sorting.0rx

/* -----------------------------------------------------------------------------
Copyright 2021 Kevin P. Barry

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
----------------------------------------------------------------------------- */

// Author: Kevin P. Barry [ta0kira@gmail.com]

define Sorting {
  sort (seq) {
    \ sortWith<#x,#x>(seq)
  }

  sortWith (seq) {
    \ seq `sortWith2` AsLessThan2<#x,#xx>.new()
  }

  sortWith2 (seq,compare) {
    \ HeapSort<#x>.inPlace(seq,compare)
  }

  reverse (seq) {
    scoped {
      Int i <- seq.size()/2-1
    } in while (i >= 0) {
      $ReadOnly[i]$
      Int j <- seq.size()-i-1
      #x temp <- seq.readAt(i)
      \ seq.writeAt(i,seq.readAt(j))
      \ seq.writeAt(j,temp)
    } update {
      i <- i-1
    }
  }

  sortList (head) {
    return sortListWith<#n,#x,#x>(head)
  }

  sortListWith (head) {
    return head `sortListWith2` AsLessThan2<#x,#xx>.new()
  }

  sortListWith2 (head,compare) {
    return MergeSort<#n,#x>.sort(head,compare)
  }

  reverseList (head) (head2) {
    if (!present(head)) {
      return empty
    }
    head2 <- head
    $Hidden[head]$

    scoped {
      optional #n prev <- empty
    } in while (true) {
      optional #n next <- require(head2).next()
      \ require(head2).setNext(prev)
      prev <- head2
      if (present(next)) {
        head2 <- next
      } else {
        break
      }
    }
  }
}

// Putting the params at the top level allows helpers to be called without
// needing to pass the params every time.
concrete HeapSort<#x> {
  @type inPlace ([ReadAt<#x>&WriteAt<#x>],LessThan2<#x>) -> ()
}

define HeapSort {
  $ReadOnlyExcept[]$

  @value [ReadAt<#x>&WriteAt<#x>] seq
  @value LessThan2<#x> compare

  inPlace (seq,compare) {
    \ #self{ seq, compare }.execute()
  }

  @value execute () -> ()
  execute () { $NoTrace$
    // Convert the container to a heap.
    scoped {
      Int i <- seq.size()/2-1
    } in while (i >= 0) {
      $ReadOnly[i]$
      \ sift(i,seq.size())
    } update {
      i <- i-1
    }

    // Traverse the heap and populate the container in place.
    scoped {
      Int i <- seq.size()-1
    } in while (i >= 0) {
      $ReadOnly[i]$
      \ swap(0,i)
      \ sift(0,i)
    } update {
      i <- i-1
    }
  }

  @value sift (Int,Int) -> ()
  sift (start,size) { $NoTrace$
    scoped {
      Int last         <- start
      Int indexLargest <- last
      $Hidden[start]$
    } in while (2*last+1 < size) {
      $ReadOnly[last]$
      Int left  <- 2*last+1
      Int right <- 2*last+2
      $ReadOnly[left,right]$
      if (seq.readAt(indexLargest) `compare.lessThan2` seq.readAt(left)) {
        indexLargest <- left
      }
      if (right < size && seq.readAt(indexLargest) `compare.lessThan2` seq.readAt(right)) {
        indexLargest <- right
      }
      if (indexLargest == last) {
        break
      }
    } update {
      \ swap(last,indexLargest)
      last <- indexLargest
    }
  }

  @value swap (Int,Int) -> ()
  swap (i,j) { $NoTrace$
    if (i != j) {
      #x temp <- seq.readAt(i)
      \ seq.writeAt(i,seq.readAt(j))
      \ seq.writeAt(j,temp)
    }
  }
}

// Putting the params at the top level allows helpers to be called without
// needing to pass the params every time.
concrete MergeSort<#n,#x> {
  #n requires ListNode<#n,#x>

  @type sort (optional #n,LessThan2<#x>) -> (optional #n)
}

define MergeSort {
  @value LessThan2<#x> compare

  sort (head,compare) {
    return #self{ compare }.iterated(head)
  }

  @value iterated (optional #n) -> (optional #n)
  iterated (head) (head2) {
    head2 <- head
    $Hidden[head]$

    scoped {
      Int chunk <- 1
      Bool dirty <- true
    } in while (dirty) {
      $ReadOnly[chunk]$
      scoped {
        optional #n tail <- empty
        optional #n next <- head2
        head2 <- empty
        dirty <- false
      } in while (present(next)) {
        optional #n left  <- next
        optional #n right <- left  `splitAt` chunk
        next              <- right `splitAt` chunk
        $Hidden[next]$
        $ReadOnly[left,right]$
        dirty <- dirty || present(right)
        optional #n newHead, optional #n newTail <- left `merge` right
        if (!present(head2)) {
          head2 <- newHead
        } else {
          \ require(tail).setNext(newHead)
        }
        tail <- newTail
      }
    } update {
      chunk <- 2*chunk
    }
  }

  @value splitAt (optional #n,Int) -> (optional #n)
  splitAt (head,n) {
    optional #n head2 <- head
    $Hidden[head]$

    scoped {
      Int i <- n
    } in while (present(head2)) {
      if (i == 1) {
        return require(head2).setNext(empty)
      } else {
        head2 <- require(head2).next()
      }
    } update {
      i <- i-1
    }

    return empty
  }

  @value merge (optional #n,optional #n) -> (optional #n,optional #n)
  merge (left,right) (head,tail) {
    head <- empty
    tail <- empty

    optional #n left2  <- left
    optional #n right2 <- right
    $Hidden[left,right]$

    while (present(left2) && present(right2)) {
      #n append <- defer
      if (require(left2).get() `compare.lessThan2` require(right2).get()) {
        left2 <- (append <- require(left2)).next()
      } else {
        right2 <- (append <- require(right2)).next()
      }
      if (!present(head)) {
        head <- append
      } else {
        \ require(tail).setNext(append)
      }
      tail <- append
    }

    if (present(left2)) {
      if (!present(head)) {
        head <- require(left2)
      } else {
        \ require(tail).setNext(require(left2))
      }
    }

    if (present(right2)) {
      if (!present(head)) {
        head <- require(right2)
      } else {
        \ require(tail).setNext(require(right2))
      }
    }

    while (present(tail)) {
      optional #n next <- require(tail).next()
      if (present(next)) {
        tail <- next
      } else {
        break
      }
    }
  }
}