The troll featured in the children's story by Julia Donaldson and David Roberts is based on the troll from what Norwegian fairy tale? 
Three Billy Goats Gruff
The Troll
The Troll by Julia Donaldson and David Roberts is a children's story about a troll and some pirates.
 The troll in this story is based on the troll from the "Three Billy Goats Gruff" fairy tale.
 However, in this story, no goats ever cross the troll's bridge and he is forced to survive on fish that he catches from the river.
 He does encounter, in turn, a spider, a mouse and a rabbit, each of which convinces the troll not to eat them by telling him that he should try a bridge further down the river that is more suitable for capturing goats as he is "sick of fish".
 Meanwhile, the pirate captain Hank Chief and his crew (Peg Polkadot, Ben Buckle and Percy Patch) are searching for the treasure that is marked on their map, but are unable to locate the correct island.
 The pirates also display very poor culinary skills.
 Eventually, the troll reaches the sea and realises that he has been tricked by the other animals; he sees what he thinks are goat tracks in the sand and sets about laying a trap for the goat in a spot not too far from the location on the pirate's treasure map.
 He duly discovers an old chest when digging a large hole to ensnare his prey and throws away the "round shiny objects" he finds therein.
 He decides to lie in wait in the chest for the goat and falls asleep.
 Predictably, the pirates then arrive and make off with their "treasure"; upon opening the chest the pirates decide to make the troll walk the plank, until Peg discovers the troll's frying pan and cookbook.
 On discovering the troll's culinary talents, they agree to spare the troll and make him their cook.
 The troll is delighted and proceeds to tell the pirates that he will make them his favourite goat stew only to be advised, to his horror, that all the pirates desire is .
.
 fish.
Three Billy Goats Gruff
"Three Billy Goats Gruff" (Norwegian: De tre bukkene Bruse ) is a Norwegian fairy tale.
 The fairy tale was collected by Peter Christen Asbjørnsen and Jørgen Moe in their "Norske Folkeeventyr", first published between 1841 and 1844.
 It has an "eat-me-when-I'm-fatter" plot (Aarne-Thompson type 122E).
The Master Thief
"The Master Thief" is a Norwegian fairy tale collected by Peter Chr.
 Asbjørnsen and Jørgen Moe.
 The Brothers Grimm included a shorter variant as tale 193 in their fairy tales.
 Andrew Lang included it in "The Red Fairy Book".
 It is Aarne–Thompson type 1525A, "Stealing the Count's Horse, Sheet, and Parson". Soria Moria Castle
Soria Moria Castle ("Soria Moria slott") is a Norwegian fairy tale made famous by Peter Christen Asbjørnsen and Jørgen Moe in their classical "Norske Folkeeventyr".
 Later Andrew Lang included the story in his series of fairy tale collections in "The Red Fairy Book". Boots and the Troll
Boots and the Troll is a Norwegian fairy tale collected by Peter Christen Asbjørnsen and Jørgen Moe in "Norwegian Folktales". Why the Sea is Salt
Why the Sea Is Salt (Norwegian: "Kvernen som maler på havsens bunn" ; the mill that grind at the bottom of the sea) is a Norwegian fairy tale collected by Peter Christen Asbjørnsen and Jørgen Moe in their "Norske Folkeeventyr".
 Andrew Lang included it in "The Blue Fairy Book" (1889). The Companion
"The Companion" (Norwegian: "Følgesvennen" ) is a Norwegian fairy tale, published in "Norwegian Folktales" (1841-1844) by Asbjørnsen and Moe. Peer Gynt
Peer Gynt ( ; ] ) is a five-act play in verse by the Norwegian dramatist Henrik Ibsen published in 1867.
 It was illustrated by Arthur Rackham as a children's book in 1936.
 Written in Danish—the common written language of Denmark and Norway in Ibsen's lifetime—it is one of the most widely performed Norwegian plays.
 Ibsen believed "Per Gynt", the Norwegian fairy tale on which the play is loosely based, to be rooted in fact, and several of the characters are modelled after Ibsen's own family, notably his parents Knud Ibsen and Marichen Altenburg.
 He was also generally inspired by Peter Christen Asbjørnsen's collection of Norwegian fairy tales, published in 1845 ("Huldre-Eventyr og Folkesagn"). The Boy Who Had an Eating Match with a Troll
The Boy Who Had an Eating Match with a Troll (Norwegian: "Askeladden som kappåt med trollet" ) is a Norwegian fairy tale collected by Asbjørnsen and Moe.
 The troll is, as commonly depicted, not very intelligent and has poor vision, while the boy is clever, outwitting the troll to win an eating contest. Bushy Bride
Bushy Bride (in Norwegian : "Buskebrura") is a Norwegian fairy tale collected by Asbjørnsen and Moe.
 It is Aarne-Thompson type 403 (The Black and the White Bride).
 It is included in Andrew Lang's Red Fairy Book.