ArrayCosmos Memory & String Algorithms
Hardware Memory & String Algorithms Visualizer

Master Array Memory & Strings.

Interactive visualizers for physical contiguous RAM pointer arithmetic, 64-byte CPU cache lines, dynamic geometric doubling, sliding window two-pointers, Dutch National Flag 3-way partitioning, Monotonic stacks, KMP LPS pattern search, Rabin-Karp rolling hashes, and Manacher's O(N) palindromes.

Explore 20 Concepts DSA Sandbox
Hardware Architecture Engine

Contiguous RAM Layout & O(1) Pointer Arithmetic

Address = Base + (i × 4 Bytes)
CPU Memory Management Unit (MMU) Calculation:Latency: 1 Clock Cycle (0.3ns)
Address(arr[2]) = 0x1000 + (2 × 4 bytes) = 0x1008

The CPU hardware executes a single LEA (Load Effective Address) opcode to compute the memory address without scanning preceding elements.

Hardware Cache Performance Engine

64-Byte CPU Cache Line & Spatial Locality

⚡ 94% L1 CACHE HIT RATIO
Active Cell: matrix[0][0] = 10Step 1 of 16
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20
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L1 Cache Hits (0.5ns latency):0
L1 Cache Misses (RAM stall):1
Memory Management Engine

Dynamic Array Capacity Doubling & Amortized O(1)

Size: 2 / Capacity: 2
Contiguous Buffer in Virtual Memory:Amortized Push: O(1)
[0]
10
[1]
20
Allocation Engine Log:

Dynamic array initialized with size: 2, capacity: 2.

Algorithmic Two-Pointer Engine

Sliding Window Subarray Stepper (Size K = 3)

Running Window Sum: 8
Contiguous Window [0 .. 2]O(1) Step Update: +5 -0
[0]
2
[1]
1
[2]
5
[3]
1
[4]
3
[5]
2
[6]
8
[7]
4
In-Place 3-Way Partitioning

Dutch National Flag Algorithm (0s, 1s, 2s Sort)

PARTITIONING IN PROGRESS
Pointers: Low=0 • Mid=0 • High=5Single-Pass O(N)
[0]
2
LOWMID
[1]
0
[2]
2
[3]
1
[4]
1
[5]
0
HIGH
Step Log:

Ready to partition array with 3 pointers: low=0, mid=0, high=5.

Monotonic Data Structure Engine

Monotonic Decreasing Stack (Next Greater Element)

Time: Strictly O(N) Linear (Each element pushed/popped at most once)
Input Temperatures:Days to Warmer Temp
[0]
73°
+0d
[1]
74°
+0d
[2]
75°
+0d
[3]
71°
+0d
[4]
69°
+0d
[5]
72°
+0d
[6]
76°
+0d
Monotonic Decreasing Stack:0 elements waiting
[ Stack Empty ]
Linear String Pattern Matching

KMP Longest Prefix Suffix (LPS) Array Builder

Search Time: O(N + M) Zero Backtracking
Pattern String: "ABABCABAB"LPS[3] = 2
LPS Analysis for index 3:

Prefix substring: "ABAB". The longest proper prefix that is also a suffix is of length 2. If mismatch occurs at index 4, KMP skips directly to index 2 without rewinding the text pointer!

Modular Hash Matching Engine

Rabin-Karp Polynomial Rolling Hash Stepper

Window Hash: 1024
Target Pattern: "AAB" (Hash: 1428)Window [0..2]: "ABC"
[0]
A
[1]
B
[2]
C
[3]
A
[4]
A
[5]
B
[6]
C
[7]
A
Optimal Palindromic Substring Engine

Manacher's Algorithm O(N) Palindrome Finder

Radius P[3] = 3 (Length: 3 chars)
Original: "babad" ➔ Delimited: "#b#a#b#a#d#"Unifies Even & Odd Palindromes
Palindrome Radius Analysis:

Centered at index 3 ('a'), the palindrome expands 3 steps in both directions. By inserting virtual # delimiters, odd palindromes (like "aba") and even palindromes (like "abba") are handled with a single unified algorithm in linear O(N) time.

Interactive Algorithm Sandbox

Array & String DSA Playground

Linear Time O(N) Engine
Algorithm Result:
[5, 17, 25, 28, 47, 54]

20 In-Depth Lessons

Kadane algorithm, Dutch National Flag, Manacher palindrome search, Aho-Corasick, and UTF-8 encoding.

CPU Cache Lab

Inspect L1/L2 cache hit vs miss latency differences between Row-Major and Column-Major loops.

Senior Flashcards

Master tough DSA & Systems interview questions on pointer math, amortized aggregate method, and KMP.