1. The Ohio State University
Arrays
CSE1222: Lecture 13
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2. The Ohio State University
Programming Problem
Write a program to:
Read in a list of integers;
Print the list in reverse order.
CSE1222: Lecture 13
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3. The Ohio State University
Arrays (1)
So far the variables we have made store one value at a time. If you need to store and use 50 integers, then 50 int variables must be declared.
These variables are called atomic or scalar, which means they cannot be further divided into smaller pieces.
CSE1222: Lecture 13
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4. One-Dimensional Arrays
Instead of using 50 int variables, declare a single array which holds 50 int values.
To declare an array for 50 int values, we use the following syntax:
int list[50];
This creates an int array called list of size 50:
list
CSE1222: Lecture 13
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5. The Ohio State University
reverse.cpp
...
const int ARRAY_SIZE(5);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
cout << "Enter list of " << ARRAY_SIZE << " integers: ";
for (int i = 0; i < ARRAY_SIZE; i++) {
cin >> list[i]; }
cout << "Reverse list: ";
for (int i = ARRAY_SIZE-1; i >= 0; i--)
cout << list[i] << " ";
cout << endl;
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6. The Ohio State University
...
const int ARRAY_SIZE(5);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
cout << "Enter list of " << ARRAY_SIZE << " integers: ";
for (int i = 0; i < ARRAY_SIZE; i++) {
cin >> list[i]; }
cout << "Reverse list: ";
for (int i = ARRAY_SIZE-1; i >= 0; i--)
cout << list[i] << " ";
cout << endl;
> reverse.exe
Enter list of 5 integers:
Reverse list:
CSE1222: Lecture 13
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7. One-Dimensional Arrays (2)
Examples of array declarations:
char name[40]; // 40 characters
double celsius[90]; // 90 doubles
bool flag[1000]; // 1000 true/false values
int list[50]; // 50 integers
list
Note: Arrays are numbered starting at 0.
The last element in array list of size 50 is list[49].
CSE1222: Lecture 13
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8. Other array declarations
Use const int variables to declare arrays:
const int CELSIUS_ARRAY_SIZE(90);
double celsius[CELSIUS_ARRAY_SIZE];
// 90 doubles
const int MAX_LIST_LENGTH(50);
int list[MAX_LIST_LENGTH]; // 50 integers
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9. The Ohio State University
Array Indices
The list array from the the previous slide holds 50 integers.
list[0] refers to the first element in the array.
list[1] is the second element.
list[2] is the third element. …
list[49] is the fiftieth element.
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10. The Ohio State University
Using Array Variables
Using array variables:
list[0] = 77; // assigns 77 to the first
// element in array list
list[1] = list[0];
list[2] = list[1] + 3;
// assigns 80 to list[2]
int i = 3;
list[2*i] = list[i-1] - list[i-2];
// assigns 3 to list[6]
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11. The Ohio State University
More array indices
list[2*i] = list[i-1] - list[i-2];
The array index can be specified using variables or expressions, but you must be careful of two things:
The variable or expression evaluates to an integer
The value is in the range of the array. In the list array from the previous slide, the index range is something between 0 and 49.
CSE1222: Lecture 13
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12. Using a loop with arrays
Arrays and for loops go hand-in-hand. Consider the following code:
const int SIZE(5);
int a[SIZE];
int b[SIZE];
// Note i = 0 and i < SIZE
for (int i = 0; i < SIZE; ++i) {
a[i] = 10;
b[i] = 10*i;
} //What does this do?
CSE1222: Lecture 13
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13. The Ohio State University
aboveAverage.cpp
// print out above average temperatures
...
int main {
const int TEMP_SIZE(6);
double temp[TEMP_SIZE]; // array of TEMP_SIZE elements
double sum(0.0), average(0.0);
// input temperatures
cout << "Enter the temperature for the last "
<< TEMP_SIZE << " days: " << endl;
for (int i = 0; i < TEMP_SIZE; i++)
cin >> temp[i]; }
CSE1222: Lecture 13
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14. aboveAverage.cpp (cont.)
// compute the sum
sum = 0.0;
for (int i = 0; i < TEMP_SIZE; i++) {
sum = sum + temp[i]; }
// compute the average
average = sum/TEMP_SIZE;
// output above average temperatures
cout << "Average temperature = " << average << endl;
cout << "Above average temperatures: ";
if (temp[i] > average)
{ cout << temp[i] << " "; }
cout << endl;
CSE1222: Lecture 13
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15. aboveAverage.cpp (cont.)
...
// output above average temperatures
cout << "Average temperature = " << average << endl;
cout << "Above average temperatures: ";
for (int i = 0; i < TEMP_SIZE; i++) {
if (temp[i] > average)
{ cout << temp[i] << " "; } }
cout << endl;
> aboveAverage.exe
Enter the temperature for the last 6 days:
Average temperature = 35
Above average temperatures:
CSE1222: Lecture 13
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16. aboveAverage.cpp (cont.)
