Searching algorithms (linear, binary) in Intro to Computing - Flowchart & Logic Diagram

Process Overview

Searching algorithms help us find a specific item in a list. Linear search checks each item one by one. Binary search splits the list in half repeatedly but needs the list to be sorted.

Flowchart

Set index = 0

↓

index

↓

Increment index by 1

↓

Set low = 0, high = length-1

|Yes↓

Set mid = (low + high) // 2

↓

mid

|No↓

mid

↓

Set high = mid - 1

This flowchart shows two searching methods: linear search checks each item one by one until it finds the target or ends; binary search repeatedly divides a sorted list to find the target faster.

Step-by-Step Trace - 11 Steps

Step 1: Start linear search with list [3, 7, 1, 9] and target 9

Step 2: Check if list[0] == 9

Step 3: Increment index to 1

Step 4: Check if list[1] == 9

Step 5: Increment index to 2

Step 6: Check if list[2] == 9

Step 7: Increment index to 3

Step 8: Check if list[3] == 9

Step 9: Start binary search with sorted list [1, 3, 7, 9, 11] and target 7

Step 10: Calculate mid = (0 + 4) // 2 = 2

Step 11: Check if list[2] == 7

Diagram

List: [1, 3, 7, 9, 11]
Indexes: 0  1  2  3   4

Binary Search Steps:
low=0, high=4
mid=2 -> value=7 (target found)

Linear Search Steps:
Check index 0 -> 1
Check index 1 -> 3
Check index 2 -> 7 (found)

This diagram shows how binary search picks the middle element to check first, while linear search checks each element from the start.

Flowchart Quiz - 3 Questions

Which searching method requires the list to be sorted?

A Both linear and binary search

B Linear search

C Binary search

D Neither linear nor binary search

Key Result

Binary search is faster than linear search but only works on sorted lists, while linear search works on any list by checking items one by one.

Practice

1. Which of the following is true about linear search?

easy

A. It checks each item one by one until it finds the target.

B. It requires the list to be sorted before searching.

C. It splits the list into halves to find the target quickly.

D. It only works on numbers, not text.

Solution

1. Step 1: Understand linear search method

   Linear search goes through each item in the list one by one to find the target.

2. Step 2: Compare with other search methods

   Binary search splits the list and requires sorting, but linear search does not.

3. Final Answer:

   It checks each item one by one until it finds the target. -> Option A

4. Quick Check:

   Linear search = check items one by one [OK]

Hint: Linear search checks items one by one [OK]

Common Mistakes:

• Thinking linear search needs sorted list
• Confusing linear search with binary search
• Believing linear search only works on numbers

2. Which of the following is the correct syntax for a linear search loop in Python to find target in arr?

easy

A. for i in arr:
if i == target
return True

B. for i in range(len(arr)):
if arr[i] = target:
return True

C. while i < len(arr):
if arr[i] == target
return True

D. for i in arr:
if i == target:
return True

Solution

1. Step 1: Check correct loop syntax

   for i in arr: if i == target: return True uses a for loop to iterate over each element in arr correctly.

2. Step 2: Verify condition and syntax

   for i in arr: if i == target: return True uses '==' for comparison and proper indentation, which is correct.

3. Final Answer:

   for i in arr: if i == target: return True -> Option D

4. Quick Check:

   Correct for loop and comparison syntax [OK]

Hint: Use '==' for comparison and proper indentation [OK]

Common Mistakes:

• Using single '=' instead of '==' for comparison
• Missing colon ':' after if statement
• Incorrect indentation causing syntax errors

3. What will be the output of the following Python code?

def binary_search(arr, target):
    low, high = 0, len(arr) - 1
    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    return -1

arr = [2, 4, 6, 8, 10]
print(binary_search(arr, 6))

medium

A. -1

B. 1

C. 2

D. 3

Solution

1. Step 1: Understand binary search on sorted list

   The list is sorted: [2, 4, 6, 8, 10]. Target is 6.

2. Step 2: Trace the binary search steps

   Initial low=0, high=4, mid=2. arr[2]=6 matches target, so return 2.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   Index of 6 in list = 2 [OK]

Hint: Binary search returns index of target if found [OK]

Common Mistakes:

• Not using zero-based index
• Confusing mid calculation
• Assuming binary search works on unsorted lists

4. The following code is intended to perform a binary search but has an error. What is the error?

def binary_search(arr, target):
    low, high = 0, len(arr)
    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    return -1

medium

A. The mid calculation should use float division.

B. The high index should be len(arr) - 1, not len(arr).

C. The loop condition should be low < high, not low <= high.

D. The function should return True instead of index.

Solution

1. Step 1: Check initialization of high index

   High is set to len(arr), which is out of valid index range (0 to len(arr)-1).

2. Step 2: Understand index range in Python lists

   List indices go from 0 to len(arr)-1, so high must be len(arr)-1 to avoid index error.

3. Final Answer:

   The high index should be len(arr) - 1, not len(arr). -> Option B

4. Quick Check:

   High index = len(arr) - 1 [OK]

Hint: High index must be last valid index (len-1) [OK]

Common Mistakes:

• Setting high to len(arr) causes index out of range
• Using float division for mid index
• Wrong loop condition causing infinite loop

5. You have a sorted list of 1024 numbers. You want to find if the number 500 is in the list. Which search method is faster and why?

hard

A. Binary search, because it splits the list and reduces search steps quickly.

B. Binary search, but only if the list is unsorted.

C. Linear search, because it works only on sorted lists.

D. Linear search, because it checks each item one by one.

Solution

1. Step 1: Identify list size and sorting

   The list has 1024 numbers and is sorted, which suits binary search.

2. Step 2: Compare search methods speed

   Binary search halves the search space each step, so it finds the target in about 10 steps (log2(1024) = 10), much faster than linear search.

3. Final Answer:

   Binary search, because it splits the list and reduces search steps quickly. -> Option A

4. Quick Check:

   Binary search faster on sorted large lists [OK]

Hint: Use binary search on sorted big lists for speed [OK]

Common Mistakes:

• Choosing linear search for large sorted lists
• Thinking binary search works on unsorted lists
• Ignoring the list size impact on search speed