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Format: 0x00RRGGBB - Red: bits 16-23 - Green: bits 8-15 - Blue: bits 0-7 """ return (r << 16) | (g << 8) | b def pack_rgba(r: int, g: int, b: int, a: int) -> int: """Pack 8-bit RGBA values into a single 32-bit integer. Format: 0xAARRGGBB - Alpha: bits 24-31 - Red: bits 16-23 - Green: bits 8-15 - Blue: bits 0-7 """ return (a << 24) | (r << 16) | (g << 8) | b # Example 4: Align to power-of-2 boundary def align_up(value: int, alignment: int) -> int: """Round value up to the nearest multiple of alignment. Alignment must be a power of 2. Example: align_up(17, 8) = 24 """ # alignment - 1 creates a mask of the low bits # Adding this ensures we cross the boundary if not already aligned # AND with ~(alignment - 1) clears those low bits return (value + alignment - 1) & ~(alignment - 1) # Example 5: Power of 2 generation def generate_powers_of_2(n: int) -> list: """Generate first n powers of 2 using left shift.""" return [1 << i for i in range(n)] # Demonstration if __name__ == "__main__": print(f"double_value(7) = {double_value(7)}") # 14 print(f"multiply_by_8(5) = {multiply_by_8(5)}") # 40 print(f"create_bit_mask(3) = {bin(create_bit_mask(3))}") # 0b1000 print(f"pack_rgb(255, 128, 64) = {hex(pack_rgb(255, 128, 64))}") # 0xff8040 print(f"align_up(17, 8) = {align_up(17, 8)}") # 24 print(f"powers of 2: {generate_powers_of_2(8)}") # [1, 2, 4, 8, 16, 32, 64, 128]73:T702,def multiply_by_constant_using_shifts(x: int, constant: int) -> int: """ Multiply x by constant using only shifts and adds. This demonstrates the principle; real implementations would hard-code the optimal sequence for each constant. """ result = 0 shift = 0 while constant > 0: if constant & 1: # If this bit is set result += x << shift constant >>= 1 shift += 1 return result # Optimized implementations for specific constants def multiply_by_3(x: int) -> int: return (x << 1) + x def multiply_by_5(x: int) -> int: return (x << 2) + x def multiply_by_7(x: int) -> int: return (x << 3) - x def multiply_by_10(x: int) -> int: return (x << 3) + (x << 1) def multiply_by_15(x: int) -> int: return (x << 4) - x def multiply_by_100(x: int) -> int: # 100 = 64 + 32 + 4 = 2^6 + 2^5 + 2^2 return (x << 6) + (x << 5) + (x << 2) # Verification if __name__ == "__main__": test_value = 13 print(f"multiply_by_3({test_value}) = {multiply_by_3(test_value)}") # 39 print(f"multiply_by_5({test_value}) = {multiply_by_5(test_value)}") # 65 print(f"multiply_by_7({test_value}) = {multiply_by_7(test_value)}") # 91 print(f"multiply_by_10({test_value}) = {multiply_by_10(test_value)}") # 130 print(f"multiply_by_15({test_value}) = {multiply_by_15(test_value)}") # 195 print(f"multiply_by_100({test_value}) = {multiply_by_100(test_value)}") # 1300 # Verify against standard multiplication for const in [3, 5, 7, 10, 15, 100]: standard = test_value * const decomposed = multiply_by_constant_using_shifts(test_value, const) assert standard == decomposed, f"Mismatch for {const}" print("All verifications passed!")74:T415,#include #include // UNSAFE: Direct left shift of signed value int unsafe_shift(int x, int n) { return x << n; // Undefined behavior if x < 0 or overflow } // SAFE: Cast to unsigned, shift, cast back int safe_shift(int x, int n) { // Cast to unsigned to get well-defined behavior unsigned int ux = (unsigned int)x; unsigned int result = ux << n; // Cast back (implementation-defined for out-of-range values) return (int)result; } // BEST: Use unsigned types throughout uint32_t best_shift(uint32_t x, unsigned int n) { // Ensure shift amount is valid if (n >= 32) return 0; // Or handle as error return x << n; } int main(void) { int x = 64; // With 8-bit illustration (imagine int8_t) // 64 << 1 would give -128 in signed interpretation // 64 << 2 would give 0 in signed interpretation (undefined!) printf("safe_shift(%d, 1) = %d ", x, safe_shift(x, 1)); // 128 printf("best_shift(%d, 1) = %u ", x, best_shift(x, 1)); // 128 return 0; }46:["$","$L71",null,{"owner":"anonymous","state":{"mutations":[],"queries":[{"dehydratedAt":1792292112090,"state":{"data":{"json":{"archivedAt":null,"id":"seed_a45eefd7ace053183db2aca078e8dfbc","slug":"data-structures-algorithms","title":"Data Structures & Algorithms","description":"Build strong algorithmic foundations, trace algorithms visually, solve progressive DSA problems, and apply invariants in real repository and code-review exercises.","image":null,"color":"#10B981","keyTopics":["Arrays & Strings","Linked Lists","Trees & Graphs","Sorting & Searching","Dynamic