...
// output above average temperatures
cout << "Average temperature = " << average << endl;
cout << "Above average temperatures: ";
for (int i = 0; i < TEMP_SIZE; i++) {
if (temp[i] > average)
{ cout << temp[i] << " "; } }
cout << endl;
> aboveAverage.exe
Enter the temperature for the last 6 days:
Average temperature = 42.5
Above average temperatures: 105
CSE1222: Lecture 13
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17. aboveAverage.cpp (cont.)
...
// output above average temperatures
cout << "Average temperature = " << average << endl;
cout << "Above average temperatures: ";
for (int i = 0; i < TEMP_SIZE; i++) {
if (temp[i] > average)
{ cout << temp[i] << " "; } }
cout << endl;
> aboveAverage.exe
Enter the temperature for the last 6 days:
Average temperature = 53.5
Above average temperatures:
CSE1222: Lecture 13
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18. logTableUnsafe.cpp (Unsafe)
...
const int TABLE_SIZE(10);
double log_table[TABLE_SIZE]; // array of TABLE_SIZE elements
int n;
cout << "Enter number of integers: ";
cin >> n;
for (int i = 0; i < n; i++) {
log_table[i] = log(double(i+1)); }
cout << "log(" << i+1 << ") = "
<< log_table[i] << endl;
CSE1222: Lecture 13
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19. logTableUnsafe.cpp (Unsafe)
> logTableUnsafe.exe
Enter number of integers: 5
log(1) = 0
log(2) =
log(3) =
log(4) =
log(5) =
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20. The Ohio State University
Why is this unsafe?
...
const int TABLE_SIZE(10);
double log_table[TABLE_SIZE]; // array of TABLE_SIZE elements
int n;
cout << "Enter number of integers: ";
cin >> n;
for (int i = 0; i < n; i++) {
log_table[i] = log(double(i+1)); }
cout << "log(" << i+1 << ") = "
<< log_table[i] << endl;
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21. The Ohio State University
logTable.cpp
...
const int TABLE_SIZE(10);
double log_table[TABLE_SIZE]; // array of TABLE_SIZE elements
int n;
cout << "Enter number of integers: ";
cin >> n;
while (n > TABLE_SIZE) {
cout << "Input error.“;
cout << " Input must be less than or equal to "
<< TABLE_SIZE << "." << endl; }
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22. The Ohio State University
logTable.cpp (cont.)
for (int i = 0; i < n; i++) {
log_table[i] = log(double(i+1)); }
cout << "log(" << i+1 << ") = "
<< log_table[i] << endl;
return 0;
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23. The Ohio State University
reverse2.cpp
...
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(0);
cout << "Enter list of non-zero integers (ending with 0): ";
cin >> x;
num = 0;
while (x != 0 && num < ARRAY_SIZE) {
list[num] = x;
num++; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
CSE1222: Lecture 13
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24. The Ohio State University
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
...
cout << "Enter list of non-zero integers (ending with 0): ";
cin >> x;
num = 0;
while (x != 0 && num < ARRAY_SIZE) {
list[num] = x;
num++; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
> reverse2.exe
Enter list of non-zero integers (end list with 0):
Reverse list:
CSE1222: Lecture 13
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25. The Ohio State University
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
...
cout << "Enter list of non-zero integers (ending with 0): ";
cin >> x;
num = 0;
while (x != 0 && num < ARRAY_SIZE) {
list[num] = x;
num++; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
> reverse2.exe
Enter list of non-zero integers (end list with 0):
Reverse list:
CSE1222: Lecture 13
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26. The Ohio State University
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
...
cout << "Enter list of non-zero integers (ending with 0): ";
cin >> x;
num = 0;
while (x != 0 && num < ARRAY_SIZE) {
list[num] = x;
num++; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
> reverse2.exe
Enter list of non-zero integers (end list with 0): 0
Reverse list:
CSE1222: Lecture 13
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27. What’s wrong with this program?
...
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(0);
cout << "Enter list of non-zero integers (ending with 0): ";
cin >> x;
num = 0;
while (x != 0) {
list[num] = x;
num++; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
CSE1222: Lecture 13
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28. What’s wrong with this program?
...
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(0);
cout << "Enter list of non-zero integers (ending with 0): ";
cin >> x;
num = 0;
while (x != 0 && n <= ARRAY_SIZE) {
list[num] = x;
num++; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
CSE1222: Lecture 13
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29. What’s wrong with this program?
...
