Two Sum Problem Classic Hash Solution in DSA Python - Execution Trace

Concept Flow - Two Sum Problem Classic Hash Solution

Start with empty hash map

↓

Iterate over each number in array

↓

Calculate complement = target - current number

↓

Check if complement in hash map?

Yes→Return indices

No↓

Add current number and index to hash map

↓

Repeat for next number

↓

If no pair found, return None

We scan the list once, storing numbers and their indices in a hash map. For each number, we check if the complement to reach the target exists in the map. If yes, we return the pair of indices.

Execution Sample

DSA Python

def two_sum(nums, target):
    hashmap = {}
    for i, num in enumerate(nums):
        complement = target - num
        if complement in hashmap:
            return [hashmap[complement], i]
        hashmap[num] = i
    return None

This code finds two numbers in 'nums' that add up to 'target' and returns their indices.

Execution Table

Step	Operation	Current Number (num)	Index (i)	Complement (target - num)	Hash Map State	Action	Result
1	Start iteration	-	-	-	{}	Initialize empty hash map	-
2	Check complement	2	0	7	{}	7 not in hash map	Add 2:0 to hash map
3	Add to hash map	2	0	7	{2:0}	-	-
4	Check complement	7	1	2	{2:0}	2 found in hash map	Return [0,1]
5	End	-	-	-	{2:0}	Pair found, stop	[0,1]

💡 Complement found in hash map at step 4, so indices [0,1] returned.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	Final
hashmap	{}	{}	{2:0}	{2:0}	{2:0}
i	-	0	0	1	1
num	-	2	2	7	7
complement	-	7	7	2	2

Key Moments - 3 Insights

Why do we check if the complement is in the hash map before adding the current number?

Because if we add the current number first, we might match it with itself. Checking first ensures we only find pairs with different indices, as shown in execution_table step 4 where complement 2 is found before adding 7.

What happens if no two numbers add up to the target?

The loop finishes without returning, so the function returns None (not shown in this example). The hash map ends up containing all numbers with their indices, but no complement match is found.

Why do we store the number as key and index as value in the hash map?

Because we need to quickly check if a complement number exists and retrieve its index to return the pair. The hash map allows O(1) lookup by number.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what is the value of 'complement'?

A 2

B 7

C 0

D 1

💡 Hint

Check the 'Complement (target - num)' column at step 4 in execution_table.

At which step does the hash map first contain the key 2?

A Step 2

B Step 3

C Step 1

D Step 4

💡 Hint

Look at the 'Hash Map State' column to see when {2:0} appears.

If the target was 10 instead of 9, what would happen at step 4?

A Complement 3 found in hash map

B Complement 2 found in hash map

C Complement 3 not found in hash map

D Complement 7 found in hash map

💡 Hint

Think about how complement is calculated and check hash map contents in variable_tracker.

Concept Snapshot

Two Sum Classic Hash Solution:
- Use a hash map to store numbers and their indices.
- For each number, compute complement = target - number.
- Check if complement is in hash map.
- If yes, return indices.
- Else, add current number and index to hash map.
- Runs in O(n) time with one pass.

Full Transcript

The Two Sum problem finds two numbers in a list that add up to a target. This classic hash solution uses a hash map to store numbers and their indices as we scan the list once. For each number, we calculate the complement needed to reach the target. We check if this complement is already in the hash map. If found, we return the pair of indices immediately. Otherwise, we add the current number and its index to the hash map and continue. This approach avoids nested loops and runs efficiently in linear time. The execution table shows step-by-step how the hash map changes and when the pair is found.