The Ohio State University Arrays CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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 The Ohio State University

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 The Ohio State University

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; CSE1222: Lecture 13 The Ohio State University

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: 1 2 3 4 5 Reverse list: 5 4 3 2 1 CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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 CSE1222: Lecture 13 The Ohio State University

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. CSE1222: Lecture 13 The Ohio State University

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] CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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 The Ohio State University

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 The Ohio State University

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 The Ohio State University

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: 10 20 30 40 50 60 Average temperature = 35 Above average temperatures: 40 50 60 CSE1222: Lecture 13 The Ohio State University

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: 20 25 30 35 40 105 Average temperature = 42.5 Above average temperatures: 105 CSE1222: Lecture 13 The Ohio State University

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: 62 65 60 54 22 58 Average temperature = 53.5 Above average temperatures: 62 65 60 54 58 CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

logTableUnsafe.cpp (Unsafe) > logTableUnsafe.exe Enter number of integers: 5 log(1) = 0 log(2) = 0.693147 log(3) = 1.09861 log(4) = 1.38629 log(5) = 1.60944 CSE1222: Lecture 13 The Ohio State University

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; CSE1222: Lecture 13 The Ohio State University

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; } CSE1222: Lecture 13 The Ohio State University

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; CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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): 1 2 3 -3 -2 -1 0 Reverse list: -1 -2 -3 3 2 1 CSE1222: Lecture 13 The Ohio State University

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): -3 -2 -1 0 1 2 3 0 Reverse list: -1 -2 -3 CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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 The Ohio State University

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 The Ohio State University

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 The Ohio State University

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): 5 6 7 0 Reverse list: 7 6 5 1 CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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): 5 6 7 0 Reverse list: 0 7 6 CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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): 5 6 7 0 Reverse list: 0 7 6 5 CSE1222: Lecture 13 The Ohio State University

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}; CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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}”. CSE1222: Lecture 13 The Ohio State University

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; CSE1222: Lecture 13 The Ohio State University

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; CSE1222: Lecture 13 The Ohio State University

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? CSE1222: Lecture 13 The Ohio State University

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”; CSE1222: Lecture 13 The Ohio State University

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]; } CSE1222: Lecture 13 The Ohio State University

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; CSE1222: Lecture 13 The Ohio State University

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: 7 5 3 8 5 6 8 1 5 2? CSE1222: Lecture 13 The Ohio State University

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; CSE1222: Lecture 13 The Ohio State University

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: 7 5 3 8 5 6 8 1 5 2? CSE1222: Lecture 13 The Ohio State University

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. CSE1222: Lecture 13 The Ohio State University

The Ohio State University Binary Search CSE1222: Lecture 13 The Ohio State University

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}”. CSE1222: Lecture 13 The Ohio State University

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. CSE1222: Lecture 13 The Ohio State University

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]) CSE1222: Lecture 13 The Ohio State University

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]) CSE1222: Lecture 13 The Ohio State University

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 The Ohio State University

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; CSE1222: Lecture 13 The Ohio State University

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; ... CSE1222: Lecture 13 The Ohio State University

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; } CSE1222: Lecture 13 The Ohio State University