1. Multidimensional Arrays Vectors of Vectors
There Could Be More than One

2. Two Dimensional Array Basics
matrices, tables and similar information is often naturally represented by a two-dimensional array
first index – row
second index - column
declaration: basicType arrayName[rows][columns];
example
int a[3][4];
accessing
a[0][1] = 23; cout << a[1][3]; c[2][4]+=55;
either index out of range is still an error
a[2][4] = 55; // error
larger dimensions are possible: int b[10][100][200];

3. Two Dimensional Arrays in Loops
nested loops are useful with multidimensional arrays
for (int i=0; i < length; ++i)
for (int j=0; j < width; ++j)
cout << a[i][j] << ” ”;

4. Arrays and Functions
if multidimensional array is used as parameters, all but first dimension have to be stated
the first dimension can be passed as separate parameter
const int width=3;
void printArray(int c[][width], int length){
for (int i=0; i < length; ++i)
for (int j=0; j < width; ++j)
cout << c[i][j] << ” ”; }

5. Vectors of Vectors alternative to multidimensional arrays
outer vector’s type is declared to be a vector
vector<vector<int>> a;
inner vectors can then be added to the outer vector
vector<int> row(width);
for(int i=0; i < length; ++i)
a.push_back(row);
vector elements can be accessed as in multidimensional array
a[1][2] = 55;
vectors retain all advantages over arrays: have extra functions, carry size, can pass by value/return, can change size on demand
example: can use size() in a loop iterating over vector
for (int i=0; i < a.size(); ++i)
for (int j=0; j < a[i].size(); ++j)
cout << a[i][j] << ” ”;

6. Ragged (Jagged) Array ragged (jagged) array: rows can vary in size
a.erase(a.begin()+1);
a.erase(a.begin()+1);
a.erase(a.begin()+1);
Ragged (Jagged) Array
ragged (jagged) array: rows can vary in size
example: program seats in a (non-square) auditorium or in airplane
what does this code do?
vector<int> row;
vector<vector<int>> a;
for(int i=0; i < 4; ++i){
row.push_back(i);
a.push_back(row); }
a.erase(a.begin()+1);
a[2].insert(a[2].begin()+1, 55);

7. Review Questions Why are multidimensional arrays necessary?
How does one declare a two-dimensional array?
What is the first index? the second index?
How does one access an element of multidimensional array?
Why are nested loops useful with multidimensional arrays?
How is multidimensional array passed as a parameter to a function?
What is vector of vectors?
How does one declare a vector of vectors? Initialize it?
How are individual elements of a vector of vectors accessed?
What are the advantages of a vector of vectors over multidimensional array?
What is ragged/jagged array? How does one determine the size of a row in a ragged array? How does one change the number of rows in a ragged array? How does one change the number of elements in a row in a ragged array?