The storage of heaps as arrays is diagrammed at Binary heap # Heap implementation. The heap's invariant is preserved after each extraction, so the only cost is that of extraction.

The heap relation mentioned above applies only between nodes and their immediate parents.

As a particular simple case, if there are only two heaps left, the strategy is to reduce the number of objects in the bigger heap to make the heaps equal.

When played as a misère game, Nim strategy is different only when the normal play move would leave no heap of size two or larger.

The modification for misère play is demonstrated by noting that the modification first arises in a position that has only one heap of size 2 or more.

This game is commonly played in practice with only one heap ( for instance with k = 3 in the game Thai 21 on Survivor: Thailand, where it appeared as an Immunity Challenge ).

When first erected, though the grain was equally well separated from the straw, yet as the whole of the straw, chaff, and grain, was indiscriminately thrown into a confused heap, the work could only with propriety be considered as half executed.

In many of Beckett's later plays, most features are stripped away and what's left is a minimalistic tableau: a woman walking slowly back and forth in Footfalls, for example, or in Breath only a junk heap on stage and the sounds of breathing.

The advantage of this custom heap over binary heaps is that if the sequence is already sorted, it takes only time to construct and deconstruct the heap, hence the better runtime.

* If the new heap is going to become part of a larger heap by the time we are done, then don't bother establishing the string property: it only needs to be done when a heap has reached its final size.

Further note, that this implementation is a little flawed: The bitmap p only holds 32 bits and therefore limits the maximum number of heaps in the entire string to 32 ( not counting the right-most heap of size LP ), which will eventually overflow if you try to sort an array of more than LP + 1

Is it still a heap when only one grain remains?

If only one of the heaps contains a tree of order j, this tree is moved to the merged heap.

Inserting a new element to a heap can be done by simply creating a new heap containing only this element and then merging it with the original heap.

In the Restoration, it was rewritten by John Dryden, who stated that he intended to uncover the " jewels " of Shakespeare's verse, hidden beneath a " heap of rubbish " ( not only some " ungrammatical " and indecorous expressions, but also much of the plot ).

The rich only select from the heap what is most precious and agreeable.

Once a key is added to the linked-list, it is considered corrupted because its value is never again relevant in any of the soft heap operations: only the common keys are compared.

Bryn Mawr Drive is only two or three miles from the Spartan, and it took me less than five minutes to get there.

Actually, only two men know what the formula is, Blake and '' -- He stopped and looked at Thor's body.

In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.

This is the only case in modern history of a people of Britannic origin submitting without continued struggle to what they view as foreign domination.

Recognizing that the Rule of Law is `` a dynamic concept which should be employed not only to safeguard the civil and political rights of the individual in a free society '', the Congress asserted that it also included the responsibility `` to establish social, economic, educational and cultural conditions under which his legitimate aspirations and dignity may be realized ''.

It is the gait of the human who must run to live: arms dangling, legs barely swinging over the ground, head hung down and only occasionally swinging up to see the target, a loose motion that is just short of stumbling and yet is wonderfully graceful.

They are huge areas which have been swept by winds for so many centuries that there is no soil left, but only deep bare ridges fifty or sixty yards apart with ravines between them thirty or forty feet deep and the only thing that moves is a scuttling layer of sand.

Others are confined to vast reservations, and not only does the Australian government justifiably not wish them to be viewed as exhibits in a zoo, but on their reservations they are extremely fugitive, shunning camps, coming together only for corroborees at which their strange culture comes to its highest pitch -- which is very low indeed.

`` Now that Bruno Walter is virtually in retirement and my dear friend Dimitri Mitropoulos is no longer with us, I am probably the only one -- with the possible exception of Leonard Bernstein -- who has this special affinity for and champions the works of Bruckner and Mahler ''.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.

I think it is essential, however, to pinpoint here the difference between the two concepts of sovereignty that went to war in 1861 -- if only to see better how imperative is our need today to clarify completely our far worse confusion on this subject.

