Kadane's Algorithm Maximum Subarray in DSA Python - Build from Scratch

Kadane's Algorithm Maximum Subarray

📖 Scenario: You are analyzing daily temperature changes to find the longest warm streak. The temperature changes are recorded as a list of numbers, where positive numbers mean warmer days and negative numbers mean colder days.

🎯 Goal: Build a program that uses Kadane's Algorithm to find the maximum sum of a continuous subarray in the list of temperature changes. This helps identify the longest warm streak.

📋 What You'll Learn

Create a list called temp_changes with the exact values: [2, -1, 3, -4, 5, -2, 6, -1]

Create a variable called max_sum and set it to the first element of temp_changes

Create a variable called current_sum and set it to 0

Use a for loop with variable change to iterate over temp_changes

Inside the loop, update current_sum by adding change

If current_sum is less than change, set current_sum to change

If current_sum is greater than max_sum, set max_sum to current_sum

Print the value of max_sum

💡 Why This Matters

🌍 Real World

Finding the longest warm streak or best period in temperature changes helps meteorologists and farmers plan better.

💼 Career

Kadane's Algorithm is a classic technique used in software engineering interviews and real-world problems involving maximum sums in sequences.

1

Create the list of temperature changes

Create a list called temp_changes with these exact values: [2, -1, 3, -4, 5, -2, 6, -1]

DSA Python

# Create the list temp_changes with the given values
# Your code here

Hint

Use square brackets to create a list and separate numbers with commas.

2

Set up variables for Kadane's Algorithm

Create a variable called max_sum and set it to the first element of temp_changes. Then create a variable called current_sum and set it to 0.

DSA Python

temp_changes = [2, -1, 3, -4, 5, -2, 6, -1]
# Create max_sum and current_sum variables
# Your code here

Hint

Use temp_changes[0] to get the first element of the list.

3

Implement Kadane's Algorithm loop

Use a for loop with variable change to iterate over temp_changes. Inside the loop, add change to current_sum. If current_sum is less than change, set current_sum to change. If current_sum is greater than max_sum, set max_sum to current_sum.

DSA Python

temp_changes = [2, -1, 3, -4, 5, -2, 6, -1]
max_sum = temp_changes[0]
current_sum = 0
# Write the for loop and update current_sum and max_sum
# Your code here

Hint

Remember to update current_sum first, then compare and update it if needed. Finally, update max_sum if current_sum is bigger.

4

Print the maximum subarray sum

Print the value of max_sum.

DSA Python

temp_changes = [2, -1, 3, -4, 5, -2, 6, -1]
max_sum = temp_changes[0]
current_sum = 0
for change in temp_changes:
    current_sum += change
    if current_sum  max_sum:
        max_sum = current_sum
# Print max_sum
# Your code here

Hint

Use print(max_sum) to show the result.

Practice

1. What does Kadane's Algorithm primarily help to find in an array?

easy

A. The longest increasing subsequence

B. The minimum element in the array

C. The total sum of all elements

D. The maximum sum of a contiguous subarray

Solution

1. Step 1: Understand the problem Kadane's Algorithm solves

   Kadane's Algorithm is designed to find the maximum sum of any contiguous subarray within a given array.

2. Step 2: Compare with other options

   Options B, C, and D describe different problems unrelated to Kadane's Algorithm.

3. Final Answer:

   The maximum sum of a contiguous subarray -> Option D

4. Quick Check:

   Maximum subarray sum = maximum sum of contiguous elements [OK]

Hint: Kadane finds max sum in continuous parts of array [OK]

Common Mistakes:

• Confusing maximum subarray sum with total array sum
• Thinking it finds minimum or longest subsequence
• Assuming it sorts the array

2. Which of the following is the correct initialization for Kadane's Algorithm variables in Python?

easy

A. max_so_far = 0; max_ending_here = float('inf')

B. max_so_far = 0; max_ending_here = 0

C. max_so_far = float('-inf'); max_ending_here = 0

D. max_so_far = null; max_ending_here = null

Solution

1. Step 1: Understand variable roles in Kadane's Algorithm

   max_so_far tracks the maximum sum found so far, so it should start very low (negative infinity) to handle negative numbers. max_ending_here tracks current subarray sum and starts at 0.

2. Step 2: Check each option

   max_so_far = 0; max_ending_here = 0 initializes max_so_far to 0, which fails if all numbers are negative. max_so_far = 0; max_ending_here = float('inf') wrongly sets max_ending_here to positive infinity. max_so_far = null; max_ending_here = null uses null, which causes errors in arithmetic.