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(1);
cout << "Enter list of non-zero integers (ending with 0): ";
num = 0;
while (x != 0 && n < ARRAY_SIZE) {
list[num] = x;
num++;
cin >> x; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
CSE1222: Lecture 13
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30. The Ohio State University
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(1);
cout << "Enter list of non-zero integers (ending with 0): ";
num = 0;
while (x != 0 && num < ARRAY_SIZE) {
list[num] = x;
num++;
cin >> x; }
...
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
> reverse2Error3.exe
Enter list of non-zero integers (end list with 0):
Reverse list:
CSE1222: Lecture 13
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31. What’s wrong with this program?
...
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(1);
cout << "Enter list of non-zero integers (ending with 0): ";
num = 0;
cin >> x;
while (x != 0 && n < ARRAY_SIZE) {
list[num] = x;
num++; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
CSE1222: Lecture 13
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32. The Ohio State University
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(0);
cout << "Enter list of non-zero integers (ending with 0): ";
num = 0;
while (x != 0 && num < ARRAY_SIZE) {
cin >> x;
list[num] = x;
num++; }
...
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
> reverse2Error4.exe
Enter list of non-zero integers (end list with 0):
Reverse list: 0 7 6
CSE1222: Lecture 13
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33. What’s wrong with this program?
...
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(1);
cout << "Enter list of non-zero integers (ending with 0): ";
num = 0;
while (x != 0 && n < ARRAY_SIZE) {
cin >> x;
list[num] = x;
num++; }
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
CSE1222: Lecture 13
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34. The Ohio State University
const int ARRAY_SIZE(100);
int list[ARRAY_SIZE]; // an array of ARRAY_SIZE elements
int num(0);
int x(1);
cout << "Enter list of non-zero integers (ending with 0): ";
num = 0;
while (x != 0 && num < ARRAY_SIZE) {
cin >> x;
list[num] = x;
num++; }
...
cout << "Reverse list: ";
for (int i = num-1; i >= 0; i--)
{ cout << list[i] << " "; }
cout << endl;
> reverse2Error5.exe
Enter list of non-zero integers (end list with 0):
Reverse list:
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35. The Ohio State University
Array Initialization
Arrays are initialized like scalar variables, except the list of values are placed in braces. For example:
int volts[5] = {2, 9, 100, 34, 27};
char grades[3] = {‘a’, ‘c’, ‘b’};
Initialization of large arrays can be split into 2 rows:
double states[10] = {5.4, 3.8, 3.4, 10.6, 9.2,
1.8, 10.3, 14.0, 2.3, 1.4};
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36. Array initialization (2)
You do not have to initialize every element of an array:
/* initializes hits[0], hits[1], and hits[2] to the values indicated; all the rest are set to 0 */
int hits[6] = {133, 25, 10001};
The size of the array may be omitted if you initialized all of its values at declaration:
/* grades has three elements */
int grades[] = {79, 90, 81};
/* same as above */
int grades[3] = {79, 90, 81};
CSE1222: Lecture 13
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37. Linear Search Algorithm
Array space[] = {7, 3, 6, 25, 3, 2, 75, 3, 5, 6};
Read input key;
Find location of key in array space[];
If key is in array space[], print:
“Found {key} at location {location}.”
If key is not found, print:
“Sorry, we did not find {key}”.
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38. The Ohio State University
linearSearch.cpp
. . .
int main() {
const int SIZE(10); // array size
int key(0); // search key (search for key)
bool found(false); // flag for linear search
// search space (does not need to be in any order)
int space[SIZE] = {7, 3, 6, 25, 3, 2, 75, 3, 5, 6};
// get search key from user
cout << "Search for: ";
cin >> key;
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39. The Ohio State University
linearSearch.cpp
. . .
for (int i = 0; i < SIZE; i++) {
if (space[i] == key)
{ // found search key at location i
cout << "Found " << key
<< " at location " << i<< endl;
found = true; }
if (!found)
cout << "Sorry, we did not find " << key << endl;
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40. The Ohio State University
...
int space[SIZE] =
{7, 3, 6, 25, 3, 2, 75, 3, 5, 6};
for (int i = 0; i < SIZE; i++) {
if (space[i] == key)
{ // found search key at location i
cout << "Found " << key
<< " at location " << i<< endl;
found = true; }
> linearSearch.exe
Search for: 2
Found 2 at location 5
Search for: 8
Sorry, we did not find 8
What about 6?
What about 3?