To my knowledge, Lincoln remains the only Head of State and Commander-in-Chief who, while fighting a fearful war whose issue was in doubt, proved man enough to say this publicly -- to give his foe the benefit of the fact that in all human truth there is some error, and in all our error, some truth.

It is all around us and our only chance now is to let it in.

in working with these patients the therapist eventually gets to do some at least private mulling over of the possible meaning of a belch, or the passage of flatus, not only because he is reduced to this for lack of anything else to analyze, but also because he learns that even these animal-like sounds constitute forms of communication in which, from time to time, quite different things are being said, long before the patient can become sufficiently aware of these, as distinct feelings and concepts, to say them in words.

Entries are summarized only when by doing so the amount of information retained in the dictionary is reduced and the time required for dictionary operations is decreased.

But her personality was such that each affair lasted only until that lover, too, had been conquered and reduced to passivity.

But I can only make this choice because I believe that the risk need not increase, but may be deliberately reduced '' ( by precautions against accidents or by limiting war??

Publishers, at times, reduced the risk of this type of arrangement, by agreeing only to pay this after a certain amount of copies had sold.

In the 1998 version, Alliaceae were a distinct family ; in the 2003 version, combining the Alliaceae with the Agapanthaceae and the Amaryllidaceae sensu stricto was recommended but optional ; in the 2009 version, only the broad circumscription of the Amaryllidaceae is allowed, with the Alliaceae reduced to a subfamily, Allioideae.

Astrology's modern representation in western popular media is usually reduced to sun sign astrology, which considers only the zodiac sign of the Sun at an individual's date of birth, and represents only 1 / 12 of the total chart.

The Liberals were reduced to a mere forty seats in Parliament, only seven of which had been won against candidates from both parties and none of these formed a coherent area of Liberal survival.

The most notable alteration is the shortening of most feasts from nine to three lessons at Matins, keeping only the Scripture readings ( the former lesson i, then lessons ii and iii together ), followed by either the first part of the patristic reading ( lesson vii ) or, for most feasts, a condensed version of the former second Nocturn, which was formerly used when a feast was reduced in rank and commemorated.

Dogs have molar teeth behind the carnassials for crushing bones, but cats have only a greatly reduced, functionless molar behind the carnassial in the upper jaw.

What it means to take the category physical object seriously as a category of being is to assert that the concept of physical objecthood cannot be reduced to or explicated in any other terms-not, for example, in terms of bundles of properties but only in terms of other items in that category.

They are reduced by at least a factor of two if commission is charged on winning bets only.

Short path distillation is a distillation technique that involves the distillate travelling a short distance, often only a few centimeters, and is normally done at reduced pressure.

The advantage is that the heating temperature can be considerably lower ( at reduced pressure ) than the boiling point of the liquid at standard pressure, and the distillate only has to travel a short distance before condensing.

It is the only extant member of the genus Cuon, which differs from Canis by the reduced number of molars and greater number of teats.

Since recuperating from the heart surgery, Bowie has reduced his musical output, making only one-off appearances on stage and in the studio.

The use of only the top three strings was popular for bass soloists and Principal bassists in orchestras in the 19th century, because it reduced the pressure on the wooden top of the bass, which was thought to create a more resonant sound.

Otherwise, it will be reduced to spiritualist idealism, such as the philosophies of Kant or Hegel, which are only ideologies, that is the material product of social existence.

Some of the limitations of Diophantus ' notation are that he only had notation for one unknown and, when problems involved more than a single unknown, Diophantus was reduced to expressing " first unknown ", " second unknown ", etc.

The new ruler faced the challenge of restoring order in a country that was in shambles — by the end of Masie Nguema's dictatorship, the state coffers were empty and the population had been reduced to only one-third of what it was at independence.

This only succeeded in putting the rising off for a day, although it greatly reduced the number of Volunteers who turned out.

It was only in 1919 that the exodus of talent from the country took place, and fiction film production was reduced to practically nothing.

This new proof is similar to Appel and Haken's but more efficient because it reduced the complexity of the problem and required checking only 633 reducible configurations.

Conversely, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).