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How linked lsts can be usd to represent long integers?

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Answered 2007-07-10 11:41:34

linked list consists of data nodes, each pointing to the next in the list. An array consists of contiguous chunks memory of predetermined size.

Linked lists are quite flexible. They can grow to any size -- up to resource limits -- and each node can be a different size. Memory allocation for a node is done as needed, usually when a new node is added.

Linked lists can be circular, or doubly-linked (pointers forward and backward), and new nodes can be inserted anywhere in the chain.

The greatest downside to linked lists is sequential access: to find any node in memory, each previous node must be examined and the pointers followed. Linked lists are also more complex to program and manage.

Arrays are fixed in size, so resources must be anticipated and consumed in advance. Each element is the same size and must contain the same data type. But access to a particular element is very fast, because its location in memory can be determined mathematically and accessed directly (offset from start of array = subscript * element size).

Note that modern languages -- especially OO languages such as C++ and Java -- blur this distinction by providing classes which offer the best of both worlds. Arrays can grow; linked list complexity is hidden from the programmer; hash tables (special arrays, really) allow for rapid indexing of arbitrary data. But under the hood, each complex data type is implemented using primitives such as arrays and linked lists

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What were the World War 2 boats used for d-day invasion called?

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How did the operation overlord compare to the landing at Anzio?

Both were amphibious attacks on an enemy coast. But a lot of planning went into Overlord, while the Anzio landings (Operation Shingle) were mounted very hurriedly, with little in depth planning, and with a strategic goal that amounted to wishful thinking. The Allied staff in the Mediterranean had considered mounting an operation along the lines of Anzio, to break the bloody deadlock on the Cassino front ninety miles south of Anzio, but had discarded the possibility, mainly because they could not anticipate having sufficient resources to carry through the operation. Overall planning called for making the landings in southern France, on the Riviera, the Mediterranean coast of France, at the same time as the landings in Normandy. 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Landing north of Rome, if the landings succeeded in causing the Germans to evacuate their forces to the south of the beachhead, would cause Rome to fall into the laps of the Allies as an extra fruit of the operation. But landing south of Rome, as the Allies did at Anzio, meant even if the Germans to the south at Cassino broke off and withdrew, Rome still had to be captured. Of course, eventually the Allies did cause the Germans to withdraw from the Cassino front - it just took four and one half months, and then the Allies did capture Rome, and it was the first time in 2000 years Rome had been captured from the south. Another problem with Churchill's plan was that the initial landing force was too small, all part of his airy optimism characterizing the entire scheme - it would only take a relatively small force, it would be over quickly so the vital LSTs would be free in time for the simultaneous landings in southern France with Overlord (then scheduled for around the first week of May). Only two divisions were in the initial landing force, one British, and one American. The American division was probably the best the US had, Army or Marine, in the entire war, but Anzio was to be its costliest campaign of the war. This was the 3rd Infantry Division, veterans of North Africa, Sicily and southern Italy. It was the "3rd ID, Reinforced" for the Anzio operation, having with it three of the four battalions of Darby's Rangers (the second battalion had been removed to England to attack Pont du Hoc on the Normandy D-Day), the joint American-Canadian First Special Service Force ("The Devil's Brigade"), and the 509th Parachute Infantry Battalion. So, with the "Reinforcements" there were an additional seven battalions to the US component, or 7/9th of the rifle strength of a division, roughly. But still this was not enough, because of the goals of the operation at Anzio. The German forces at Cassino depended on two highways runing south out of Rome for their supplies, Highway 7, near the landing beaches running near the coast, and Highway 6, which was about 25 miles inland. So even a bit of cursory thought would reveal that this initial landing force of two divisions - even if one of them was "Reinforced" - was going to have to take and hold a perimeter of more than fifty miles, if it was to successfully interrupt the flow of supplies to the Germans in the south, and cause them to withdraw. As it worked out, the landing force never did get to Highway 6, though after the breakout from the beachhead in late May (after four months of punishment) they did get close enough to hear the German traffic moving north on it, before Mark Clark ordered them to turn left and make straight for Rome, for fear the British (despite their promises) would try to steal the glory of capturing Rome from him and the US 5th Army. Another problem with this whole "strategic" notion of the Anzio campaign was that there were ample side roads available, further east than Highway 6, used successfully by Germans fleeing from the south, which could have been used to supply the Cassino front if the Germans wanted to keep fighting there, so even successfully capturing both Highways 6 and 7 by the landing force would not necessarily have resulted in achieving the goal of forcing a German withdrawal from the south. The Anzio landings were easy at first. The Germans had not expected that the Allies would be so foolish as to land there, of all places, so the Anzio-Nettuno area was undefended, with only part of an engineer battalion on the scene. For long weeks though, until Allied strength in the beachhead was built up, there were not sufficient troops to form an actual front line - all that could be managed was a string of strong points. Other problems at Anzio included that the entire beachhead was within range of German artillery, and since the entire beachhead was also ringed by hills, all held by the Germans, they had excellent observation to direct and correct their artillery fire, which made it swiftly fatal to try to move around in the beachhead during daylight. Far from withdrawing, trembling with fear at this bold Allied move, the German commander in Italy, "Smiling Albert" Kesselring, activated a new Field Army HQ and brought in troops from as far away as Yugoslavia, and within a week had the beachhead tightly hemmed in. There was no question of the landing force reaching its goals, way out there at Highway 6; the question was whether they would be annihilated and driven back into the sea, and it was a very near thing, heavy German attacks in early February coming very near to accomplishing just exactly that. So many, many more Allied divisions had to be fed into the fight, at first just to hang on, and then to build up sufficient strength to make a breakout, and the LSTs had to be kept in Italy as the sole lifeline of supply for this ever growing force. (Churchill said, somewhat disingenuously since the slender landing force was his idea, that he had hoped to fling a wildcat ashore, and instead had beached a whale). Eventually of course, the Germans in the south did withdraw, Rome was captured, but at a heavy cost. And the southern France landings had to be delayed two and one half months, until August 15. One silverlining to that delay was the German forces which had been on the Riviera coast in early June had by mid-August departed for Normandy, so the southern France landings were not heavily opposed. This all was the result of poor planning, poor selection of a landing place, over-optimistic assumptions as far as achievable goals and German reactions.

