np.searchsorted() for insertion points in NumPy - Step-by-Step Execution

Concept Flow - np.searchsorted() for insertion points

Start with sorted array

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Choose value to insert

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np.searchsorted() finds index

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Return insertion index

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Use index to insert value without breaking order

np.searchsorted() finds the position where a value should be inserted in a sorted array to keep it sorted.

Execution Sample

NumPy

import numpy as np
arr = np.array([10, 20, 30, 40])
idx = np.searchsorted(arr, 25)
print(idx)

Finds the index where 25 should be inserted in the sorted array [10,20,30,40].

Execution Table

Step	Array	Value to Insert	Search Direction	Index Found	Explanation
1	[10, 20, 30, 40]	25	left (default)	2	25 fits between 20 (index 1) and 30 (index 2)
2	[10, 20, 30, 40]	5	left (default)	0	5 is less than 10, insert at start
3	[10, 20, 30, 40]	40	left (default)	3	40 equals element at index 3, insert before it
4	[10, 20, 30, 40]	40	right	4	With side='right', insert after existing 40
5	[10, 20, 30, 40]	50	left (default)	4	50 is greater than all, insert at end

💡 All insert positions found to keep array sorted.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5
arr	[10, 20, 30, 40]	[10, 20, 30, 40]	[10, 20, 30, 40]	[10, 20, 30, 40]	[10, 20, 30, 40]	[10, 20, 30, 40]
value	N/A	25	5	40	40	50
side	left (default)	left	left	left	right	left
index	N/A	2	0	3	4	4

Key Moments - 3 Insights

Why does np.searchsorted return 3 for value 40 with default side='left'?

Because side='left' means insert before existing equal values. Since 40 is at index 3, insertion index is 3 (see execution_table row 3).

What changes when side='right' is used for value 40?

With side='right', insertion happens after existing equal values. So for 40, index is 4 (see execution_table row 4).

Why is the insertion index 0 for value 5?

Because 5 is smaller than all elements, it should be inserted at the start (index 0), keeping array sorted (see execution_table row 2).

Visual Quiz - 3 Questions

Look at the execution_table row 1. What index does np.searchsorted return for inserting 25?

A 1

B 2

C 3

D 0

💡 Hint

Check the 'Index Found' column in row 1 of execution_table.

At which step does np.searchsorted return the insertion index at the end of the array?

A Step 5

B Step 3

C Step 2

D Step 4

💡 Hint

Look for the largest index equal to array length in 'Index Found' column.

If side='right' is used for value 40, what insertion index is returned?

A 3

B 2

C 4

D 1

💡 Hint

Check execution_table row 4 for side='right' insertion index.

Concept Snapshot

np.searchsorted(sorted_array, value, side='left')
- Finds index to insert value in sorted_array
- side='left' inserts before equal values
- side='right' inserts after equal values
- Keeps array sorted after insertion
- Returns integer index for insertion

Full Transcript

np.searchsorted() helps find where to insert a value in a sorted array so the order stays correct. It takes a sorted array and a value to insert. By default, it finds the leftmost place to insert the value, meaning before any equal values. You can change this with the side parameter to 'right' to insert after equal values. The function returns the index where the value should go. For example, in [10, 20, 30, 40], inserting 25 returns index 2 because 25 fits between 20 and 30. Inserting 40 with side='left' returns 3, before the existing 40. With side='right', it returns 4, after the existing 40. This helps keep arrays sorted when adding new elements.