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I am consuming the New York Times Best Sellers API, so that I can get the list of books for each category in the Best Sellers. My code goes thus:

import "dart:convert";
import "package:flutter/material.dart";
import "package:http/http.dart" as http;
import "package:best_sellers/api.dart";

class BestSellersList extends StatefulWidget 
 final API api;
 final List<dynamic> categories;

 BestSellersList(Key key, @required this.api, @required this.categories) : super(key: key);

 @override
 _BestSellersList createState() => _BestSellersList();


class _BestSellersList extends State<BestSellersList> 
 String base, key;
 List<dynamic> categories;
 Future<List<dynamic>> books;

 Future<List<dynamic>> fetchBooks() async 
 try 
 final books = categories.map((category) async 
 final listNameEncoded = category["list_name_encoded"];
 final uri = "$base/$listNameEncoded?api-key=$key";
 final response = await http.get(uri);
 if (response.statusCode == 200) 
 final responseBody = json.decode(response.body);
 final books = responseBody["results"]["books"];
 return books;
 else throw Exception(); 
 ).toList();

 if (books.isNotEmpty) 
 return books;
 
 throw Exception();
 catch(e) /**/ 
 

 void updateBooks() 
 setState(() 
 books = updateBooks();
 );
 

 @override
 initState() 
 super.initState();
 base = widget.api.base;
 key = widget.api.key;
 categories = widget.categories;
 print("categories.length: $categories.length"); // categories.length: 55
 updateBooks();
 

 @override
 Widget build(BuildContext context) 
 return FutureBuilder(
 future: books,
 builder: (context, snapshot) 
 if (snapshot.hasData) 
 return ListView.builder(
 itemCount: snapshot.data.length,
 itemBuilder: (context, index) 
 final displayName = snapshot.data[index]["display_name"];
 return ListTile(title: Text(displayName));
 
 );
 else if (snapshot.hasError) 
 return Center(child: Column(
 children: [
 Text(snapshot.error.toString()),
 RaisedButton(
 onPressed: () => updateBooks(),
 child: Text("RETRY"),
 ),
 ],
 ));
 

 return Center(child: CircularProgressIndicator());
 
 );
 

On running my code, I get this stack trace:

 I/flutter ( 5231): ══╡ EXCEPTION CAUGHT BY WIDGETS LIBRARY
╞═══════════════════════════════════════════════════════════
I/flutter ( 5231): The following StackOverflowError was thrown building FutureBuilder<List<dynamic>>(state:
I/flutter ( 5231): _FutureBuilderState<List<dynamic>>#a3252):
I/flutter ( 5231): Stack Overflow
I/flutter ( 5231): When the exception was thrown, this was the stack:
I/flutter ( 5231): #0 State.mounted (package:flutter/src/widgets/framework.dart:969:3)
I/flutter ( 5231): #1 State.setState.<anonymous closure>
(package:flutter/src/widgets/framework.dart:1113:63)
I/flutter ( 5231): #2 State.setState (package:flutter/src/widgets/framework.dart:1123:6)
I/flutter ( 5231): #3 _BestSellersList.updateBooks (package:best_sellers/best_sellers_list.dart:44:9)
I/flutter ( 5231): #4 _BestSellersList.updateBooks.<anonymous closure>
(package:best_sellers/best_sellers_list.dart:45:19)
I/flutter ( 5231): #5 State.setState (package:flutter/src/widgets/framework.dart:1124:30)
I/flutter ( 5231): #6 _BestSellersList.updateBooks (package:best_sellers/best_sellers_list.dart:44:9)
I/flutter ( 5231): #7 _BestSellersList.updateBooks.<anonymous closure>
(package:best_sellers/best_sellers_list.dart:45:19)
I/flutter ( 5231): #8 State.setState (package:flutter/src/widgets/framework.dart:1124:30)
I/flutter ( 5231): #9 _BestSellersList.updateBooks (package:best_sellers/best_sellers_list.dart:44:9)
I/flutter ( 5231): #10 _BestSellersList.updateBooks.<anonymous closure>
(package:best_sellers/best_sellers_list.dart:45:19)
I/flutter ( 5231): #11 State.setState (package:flutter/src/widgets/framework.dart:1124:30)
I/flutter ( 5231): #12 _BestSellersList.updateBooks (package:best_sellers/best_sellers_list.dart:44:9)
I/flutter ( 5231): #13 _BestSellersList.updateBooks.<anonymous closure>
(package:best_sellers/best_sellers_list.dart:45:19)
 ...................................................
 ...................................................
 ...................................................
 I/flutter ( 5231): ══╡ EXCEPTION CAUGHT BY WIDGETS LIBRARY
╞═══════════════════════════════════════════════════════════
I/flutter ( 5231): The following StackOverflowError was thrown building FutureBuilder<List<dynamic>>(state:
I/flutter ( 5231): _FutureBuilderState<List<dynamic>>#a3252):
I/flutter ( 5231): Stack Overflow
I/flutter ( 5231): When the exception was thrown, this was the stack:
I/flutter ( 5231): #0 State.mounted (package:flutter/src/widgets/framework.dart:969:3)
I/flutter ( 5231): #1 State.setState.<anonymous closure>
(package:flutter/src/widgets/framework.dart:1113:63)
I/flutter ( 5231): #2 State.setState (package:flutter/src/widgets/framework.dart:1123:6)
I/flutter ( 5231): #3 _BestSellersList.updateBooks (package:best_sellers/best_sellers_list.dart:44:9)
I/flutter ( 5231): #4 _BestSellersList.updateBooks.<anonymous closure>
(package:best_sellers/best_sellers_list.dart:45:19)
I/flutter ( 5231): #5 State.setState (package:flutter/src/widgets/framework.dart:1124:30)
I/flutter ( 5231): #6 _BestSellersList.updateBooks (package:best_sellers/best_sellers_list.dart:44:9)
I/flutter ( 5231): #7 _BestSellersList.updateBooks.<anonymous closure>
(package:best_sellers/best_sellers_list.dart:45:19)
I/flutter ( 5231): #8 State.setState (package:flutter/src/widgets/framework.dart:1124:30)
I/flutter ( 5231): #9 _BestSellersList.updateBooks (package:best_sellers/best_sellers_list.dart:44:9)
I/flutter ( 5231): #10 _BestSellersList.updateBooks.<anonymous closure>
(package:best_sellers/best_sellers_list.dart:45:19)
I/flutter ( 5231): #11 State.setState (package:flutter/src/widgets/framework.dart:1124:30)
I/flutter ( 5231): #12 _BestSellersList.updateBooks (package:best_sellers/best_sellers_list.dart:44:9)
I/flutter ( 5231): #13 _BestSellersList.updateBooks.<anonymous closure>
(package:best_sellers/best_sellers_list.dart:45:19)

I understand that the bug is located in the fetchBooks() method, which in turn is invoked by the updateBooks() method, and that a StackoverflowError is caused by an excessively deep or infinite recursion. The categories list I'm iterating over has 55 items.

Here is the cycle:

 void updateBooks() // called from vvv
 setState(() 
 books = updateBooks(); // <<<< calls ^^^
 );
 

you might want something like

 void updateBooks() async 
 var result = await fetchBooks();
 setState(() 
 books = result;
 );