001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
093
094
095
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
// Exercise 2.4.29
package algs24;
import stdlib.*;
import java.util.Iterator;
import java.util.NoSuchElementException;

// To turn on assertions for a program in eclipse,
// run the program once, then go to the menubar and select
//   Run > Run Configurations... > Arguments > VM Arguments
// And add
//   -ea
// As a VM argument
public class MyMinMaxPQ<K extends Comparable<? super K>> implements Iterable<K> {
  private int N;    // number of items on priority queue
  private int MAXN; // size of the the arrays
  private K[] a;  // minheap
  private K[] b;  // maxheap

  // the array ab maps from a to b
  // the array ba maps from b to a
  // they are inverses, so i == ba[ab[i]] == ab[ba[i]] for any i
  //
  private int[] ab; // index a to b: a[i] == b[ab[i]]
  private int[] ba; // index b to a: b[i] == a[ba[i]]


  @SuppressWarnings("unchecked")
  /** Create an empty priority queue with the given initial capacity, using the given comparator. */
  public MyMinMaxPQ (int capacity) {
    MAXN = capacity;
    a = (K[]) new Comparable[MAXN + 1];
    b = (K[]) new Comparable[MAXN + 1];
    ab = new int[MAXN + 1];
    ba = new int[MAXN + 1];
    N = 0;
  }

  /** Is the priority queue empty? */
  public boolean isEmpty () { return N == 0; }

  /** Is the priority queue full? */
  public boolean isFull () { return N == MAXN; }

  /** Return the number of items on the priority queue. */
  public int size () { return N; }

  /**
   * Return the smallest key on the priority queue. Throw an exception if the
   * priority queue is empty.
   */
  public K min () {
    if (isEmpty ()) throw new Error ("Priority queue underflow");
    return a[1];
  }

  /** Add a new key to the priority queue. */
  public void insert (K x) {
    if (isFull ()) throw new Error ("Priority queue overflow");
    // add x, and percolate it up to maintain heap invariant
    N++;
    a[N] = x;
    b[N] = x;
    ab[N] = N;
    ba[N] = N;
    aSwim (N);
    bSwim (N);
    assert isMinMaxHeap ();
  }

  /**
   * Delete and return the smallest key on the priority queue. Throw an
   * exception if the priority queue is empty.
   */
  public K delMin () {
    if (N == 0) throw new Error ("Priority queue underflow");
    // TODO
    assert isMinMaxHeap ();
    return null;
  }
  /**
   * Delete and return the largest key on the priority queue. Throw an
   * exception if the priority queue is empty.
   */
  public K delMax () {
    if (N == 0) throw new Error ("Priority queue underflow");
    // TODO
    assert isMinMaxHeap ();
    return null;
  }

  /* *********************************************************************
   * Helper functions to restore the heap invariant.
   **********************************************************************/

  private void aSwim (int k) {
    while (k > 1 && aGreater (k / 2, k)) {
      aExch (k, k / 2);
      k = k / 2;
    }
  }
  private void aSink (int k) {
    while (2 * k <= N) {
      int j = 2 * k;
      if (j < N && aGreater (j, j + 1)) j++;
      if (!aGreater (k, j)) break;
      aExch (k, j);
      k = j;
    }
  }
  private void bSwim (int k) {
    while (k > 1 && bLess (k / 2, k)) {
      bExch (k, k / 2);
      k = k / 2;
    }
  }
  private void bSink (int k) {
    while (2 * k <= N) {
      int j = 2 * k;
      if (j < N && bLess (j, j + 1)) j++;
      if (!bLess (k, j)) break;
      bExch (k, j);
      k = j;
    }
  }

  /* *********************************************************************
   * Helper functions for compares and swaps.
   **********************************************************************/
  private boolean aGreater (int i, int j) {
    return a[i].compareTo (a[j]) > 0;
  }
  private boolean bLess (int i, int j) {
    return b[i].compareTo (b[j]) < 0;
  }
  private void swap (K[] a, int i, int j) {
    K tmp = a[i];
    a[i] = a[j];
    a[j] = tmp;
  }
  private void swap (int[] a, int i, int j) {
    int tmp = a[i];
    a[i] = a[j];
    a[j] = tmp;
  }
  private void aExch (int ai, int aj) {
    int bi = ab[ai];
    int bj = ab[aj];
    swap (a, ai, aj);
    swap (ab, ai, aj);
    swap (ba, bi, bj);
  }
  private void bExch (int bi, int bj) {
    int ai = ba[bi];
    int aj = ba[bj];
    swap (b, bi, bj);
    swap (ab, ai, aj);
    swap (ba, bi, bj);
  }

  private void showHeap () {
    StdOut.print ("a:  ");
    for (int i = 1; i <= N; i++)
      StdOut.print (a[i] + " ");
    StdOut.println ();
    StdOut.print ("b:  ");
    for (int i = 1; i <= N; i++)
      StdOut.print (b[i] + " ");
    StdOut.println ();
    /*
     * StdOut.print ("ab: "); for (int i = 1; i <= N; i++) StdOut.print
     * (ab[i] + " "); StdOut.println (); StdOut.print ("ba: "); for (int i =
     * 1; i <= N; i++) StdOut.print (ba[i] + " "); StdOut.println ();
     */
  }
  private void check () {
    for (int i = 1; i <= N; i++) {
      // a and b have the same data, mapped by ab and ba
      assert a[i] == b[ab[i]];
      assert b[i] == a[ba[i]];
      // ab and ba are inverses
      assert i == ab[ba[i]];
      assert i == ba[ab[i]];
    }
  }

