How does difficult terrain work for big creatures when part of it leaves and another part enters same terrain during the same move.
For example，if a huge creature moves through a medium one, does it take 35ft? 10 for each 5ft of its space and 5ft when last part leave?
In 4e, you only count the space that you are entering for the first time, not the space that you already occupies.
In 5e, there doesn't seem to be a rule regarding big creatures and difficult terrain.
Let's take a good look at the rules involved first, then we can use logic to intuit what to do with large creatures in difficult terrain.
The Rules say:
You move at half speed in difficult terrain—moving 1 foot in difficult terrain costs 2 feet of speed
(PHB 182)
Types of Difficult Terrain:
dense forests, deep swamps, rubble-filled ruins, steep mountains, and ice-covered ground—[are] all considered difficult terrain
(PHB 182)
The DMG adds webs(p105) and climbing on a larger creature(p.271) to this list. Also of note are ball bearings and caltrops (PHB , which do not create difficult terrain per se, but moving through a square full of either one at half movement (as if treating it as difficult terrain) negates the other effect of the these hazards. Then, there are spells that make an area into difficult terrain, but since there are a lot of these and they mainly mimic one of the aforementioned effects, I won't address them specifically.
Dense Forests: are hard to push through, cause you to have to weave around, snag on your clothes, etc.
Deep Swamps: are hard to push through, cause you to have to weave around, your feet get stuck in mud, etc.
Rubble-filled Ruins: cause you to have to weave around, may shift under your weight, etc.
Steep Mountains: require more energy to traverse, may cause you to have to backtrack or climb vertically, could trigger rockslides, etc.
Ice-covered Ground: walking slower helps you to avoid slipping and falling.
Webs: taking care by moving slowly helps you to not become stuck and restrained by the web.
Climbing on Larger Creatures: the constantly shifting, unpredictable surface hampers movement.
Ball Bearings and Caltrops: taking care by moving slowly lets you avoid stepping on something that you wish to avoid.
Some of these examples reduce movement because the creature moving has to be careful of a hazard (Rubble-filled Ruins, Ice, Webs, Ball Bearings and Caltrops), others reduce movement by actively impeding progress (Dense Forests and Deep Swamps), and others because traversing the terrain is physically more demanding (Deep Swamps and Steep Mountains).
The most important thing to consider when handling a large creature moving through difficult terrain are:
Is the terrain still difficult at that size?
Normal stairs would be difficult for a Tiny creature, but wouldn't be for a Small or larger creature, similarly, some steep surfaces may not present a problem for a creature large enough to simply step up to the next level. Similarly, tall grass may seem like a Dense Forest to a Tiny creature, and a Dense Forest may seem like no more than tall grass to a sufficiently large creature. The depth of a swamp is also relative to the size of the creature traversing it. Things like slipperiness and avoiding hazards would still be a problem for most creatures, no matter how big they are.
How does the large creature move?
Is the size of the Hazard small enough for the large creature to simply bypass by stepping over it? If they don't notice it, would it potentially still impede their movement, such as making them slip or get stuck? In such a case, where it would, where are the creature's feet? For a bipedal creature, such as a troll, ogre, or giant, I would assume that their feet are near the center of the spot they occupy and treat them as triggering the hazardous terrain while the center of their space is within the effected area. For a quadruped, I would assume that their feet were at the corners of the square, and for a creature that slithers or has many legs, then they may either trigger the effect in their whole area they occupy, or negate it entirely, depending on the situation.
Another good way to handle this is to roll Percentile Dice and if the number rolled is less than the percent of the creature's squares that occupy the hazardous terrain, then they treat it as difficult terrain, otherwise they don't.
This is the better way to do it when logic does not strictly suggest another solution.
By RAW, if any part of the terrain a creature moves over is difficult terrain, then the extra movement is spent.
In other ways, a big creature always pays movement for the "most difficult" terrain it moves over.
You move at half speed in difficult terrain— moving 1 foot in difficult terrain costs 2 feet of speed (...)
The DM can rule that a terrain (that is difficult for medium-ish creatures) is not difficult for a really big creature.
It makes sense that a huge dragon is not hindered by the loose rubble of a castle floor.
But on the other way, some terrain that is just cluttered for medium creatures (let's take a rocky field with some round 2' rocks all around every other square) is difficult for bigger creatures. A dragon could slip on one of those "pebbles" for example. Medium and smaller creatures just go around the rocks.
Excellent question. This appears to be a writing error.
5e's statement of "Every foot of movement in difficult terrain costs 1 extra foot" doesn't appear to intend for a square of difficult terrain on a grid to penalize huge creatures moving through it x3 more than medium (and I've not known anyone to play that way). By the same token: you wouldn't use this text to say, penalize a 5'x 5' creature more than a 1'x 1'.
Compare against 4e (as mentioned in the original question) or 3e's "When movement is hampered, each square moved into usually counts as two squares". I believe the 5e writer simply wasn't as precise as earlier editions (likely to accommodate gridless play).