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41. Search for Duplicates Algorithm
Read in input list;
for each element x in the list do:
for each element y following x in the list do:
If (x == y), then print:
“Duplicate entry {location of x} = Entry {location of y} = y”;
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42. The Ohio State University
duplicate.cpp
// print duplicate entries in input list
#include <iostream>
using namespace std;
int main() {
const int SIZE(10); // array size
int list[SIZE];
cout << "Enter list of " << SIZE << " integers: ";
for (int i = 0; i < SIZE; i++)
cin >> list[i]; }
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43. The Ohio State University
duplicate.cpp (cont.)
for (int i = 0; i < SIZE; i++) {
for (int j = i+1; j < SIZE; j++)
if (list[i] == list[j])
cout << "Duplicate entry " << i
<< " = Entry " << j
<< " = " << list[j] << endl; }
return 0;
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44. The Ohio State University
...
for (int i = 1; i < SIZE; i++) {
for (int j = i+1; j < SIZE; j++)
if (list[i] == list[j])
cout << "Duplicate entry " << i
<< " = Entry " << j
<< " = " << list[j] << endl; }
What does this output on input: ?
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45. Duplicates Algorithm: Version 2
Read in input list;
for each element x in the list do:
found_duplicate ← false;
for each element y following x in the list do:
If ((x = y) and (found_duplicate = false)), then
Print:
“Duplicate entry {location of x} = Entry {location of y} = y”;
found_duplicate ← true;
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46. The Ohio State University
...
for (int i = 1; i < SIZE; i++) {
found_duplicate = false;
for (int j = i+1; j < SIZE; j++)
if (list[i] == list[j] && !found_duplicate)
cout << "Duplicate entry " << i
<< " = Entry " << j
<< " = " << list[j] << endl;
found_duplicate = true; }
What does this output on input: ?
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47. Common Programming Errors
Addressing indices that are out of bounds of the array range. This will run-time crash or at the very least a logical error. Be careful especially when using expressions to compute the indices.
Remember, indexing starts with 0, not 1!!!
Forgetting to declare the array (either altogether or forgetting the [])
Forgetting to initialize an array. Some compilers set everything to zero, some do not.
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48. The Ohio State University
Binary Search
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49. Linear Search Algorithm
Array space[] = {7, 3, 6, 25, 3, 2, 75, 3, 5, 6};
Read input key;
Find the first location of key in array space[];
If key is in array space[], print:
“Found {key} at location {location}.”
If key is not found, print:
“Sorry, we did not find {key}”.
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50. The Ohio State University
Binary Seach
Array list[] = {2, 3, 5, 6, 6, 7, 10, 12, 25, 75};
Given a list in sorted order and a key:
Find a location of the key in the list.
Guess a number between 1 and 100.
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51. Binary Search Algorithm
Array list[] = (list[0], list[1], list[2], …, list[9])
Input: key
Compare key to list[5];
If (key = list[5]), then “FOUND KEY!”;
If (key < list[5]), then search (list[0], list[1], …, list[4])
If (key > list[5]), then search (list[6], list[7], …, list[9])
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52. Search (list[0], list[1], …, list[4])
(list[0], list[1], list[2], …, list[4])
Compare key to list[2];
If (key = list[2]), then “FOUND KEY!”;
If (key < list[2]), then search (list[0], list[1])
If (key > list[2]), then search (list[3], list[4])
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53. Binary Search Algorithm
(list[0], list[1], list[2], …, list[N-1])
left ← 0;
right ← N-1;
While (key is not found) do
midpoint ← (left + right)/2;
If (key = list[midpoint]), then “FOUND KEY!”;
If (key < list[midpoint]), then right ← midpoint-1;
If (key > list[midpoint]), then left ← midpoint+1;
If (right < left), then quit search; (key is not in list)
CSE1222: Lecture 13
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54. Binary Search Algorithm
(list[0], list[1], list[2], …, list[N-1])
left ← 0;
right ← N-1;
While (key is not found and left ≤ right) do
midpoint ← (left + right)/2;
If (key = list[midpoint]), then “FOUND KEY!”;
If (key < list[midpoint]), then right ← midpoint-1;
If (key > list[midpoint]), then left ← midpoint+1;
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55. The Ohio State University
binarySearch.cpp
int main() {
const int SIZE(10); // array size
const key(0); // search for key
int left(0), right(0), midpoint(0); // index array
bool found(false); // flag found key
// this is an ORDERED LIST
int list[SIZE] = {2, 3, 5, 6, 6, 7, 10, 12, 25, 75};
// get search key from user
cout << "Search for: ";
cin >> key;
...
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56. The Ohio State University
binarySearch.cpp
...
left = 0;
right = SIZE - 1;
while (left <= right && !found) {
midpoint = (left + right) / 2; // the floor (int division)
if (key == list[midpoint])
{ found = true; } // key is at midpoint
else if (key < list[midpoint])
{ right = midpoint - 1; } // consider left half of list
else
{ left = midpoint + 1; } // consider right half of list }
if (found)
{ cout << "Found " << key << " at location "
<< midpoint << endl;
{ cout << "Sorry, we did not find " << key << endl; }
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