3. Final Answer:

   max_so_far = float('-inf'); max_ending_here = 0 -> Option C

4. Quick Check:

   Initialize max_so_far very low, max_ending_here zero [OK]

Hint: Start max_so_far very low to handle negatives [OK]

Common Mistakes:

• Initializing max_so_far to 0 causes wrong results with negatives
• Using null causes type errors
• Setting max_ending_here to infinity breaks logic

3. What is the output of the following code?

def max_subarray_sum(arr):
    max_so_far = float('-inf')
    max_ending_here = 0
    for x in arr:
        max_ending_here += x
        if max_so_far < max_ending_here:
            max_so_far = max_ending_here
        if max_ending_here < 0:
            max_ending_here = 0
    return max_so_far

print(max_subarray_sum([-2, 3, 2, -1, 4, -5]))

medium

A. 8

B. 7

C. 6

D. 5

Solution

1. Step 1: Trace the loop and update sums

   Start max_so_far = float('-inf'), max_ending_here = 0
   Iteration 1: x=-2, max_ending_here= -2; max_so_far updated to -2; -2<0 reset to 0 (max_so_far=-2)
   Iteration 2: x=3, max_ending_here=3 > -2, max_so_far=3
   Iteration 3: x=2, max_ending_here=5 >3, max_so_far=5
   Iteration 4: x=-1, max_ending_here=4 <5 no update, 4>=0 no reset
   Iteration 5: x=4, max_ending_here=8 >5, max_so_far=8
   Iteration 6: x=-5, max_ending_here=3 <8 no update, 3>=0 no reset

2. Step 2: Final return value

   max_so_far is 8, so the function returns 8.

3. Final Answer:

   8 -> Option A

4. Quick Check:

   Max subarray sum = 8 [OK]

Hint: Add elements, reset sum if negative, track max sum [OK]

Common Mistakes:

• Not resetting max_ending_here when negative
• Updating max_so_far incorrectly
• Miscounting sums during iteration

4. Identify the bug in this Kadane's Algorithm implementation:

def max_subarray(arr):
    max_so_far = 0
    max_ending_here = 0
    for i in range(len(arr)):
        max_ending_here = max_ending_here + arr[i]
        if max_so_far < max_ending_here:
            max_so_far = max_ending_here
        elif max_ending_here < 0:
            max_ending_here = 0
    return max_so_far

print(max_subarray([-3, -2, -1]))

medium

A. max_so_far initialized to 0 causes wrong result for all negatives

B. Using elif instead of if causes skipping reset of max_ending_here

C. Loop should start from 1, not 0

D. max_ending_here should be initialized to float('-inf')

Solution

1. Step 1: Trace execution on [-3, -2, -1]

   max_so_far=0, max_ending_here=0.
   i=0, x=-3: meh=-3; 0 < -3? no; elif -3<0: yes, meh=0.
   i=1, x=-2: meh=-2; no update; reset meh=0.
   i=2, x=-1: meh=-1; no update; reset.
   Returns 0, but correct max subarray sum is -1.

2. Step 2: Why A and not others

   Init max_so_far=0 prevents update when all negative (meh never >0). B: elif ok here (if never true, always resets). C: range correct. D: meh=0 correct.

3. Final Answer:

   max_so_far initialized to 0 causes wrong result for all negatives -> Option A

4. Quick Check:

   Init max_so_far to float('-inf') for negatives [OK]

Hint: Initialize max_so_far to float('-inf') to handle all-negative arrays [OK]

Common Mistakes:

• Initializing max_so_far to 0 fails with all negatives
• Using elif causes reset to be skipped
• Wrong loop range causes index errors

5. Given an array of integers, how can Kadane's Algorithm be adapted to also return the start and end indices of the maximum sum subarray?
Choose the best approach.

hard

A. Use a nested loop to check all subarrays and record indices

B. Track current start index when resetting max_ending_here; update global start and end when max_so_far changes

C. Store all subarrays and pick the max sum after the loop ends

D. Return max_so_far only; indices cannot be found with Kadane's Algorithm

Solution

1. Step 1: Understand Kadane's Algorithm extension

   To find indices, track the start index of the current subarray when max_ending_here resets to 0. When max_so_far updates, record current start and end indices.

2. Step 2: Compare with other options

   Store all subarrays and pick the max sum after the loop ends is inefficient and not Kadane's approach. Use a nested loop to check all subarrays and record indices is brute force, not Kadane's. Return max_so_far only; indices cannot be found with Kadane's Algorithm is incorrect; indices can be found.

3. Final Answer:

   Track current start index when resetting max_ending_here; update global start and end when max_so_far changes -> Option B

4. Quick Check:

   Track start on reset, update indices on max update [OK]

Hint: Track start index on reset, update when max_so_far changes [OK]

Common Mistakes:

• Ignoring index tracking in Kadane's Algorithm
• Using brute force instead of Kadane's logic
• Assuming indices can't be found with Kadane's