0-indexed)
+///     is the partition class to which elements[i] belongs in the current
+///     partition
+/// initialized: marks if the Partition element was just initialized and hence
+///    was not generated by next()
+pub struct Partition<'a, T> where T: Copy {
+    elements: &'a Vec<T>,
+    index_map: Vec<usize>,
+    initialized: bool,
+}
+
+type PartitionRepresentation<T> = Vec<Vec<T>>;
+
+
+impl<'a, T> Partition<'a, T> where T: Copy {
+    // extracts the current partition of the iterator
+    fn create_partition(&self) -> PartitionRepresentation<T> {
+        // max_index is the highest number used for a class in the partition.
+        // Since the first class is numbered 0, there are max_index + 1 different classes.
+        if let Some(&max_index) = self.index_map.iter().max() {
+            // initialize Vec's for the classes
+            let mut partition_classes = vec![Vec::new(); max_index + 1];
+            for i in 0..self.index_map.len() {
+                // elements[i] belongs to the partition class index_map[i]
+                partition_classes[self.index_map[i]].push(self.elements[i]);
+            }
+            return partition_classes;
+        } else {
+            // The index_map might have length 0, which means that there are no elements.
+            // There is precisely one partition of the empty set, namely the partition with no classes.
+            return Vec::new();
+        }
+    }
+}
+impl<'a, T> Iterator for Partition<'a, T> where T: Copy {
+    type Item = PartitionRepresentation<T>;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        if self.initialized {
+            self.initialized = false;
+            return Some(self.create_partition());
+        }
+        // search for the highest index at which the index_map is incrementable (see the linked post)
+        for index in (1..self.index_map.len()).rev() {
+            if (0..index).any(|x| self.index_map[x] == self.index_map[index]) {
+                // increment the incrementable index
+                self.index_map[index] += 1;
+                // set all following entries to the lexicographically smallest suffix that makes the
+                // index_map viable (see linked post), i.e. to zero.
+                for x in index + 1..self.index_map.len() {
+                    self.index_map[x] = 0;
+                }
+                return Some(self.create_partition());
+            }
+        }
+        // if there is no incrementable index, we have enumerated the last possible partition.
+        return None;
+    }
+}
+/// Returns an Iterator over all partitions of the given Vec.
+/// Example usage:
+/// ```
+/// for partition in partitions(&vec![7,8,9]){
+///     println!("{:?}", partition);
+/// }
+/// ```
+pub fn partitions<'a, T>(v: &'a Vec<T>) -> Partition<'a, T> where T: Copy {
+    Partition::<T> { elements: v, index_map: vec![0; v.len()], initialized: true }
+}
\ No newline at end of file