Why did the d-day invasion take so long to implement?

Two main reasons: the British, having just been ejected from the Continent in 1940, were skittish about a head-on assault into the German strength, which if it failed, might preclude making the effort again for several years, by which time the Germans might be so strong as to make the effort all but impossible. The British preferred a peripheral strategy, for as long as possible, poking around at the edges of Germany's conquests to draw off strength. Churchill was forever nattering on about the "soft underbelly" of the Axis in the Mediterranean. He never wanted anybody thinking about the question of, all right, supposing you HAVE successfully invaded and conquered Italy, or Greece? What then? Where can you go from there? Any possible Mediterranean area of attack was separated from central Germany by very, very high mountains, extremely rugged mountains, well-nigh impassable for an army with tanks, especially if the passes were heavily defended. In the case of Italy, NEUTRAL Switzerland - and the Alps, were in the way of a path to Germany. Stalin, with Russia fighting desperately for its very life, was needless to say more than a little bit vocally impatient with these peripheral nibblings favored by the British. Also impatient was General George C. Marshall, the US Army Chief of Staff, who was the architect of victory in WWII. He was in charge of the US Army AND the Army Air Force (the Air Force did not become an independent branch of the service until the war was over, in 1947). Marshall wanted to get on with it, and land on the coast of western France and head for Berlin. But the US had gotten a little bit sidetracked. Along with the British we had invaded North Africa in November, 1942, not because of any strategic necessity as far as ultimate victory required, but because Roosevelt and Churchill had promised Stalin a "second front" by the end of the year. Stalin, quite reasonably, allowed himself to believe that this meant an invasion of France, as he was intended to infer. Africa was a poor substitute and drew off only a tiny percentage of German strength, but it did allow the US Army to gain some experience and overcome some teething troubles. While the fighting was still going on in Africa Churchill and Roosevelt had the Casablanca Conference, in January 1943. General Marshall went there, with only a few aides, determined to obtain agreement to a cross-Channel invasion in 1943. The British sent an entire ship, a ship, full of staff officers, all bearing charts and graphs and plans, all to demonstrate that once Africa was finished, the next move must be Sicily. Sicily, mind you. The British later on at least had the grace to admit this was completely wrong. The correct move would have been to go for Sardinia, or Corsica, if we just HAD to keep piddling around the Med. From either of those, southern France could be reached, or Italy NORTH of Rome. The Allies in possession of Sardinia or Corsica would force the Germans to stretch their defenses to cover all those possibly threatened areas. From Sicily, given the limited range of land-based aircraft of the day, which was a necessary ingredient to the next step of invasions, the ONLY place to go was onto the mainland of Italy, and worst of all, Italy south of Rome. This suited Churchill just FINE! So Marshall was argued down, there was no commitment to a cross-Channel attack in 1943 at Casablanca, and only a half-hearted and insincere agreement of the British to one in 1944, which they later tried to weasel out of, but by that time Marshall had had a belly full and was brooking no more stalling. So in 1943 the US and British invaded Sicily and then Italy. It wasn't all a waste of time, Italy did surrender. But the Germans kept on fighting in Italy, in a country which greatly favored the defenders, and at the peak of the Italian campaign the western allies were occupying no more than 10% of German strength. Late in 1943 Churchill went on a Mediterranean inspection tour, and got the flu. He went to bed to recover, and when he felt a little better, commenced meddling. He couldn't help himself. He revived a plan, which had been considered and discarded, to land near Rome, behind the German lines. He insisted this would cause the Germans south of Rome to collapse and flee northward. Instead what we got was the Anzio campaign, nearly five months of bloody stalemate that helped postpone the Normandy landings from May to June because so many LSTs were needed to supply the whale we had beached at Anzio. The decision was made to delay the Normandy D-Day from the favorable period of the right combinations of phase of the moon and tides in early May to early June, the next favorable time. This was to get the benefit of an additional month of LST production. LSTs were "Landing Ship, Tanks", sizable vessels which could run their noses right up onto a beach and disgorge an entire company of infantry, or a dozen tanks, which need never get wet in the landing. This points up the other factor which made D-Day so long in coming. The US, eager as Marshall was to close with the enemy, was not ready. Only by the time the landings actually took place did the US have what turned out to be just barely enough trained men in completed units of division strength, and sufficient shipping, and only by June of 1944 had air supremacy been achieved.