Faster each permutation

src/libcore/vec.rs

@@ -1291,6 +1291,46 @@ pub fn reverse<T>(v: &[mut T]) {
     while i < ln / 2 { v[i] <-> v[ln - i - 1]; i += 1; }
 }
 
+/**
+ * Reverse part of a vector in place.
+ *
+ * Reverse the elements in the vector between `start` and `end - 1`.
+ *
+ * If either start or end do not represent valid positions in the vector, the
+ * vector is returned unchanged.
+ *
+ * # Arguments
+ *
+ * * `v` - The mutable vector to be modified
+ *
+ * * `start` - Index of the first element of the slice
+ *
+ * * `end` - Index one past the final element to be reversed.
+ *
+ * # Example
+ *
+ * Assume a mutable vector `v` contains `[1,2,3,4,5]`. After the call:
+ *
+ * ~~~
+ *
+ * reverse_part(v, 1, 4);
+ *
+ * ~~~
+ *
+ * `v` now contains `[1,4,3,2,5]`.
+ */
+pub fn reverse_part<T>(v : &[mut T], start : uint, end : uint) {
+    let sz = v.len();
+    if start >= sz || end > sz { return; }
+    let mut i = start;
+    let mut j = end - 1;
+    while i < j {
+        v[i] <-> v[j];
+        i += 1;
+        j -= 1;
+    }
+}
+
 /// Returns a vector with the order of elements reversed
 pub pure fn reversed<T: Copy>(v: &[const T]) -> ~[T] {
     let mut rs: ~[T] = ~[];
@@ -1457,31 +1497,74 @@ pub fn each2<U, T>(v1: &[U], v2: &[T], f: fn(u: &U, t: &T) -> bool) {
  *
  * The total number of permutations produced is `len(v)!`.  If `v` contains
  * repeated elements, then some permutations are repeated.
+ *
+ * See [Algorithms to generate
+ * permutations](http://en.wikipedia.org/wiki/Permutation).
+ *
+ *  # Arguments
+ *
+ *  * `values` - A vector of values from which the permutations are
+ *  chosen
+ *
+ *  * `fun` - The function to iterate over the combinations
  */
-pure fn each_permutation<T: Copy>(v: &[T], put: fn(ts: &[T]) -> bool) {
-    let ln = len(v);
-    if ln <= 1 {
-        put(v);
-    } else {
-        // This does not seem like the most efficient implementation.  You
-        // could make far fewer copies if you put your mind to it.
-        let mut i = 0u;
-        while i < ln {
-            let elt = v[i];
-            let mut rest = slice(v, 0u, i);
-            unsafe {
-                rest.push_all(const_view(v, i+1u, ln));
-                for each_permutation(rest) |permutation| {
-                    if !put(append(~[elt], permutation)) {
-                        return;
-                    }
-                }
-            }
-            i += 1u;
+pub pure fn each_permutation<T : Copy>(values : &[T],
+                                       fun : &fn(perm : &[T]) -> bool) {
+    let length = values.len();
+    let mut permutation = vec::from_fn(length, |i| values[i]);
+    if length <= 1 {
+        fun(permutation);
+        return;
+    }
+    let mut indices = vec::from_fn(length, |i| i);
+    loop {
+        if !fun(permutation) { return; }
+        // find largest k such that indices[k] < indices[k+1]
+        // if no such k exists, all permutations have been generated
+        let mut k = length - 2;
+        while k > 0 && indices[k] >= indices[k+1] {
+            k -= 1;
+        }
+        if k == 0 && indices[0] > indices[1] { return; }
+        // find largest l such that indices[k] < indices[l]
+        // k+1 is guaranteed to be such
+        let mut l = length - 1;
+        while indices[k] >= indices[l] {
+            l -= 1;
+        }
+        // swap indices[k] and indices[l]; sort indices[k+1..]
+        // (they're just reversed)
+        indices[k] <-> indices[l];
+        unsafe {
+            reverse_part(indices, k+1, length);
+        }
+        // fixup permutation based on indices
+        for uint::range(k, length) |i| {
+            permutation[i] = values[indices[i]];
         }
     }
 }
 
