DSAverse

Initializing Sorting Algorithms...

Sorting Algorithm

Binary Tree

Graph Traversal

Preparing interactive visualizations for optimal learning experience...

DSAverse

Initializing Sorting Algorithms...

Sorting Algorithm

Binary Tree

Graph Traversal

Preparing interactive visualizations for optimal learning experience...

Back to Searching

Ternary Search Visualizer

Watch how Ternary Search divides the array into three parts, eliminating 2/3 of the search space at each step.

Time: O(log₃ n)

Space: O(1)

Requirement: Sorted Array

Three-way Division

Target Value: 25

Search Range: [0, 14] | Comparisons: 0

Animation Speed: Normal

Target: 25 | Step: 1 of 0

Current Step:

Click Start to begin Ternary Search visualization

Ternary Search

Time Complexity:O(log₃ n)

Space Complexity:O(1)

Comparisons:2 per iteration

Division:Three parts

Color Legend

Mid Points (M1, M2)

Search Boundaries (L, R)

Target Found

Active Search Space

Eliminated Space

vs Binary Search

Ternary:2 comparisons/step

Binary:1 comparison/step

Elimination:2/3 vs 1/2

Despite eliminating more space, ternary search typically performs more total comparisons than binary search.

How It Works

1Divide array into three equal parts
2Check both mid points (mid1, mid2)
3Eliminate 2/3 of search space
4Repeat on remaining 1/3

Python Implementation

def ternary_search(arr, target, left=0, right=None):
    if right is None:
        right = len(arr) - 1
    
    if left > right:
        return -1
    
    # Divide array into three parts
    mid1 = left + (right - left) // 3
    mid2 = right - (right - left) // 3
    
    # Check if target is at mid1 or mid2
    if arr[mid1] == target:
        return mid1
    if arr[mid2] == target:
        return mid2
    
    # Search in appropriate third
    if target < arr[mid1]:
        return ternary_search(arr, target, left, mid1 - 1)
    elif target > arr[mid2]:
        return ternary_search(arr, target, mid2 + 1, right)
    else:
        return ternary_search(arr, target, mid1 + 1, mid2 - 1)

Real-world Applications

• Finding peaks in unimodal functions
• Optimization problems in mathematics
• Game theory and decision trees
• Scientific computing simulations
• When elimination rate matters more
• Educational purposes for algorithm analysis

DSAverse

Initializing Sorting Algorithms...

Sorting Algorithm

Binary Tree

Graph Traversal

Preparing interactive visualizations for optimal learning experience...

Back to Searching

Ternary Search Visualizer

Watch how Ternary Search divides the array into three parts, eliminating 2/3 of the search space at each step.

Time: O(log₃ n)

Space: O(1)

Requirement: Sorted Array

Three-way Division

Target Value: 25

Search Range: [0, 14] | Comparisons: 0

Animation Speed: Normal

Target: 25 | Step: 1 of 0

Current Step:

Click Start to begin Ternary Search visualization

Ternary Search

Time Complexity:O(log₃ n)

Space Complexity:O(1)

Comparisons:2 per iteration

Division:Three parts

Color Legend

Mid Points (M1, M2)

Search Boundaries (L, R)

Target Found

Active Search Space

Eliminated Space

vs Binary Search

Ternary:2 comparisons/step

Binary:1 comparison/step

Elimination:2/3 vs 1/2

Despite eliminating more space, ternary search typically performs more total comparisons than binary search.

How It Works

1Divide array into three equal parts
2Check both mid points (mid1, mid2)
3Eliminate 2/3 of search space
4Repeat on remaining 1/3

Python Implementation

def ternary_search(arr, target, left=0, right=None):
    if right is None:
        right = len(arr) - 1
    
    if left > right:
        return -1
    
    # Divide array into three parts
    mid1 = left + (right - left) // 3
    mid2 = right - (right - left) // 3
    
    # Check if target is at mid1 or mid2
    if arr[mid1] == target:
        return mid1
    if arr[mid2] == target:
        return mid2
    
    # Search in appropriate third
    if target < arr[mid1]:
        return ternary_search(arr, target, left, mid1 - 1)
    elif target > arr[mid2]:
        return ternary_search(arr, target, mid2 + 1, right)
    else:
        return ternary_search(arr, target, mid1 + 1, mid2 - 1)

Real-world Applications

• Finding peaks in unimodal functions
• Optimization problems in mathematics
• Game theory and decision trees
• Scientific computing simulations
• When elimination rate matters more
• Educational purposes for algorithm analysis