  private boolean isMinMaxHeap () {
    check ();
    return isMaxHeap (1) && isMinHeap (1);
  }
  private boolean isMaxHeap (int k) {
    if (k > N) return true;
    int left = 2 * k, right = 2 * k + 1;
    if (left <= N && bLess (k, left))   { StdOut.format ("Not a max heap k=%d left=%d\n",  k, left);  showHeap(); return false; }
    if (right <= N && bLess (k, right)) { StdOut.format ("Not a max heap k=%d right=%d\n", k, right); showHeap(); return false; }
    return isMaxHeap (left) && isMaxHeap (right);
  }
  private boolean isMinHeap (int k) {
    if (k > N) return true;
    int left = 2 * k, right = 2 * k + 1;
    //StdOut.format ("checkmin: %s %s %s\n", a[k], a[left], a[right]);
    if (left <= N && aGreater (k, left))   { StdOut.format ("Not a min heap k=%d left=%d\n",  k, left);  showHeap(); return false; }
    if (right <= N && aGreater (k, right)) { StdOut.format ("Not a min heap k=%d right=%d\n", k, right); showHeap(); return false; }
    return isMinHeap (left) && isMinHeap (right);
  }


  /* *********************************************************************
   * Iterator
   **********************************************************************/

  /**
   * Return an iterator that iterates over all of the keys on the priority
   * queue in ascending order.
   * <p>
   * The iterator doesn't implement <tt>remove()</tt> since it's optional.
   */
  public Iterator<K> iterator () { return new HeapIterator (); }
  private class HeapIterator implements Iterator<K> {
    // create a new pq
    private MyMinMaxPQ<K> copy;

    // add all items to copy of heap
    // takes linear time since already in heap order so no keys move
    public HeapIterator () {
      copy = new MyMinMaxPQ<> (size ());
      for (int i = 1; i <= N; i++)
        copy.insert (a[i]);
    }

    public boolean hasNext () { return !copy.isEmpty (); }
    public void remove () { throw new UnsupportedOperationException (); }
    public K next () {
      if (!hasNext ()) throw new NoSuchElementException ();
      return copy.delMin ();
    }
  }

  /**
   * A test client.
   */
  private static int randomValue () { return StdRandom.uniform (100); }
  private static MyMinMaxPQ<Integer> randomPQ (int maxSize) {
    int minCapacity = 5;
    int capacity = StdRandom.uniform(maxSize)+minCapacity;
    MyMinMaxPQ<Integer> pq = new MyMinMaxPQ<> (capacity);
    for (int i=StdRandom.uniform (capacity); i>0; i--)
      pq.insert (randomValue());
    return pq;
  }
  private static void randomOps (MyMinMaxPQ<Integer> pq, int NUMOPS, boolean log) {
    for (int i=NUMOPS; i>0; i--) {
      switch (StdRandom.uniform (4)) {
      case 0:
        if (! pq.isEmpty()) {
          int x = pq.delMin();
          if (log) { StdOut.format ("delMin=%d\n", x); pq.showHeap(); }
        }
        break;
      case 1:
        if (! pq.isEmpty()) {
          int x = pq.delMax();
          if (log) { StdOut.format ("delMax=%d\n", x); pq.showHeap(); }
        }
        break;
      default:
        if (! pq.isFull()) {
          int x = randomValue();
          pq.insert(x);
          if (log) { StdOut.format ("insert=%d\n", x); pq.showHeap(); }
        }
        break;
      }
    }
  }
  private static void randomEmpty (MyMinMaxPQ<Integer> pq, boolean log) {
    while (! pq.isEmpty ())
      switch (StdRandom.uniform (2)) {
      case 0:
        if (! pq.isEmpty()) {
          int x = pq.delMin();
          if (log) { StdOut.format ("delMin=%d\n", x); pq.showHeap(); }
        }
        break;
      case 1:
        if (! pq.isEmpty()) {
          int x = pq.delMax();
          if (log) { StdOut.format ("delMax=%d\n", x); pq.showHeap(); }
        }
        break;
      }
  }
  private static boolean assertionsAreOn () {
    StdOut.println ("ASSERTIONS ARE ON!");
    return true;
  }
  public static void main (String[] args) {
    StdRandom.setSeed (0);
    for (int i=100; i>0; i--) {
      MyMinMaxPQ<Integer> pq = randomPQ (10);
      randomOps (pq, 10, true);
      randomEmpty (pq, true);
    }
    for (int i=100; i>0; i--) {
      MyMinMaxPQ<Integer> pq = randomPQ (1000);
      randomOps (pq, 10000, false);
      randomEmpty (pq, false);
    }
    StdOut.println ("If you don't see a statement below saying that assertions are on, then they are not on.");
    StdOut.println ("That means that you have not really tested anything!");
    StdOut.println ("You must enable assertions!");
    StdOut.println ("To enable assertions, see the instructions at the top of this .java file.");
    assert assertionsAreOn();


    //MyMinMaxPQ<Integer> pq = new MyMinMaxPQ<> (100);
    //StdIn.fromString ("10 20 30 40 50 + - + 05 25 35 - + - 70 80 05 + - - + ");  // This is not a very good test
    //StdIn.fromString ("10 20 40 50 30 + 70 60 - 30 - 50 20 +");                  // This is a good test
    //while (!StdIn.isEmpty ()) {
    //    pq.showHeap ();
    //    String item = StdIn.readString ();
    //    if (item.equals ("-")) StdOut.println ("min: " + pq.delMin ());
    //    else if (item.equals ("+")) StdOut.println ("max: " + pq.delMax ());
    //    else pq.insert (Integer.parseInt (item));
    //}
    //StdOut.println ("(" + pq.size () + " left on pq)");
  }
}