+/**
+ * Iterate over all permutations of vector `values`.
+ *
+ * This is an alternative to each_permutation that uses references to
+ * avoid copying the elements of the values vector.
+ *
+ * To avoid copying, the iterator will be passed a reference to a vector
+ * containing references to the elements in the original `values` vector.
+ *
+ * # Arguments
+ *
+ * * `values` - A vector of values from which the permutations are chosen
+ *
+ * * `fun` - The function to iterate over the permutations
+ */
+pub pure fn each_permutation_ref<T>(values : &v/[T],
+                                    fun : &fn(perm : &[&v/T]) -> bool) {
+    each_permutation(vec::from_fn(values.len(), |i| &values[i]), fun);
+}
+
 pub pure fn windowed<TT: Copy>(nn: uint, xx: &[TT]) -> ~[~[TT]] {
     let mut ww = ~[];
     assert 1u <= nn;
@@ -3995,6 +4078,97 @@ mod tests {
         }
     }
 
+    fn dup<T:Copy>(values : &[&T]) -> ~[T] {
+        from_fn(values.len(), |i| *values[i])
+    }
+
+    #[test]
+    fn test_reverse_part() {
+        let mut values = [1,2,3,4,5];
+        reverse_part(values,1,4);
+        assert values == [1,4,3,2,5];
+    }
+
+    #[test]
+    fn test_permutations0() {
+        let values = [];
+        let mut v : ~[~[int]] = ~[];
+        for each_permutation(values) |p| {
+            v.push(vec::from_slice(p));
+        }
+        assert v == ~[~[]];
+    }
+
+    #[test]
+    fn test_permutations0_ref() {
+        let values = [];
+        let mut v : ~[~[int]] = ~[];
+        for each_permutation_ref(values) |p| {
+            v.push(dup(p));
+        }
+        assert v == ~[~[]];
+    }
+
+    #[test]
+    fn test_permutations1() {
+        let values = [1];
+        let mut v : ~[~[int]] = ~[];
+        for each_permutation(values) |p| {
+            v.push(vec::from_slice(p));
+        }
+        assert v == ~[~[1]];
+    }
+
+    #[test]
+    fn test_permutations1_ref() {
+        let values = [1];
+        let mut v : ~[~[int]] = ~[];
+        for each_permutation_ref(values) |p| {
+            v.push(dup(p));
+        }
+        assert v == ~[~[1]];
+    }
+
+    #[test]
+    fn test_permutations2() {
+        let values = [1,2];
+        let mut v : ~[~[int]] = ~[];
+        for each_permutation(values) |p| {
+            v.push(vec::from_slice(p));
+        }
+        assert v == ~[~[1,2],~[2,1]];
+    }
+
+    #[test]
+    fn test_permutations2_ref() {
+        let values = [1,2];
+        let mut v : ~[~[int]] = ~[];
+        for each_permutation_ref(values) |p| {
+            v.push(dup(p));
+        }
+        assert v == ~[~[1,2],~[2,1]];
+    }
+
+    #[test]
+    fn test_permutations3() {
+        let values = [1,2,3];
+        let mut v : ~[~[int]] = ~[];
+        for each_permutation(values) |p| {
+            v.push(vec::from_slice(p));
+        }
+        assert v == ~[~[1,2,3],~[1,3,2],~[2,1,3],~[2,3,1],~[3,1,2],~[3,2,1]];
+    }
+
+    #[test]
+    fn test_permutations3_ref() {
+        let values = [1,2,3];
+        let mut v : ~[~[int]] = ~[];
+        for each_permutation_ref(values) |p| {
+            v.push(dup(p));
+        }
+        assert v == ~[~[1,2,3],~[1,3,2],~[2,1,3],~[2,3,1],~[3,1,2],~[3,2,1]];
+    }
+
 }
 
 // Local Variables: