Merging on different column names in Pandas - Time & Space Complexity

Time Complexity: Merging on different column names

O(n)

Understanding Time Complexity

We want to understand how the time needed to merge two tables changes as the tables get bigger.

Specifically, we ask: How does merging on columns with different names affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

# Create two dataframes with different column names for keys
df1 = pd.DataFrame({
    'key1': [1, 2, 3],
    'value1': ['A', 'B', 'C']
})

df2 = pd.DataFrame({
    'key2': [1, 2, 4],
    'value2': ['D', 'E', 'F']
})

# Merge on different column names using left_on and right_on
merged = pd.merge(df1, df2, left_on='key1', right_on='key2')

This code merges two tables by matching values from different column names.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing each key in the first table to keys in the second table to find matches.
• How many times: For each row in the first table, the merge process looks up matching rows in the second table.

How Execution Grows With Input

As the number of rows in both tables grows, the work to find matching keys grows too.

Input Size (n)	Approx. Operations
10	About 10 lookups
100	About 100 lookups
1000	About 1000 lookups

Pattern observation: The number of operations grows roughly in direct proportion to the size of the input tables.

Final Time Complexity

Time Complexity: O(n)

This means the time to merge grows linearly with the number of rows in the first table (assuming the second table's keys are indexed).

Common Mistake

[X] Wrong: "Merging on different column names makes the merge slower than merging on same-named columns."

[OK] Correct: The column names do not affect how many comparisons happen; the merge uses the values, so the time depends on the number of rows, not the column names.

Interview Connect

Understanding how merging scales helps you explain data joining tasks clearly and shows you know what happens behind the scenes.

Self-Check

"What if we merged two tables where one key column is not unique? How would the time complexity change?"

Practice

1.

What does the left_on and right_on parameters do in pandas.merge()?

easy

A. They specify columns with different names to join on from left and right DataFrames.

B. They rename columns in the DataFrames before merging.

C. They filter rows based on column values before merging.

D. They sort the DataFrames before merging.

Solution

1. Step 1: Understand merge parameters

   The left_on and right_on parameters specify which columns to join on when the column names differ between DataFrames.

2. Step 2: Clarify their purpose

   They do not rename or filter data but tell pandas which columns to match for merging.

3. Final Answer:

   They specify columns with different names to join on from left and right DataFrames. -> Option A

4. Quick Check:

   left_on/right_on = specify join columns [OK]

Hint: Use left_on and right_on to join different column names [OK]

Common Mistakes:

• Thinking they rename columns
• Confusing with filtering rows
• Assuming they sort data

2.

Which of the following is the correct syntax to merge df1 and df2 on columns 'id' in df1 and 'user_id' in df2?

df1 = pd.DataFrame({'id': [1, 2], 'val': ['A', 'B']})
df2 = pd.DataFrame({'user_id': [1, 3], 'score': [10, 20]})

easy

A. pd.merge(df1, df2, left_on='user_id', right_on='id')

B. pd.merge(df1, df2, on='id', right_on='user_id')

C. pd.merge(df1, df2, left_on='id', right_on='user_id')

D. pd.merge(df1, df2, on=['id', 'user_id'])

Solution

1. Step 1: Identify correct parameters

   Since columns have different names, use left_on='id' and right_on='user_id' to specify join keys.

2. Step 2: Check syntax correctness

   pd.merge(df1, df2, left_on='id', right_on='user_id') correctly uses pd.merge(df1, df2, left_on='id', right_on='user_id'). Others misuse on or swap keys.

3. Final Answer:

   pd.merge(df1, df2, left_on='id', right_on='user_id') -> Option C

4. Quick Check:

   left_on='id', right_on='user_id' = correct syntax [OK]

Hint: Use left_on for left, right_on for right column names [OK]

Common Mistakes:

• Using on with different column names
• Swapping left_on and right_on
• Passing both columns in on as a list

3.

