c++ - for_each & ranged base for on 2D array -

i trying print 2d array using for_each , range based for loop.

my program goes this:-

#include <iostream> #include <algorithm> using namespace std; int main() {   int a[3][3]={{1,2,3},{4,5,6},{7,8,9}};   //for_each (begin(a), end(a), [] (int x) { cout<<x<<" ";}); code throws error    for_each (begin(a[0]), end(a[2]), [] (int x) { cout<<x<<" ";});  //this code works well, why ?    cout<<endl;     (auto &row: a)  // without & row, error thrown   {      (auto x:row)  // no & needed x, why ?      {         cout<<x<<" ";      }   }   return 0; } 

why did first for_each throw errors , why & symbol necessary row? type? row pointer?

for_each (begin(a), end(a), [] (int x) { cout<<x<<" ";}); 

begin(a) yields int(*)[3] (pointer array of size [3]), , dereferencing yields int(&)[3], while lambda expression expects int argument.

for_each (begin(a[0]), end(a[2]), [] (int x) { cout<<x<<" ";}); 

begin(a[0]) yields int* points first element in first row of a, , end(a[2]) yields int* pointing 1 past last element in last row of a, works.

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now range-based for part.

if remove & line for (auto& row : a) error occurs on following line for(auto x : row). because of way range-based for specified. clause pertinent use case is

if __range array, begin_expr __range , end_expr (__range + __bound), __bound number of elements in array (if array has unknown size or of incomplete type, program ill-formed)

hereon i'll referring identifiers mentioned in explanation section of linked page.

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consider case for (auto& row : a):

__range deduced int(&)[3][3] (reference array of size [3][3]). __begin deduced int(*)[3] (pointer array of size [3]) because type of __range decays pointer first row of 2d array. range_expression have auto& row, row deduced int(&)[3] (reference array of size [3]).

next, same process repeated inner range-based for. in case, __range int(&)[3] , array clause quoted above applies; remaining type deduction process similar described above.

__range = int(&)[3] __begin = int* x       = int 

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now consider case for (auto row : a):

__range, __begin , __end deduced same. crucial difference in case range_expression auto row, causes decay of int(*)[3] type __begin deduced as. means row deduced int *, , none of 3 clauses determination of begin_expr/end_expr described handle raw pointer. results in compilation error within nested for loop.