What is the output of the following code?

import pandas as pd

df1 = pd.DataFrame({'key1': ['A', 'B', 'C'], 'val1': [1, 2, 3]})
df2 = pd.DataFrame({'key2': ['B', 'C', 'D'], 'val2': [4, 5, 6]})

result = pd.merge(df1, df2, left_on='key1', right_on='key2', how='inner')
print(result)

medium

A. key1 val1 key2 val2
0 A 1 A 4
1 B 2 B 5

B. key1 val1 key2 val2
0 A 1 B 4
1 B 2 C 5

C. Empty DataFrame
Columns: [key1, val1, key2, val2]
Index: []

D. key1 val1 key2 val2
0 B 2 B 4
1 C 3 C 5

Solution

1. Step 1: Understand merge keys and type

   We merge on key1 from df1 and key2 from df2 with how='inner', so only matching keys appear.

2. Step 2: Find matching keys

   Matching keys are 'B' and 'C'. Rows with 'A' and 'D' are excluded.

3. Final Answer:

   key1 val1 key2 val2 0 B 2 B 4 1 C 3 C 5 -> Option D

4. Quick Check:

   Inner join on matching keys = rows with B and C [OK]

Hint: Inner merge keeps only matching keys from both sides [OK]

Common Mistakes:

• Expecting all rows to appear
• Mixing up left_on and right_on
• Confusing inner with outer join

4.

What is wrong with this code snippet?

import pandas as pd

df1 = pd.DataFrame({'A': [1, 2], 'B': [3, 4]})
df2 = pd.DataFrame({'X': [1, 3], 'Y': [5, 6]})

merged = pd.merge(df1, df2, left_on='A', right_on='B')
print(merged)

medium

A. It will raise a KeyError because 'B' is not in df2.

B. It uses wrong parameter names for merge.

C. It tries to merge on columns that do not match logically.

D. It merges correctly without errors.

Solution

1. Step 1: Check columns in each DataFrame

   df1 has columns 'A' and 'B'. df2 has columns 'X' and 'Y'. The code tries to merge on left_on='A' and right_on='B'.

2. Step 2: Identify error cause

   Since df2 does not have column 'B', pandas will raise a KeyError.

3. Final Answer:

   It will raise a KeyError because 'B' is not in df2. -> Option A

4. Quick Check:

   right_on column must exist in right DataFrame [OK]

Hint: Check if merge columns exist in respective DataFrames [OK]

Common Mistakes:

• Assuming columns exist in both DataFrames
• Confusing left_on and right_on columns
• Ignoring error messages

5.

You have two DataFrames:

df_customers = pd.DataFrame({'cust_id': [101, 102, 103], 'name': ['Alice', 'Bob', 'Charlie']})
df_orders = pd.DataFrame({'customer': [102, 101, 104], 'order_id': [5001, 5002, 5003]})

You want to merge these to get customer names with their orders, including customers without orders and orders without customers. Which code correctly does this?

hard

A. pd.merge(df_customers, df_orders, left_on='cust_id', right_on='customer', how='inner')

B. pd.merge(df_customers, df_orders, left_on='cust_id', right_on='customer', how='outer')

C. pd.merge(df_customers, df_orders, left_on='name', right_on='customer', how='left')

D. pd.merge(df_customers, df_orders, on='cust_id', how='inner')

Solution

1. Step 1: Identify columns to join on

   Customer IDs are cust_id in df_customers and customer in df_orders. So use left_on='cust_id' and right_on='customer'.

2. Step 2: Choose join type for all data

   To include all customers and all orders (even unmatched), use how='outer' for full outer join.

3. Final Answer:

   pd.merge(df_customers, df_orders, left_on='cust_id', right_on='customer', how='outer') -> Option B

4. Quick Check:

   Outer join + left_on/right_on = all data combined [OK]

Hint: Use how='outer' with left_on/right_on for full merge [OK]

Common Mistakes:

• Using inner join loses unmatched rows
• Merging on wrong columns
• Using name column instead of ID