Programming","Recursion & Backtracking","Bit Manipulation","Advanced Data 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Structures & Algorithms","topic":"Bit Shifting — Left & Right Shifts","title":"Bit Shifting — Left & Right Shifts","description":"Master the art of bit shifting operations—left shifts for multiplication, right shifts for division—and understand the crucial differences between logical and arithmetic shifts. Learn to leverage these powerful operations for efficient computation while avoiding common pitfalls like overflow and bit loss.","difficulty":"INTERMEDIATE","estimatedMinutes":60,"pages":[{"id":"seed_eb72d21a43a1c82c1341689b5c9fa344","title":"Left Shift — Multiply by 2","order":0,"content":[{"id":"opening-hook","title":"The Fastest Multiplication in Computing","content":[{"data":{"content":"Imagine you could perform certain multiplications in a single CPU cycle—faster than the dedicated multiplication instruction itself. This isn't a theoretical fantasy; it's the reality of bit shifting, one of the most fundamental and powerful operations in all of computing.\n\nThe **left shift operator** (`<<`) doesn't just move bits around—it performs multiplication by powers of 2 at the hardware's absolute maximum speed. Understanding this operation deeply transforms how you think about arithmetic, memory alignment, and performance optimization."},"type":"text"},{"data":{"icon":"Target","title":"What You Will Learn","content":"By the end of this page, you will understand exactly how left shifting works at the bit level, why it's mathematically equivalent to multiplication by 2, how to use it for efficient computation, and the critical edge cases where this relationship breaks down. You'll gain the intuition to recognize when left shifts can optimize your code and when they might cause subtle bugs.","variant":"info"},"type":"callout"}]},{"id":"mechanics-of-left-shift","title":"The Mechanics of Left Shift","content":[{"data":{"content":"Before we explore the mathematical properties of left shift, we must understand exactly what happens at the bit level. The left shift operation is deceptively simple in its mechanics but profound in its implications.\n\n**The operation:** When you perform `x << n`, every bit in the binary representation of `x` moves `n` positions to the left. The `n` rightmost positions are filled with zeros, and bits that overflow beyond the width of the data type are discarded.\n\nLet's trace through a concrete example with an 8-bit unsigned integer:"},"type":"text"},{"data":{"rows":[["5 << 0","00000101","00000101","5"],["5 << 1","00000101","00001010","10"],["5 << 2","00000101","00010100","20"],["5 << 3","00000101","00101000","40"],["5 << 4","00000101","01010000","80"],["5 << 5","00000101","10100000","160"],["5 << 6","00000101","01000000","64 (overflow!)"],["5 << 7","00000101","10000000","128 (overflow!)"]],"caption":"Left Shifting the Value 5 by Different Amounts","headers":["Expression","Binary Before","Binary After","Decimal Result"]},"type":"table"},{"data":{"content":"Notice what happens at shift amounts 6 and 7: the original bits start falling off the left edge. The value 5 in binary is `101`. When we shift left by 6, only the rightmost bit of the original value (`1`) remains in the 8-bit result as `01000000` (64). The other bits have been discarded.\n\nThis is the first critical insight: **left shift is not truly multiplication when overflow occurs**. The mathematical equivalence only holds when all significant bits remain within the data type's bounds."},"type":"text"},{"data":{"icon":"AlertCircle","title":"The Overflow Boundary","content":"In an n-bit unsigned integer, left shifting a value x by k positions produces the correct multiplication result (x × 2^k) only when that result fits within n bits—that is, when x × 2^k < 2^n. Beyond this boundary, high-order bits are silently lost, and the operation wraps around (in most languages) rather than signaling an error.","variant":"warning"},"type":"callout"}],"titleType":"number","titleNumber":1},{"id":"mathematical-foundation","title":"The Mathematical Foundation","content":[{"data":{"content":"Why does shifting bits left multiply by powers of 2? The answer lies in the positional nature of binary representation.\n\nRecall that any integer can be expressed as a sum of powers of 2. For a number written as a sequence of bits b₍ₙ₋₁₎b₍ₙ₋₂₎...b₁b₀:\n\n**value = bₙ₋₁ × 2^(n-1) + bₙ₋₂ × 2^(n-2) + ... + b₁ × 2¹ + b₀ × 2⁰**\n\nFor the number 5 (binary `101`), this is:\n\n**5 = 1 × 2² + 0 × 2¹ + 1 × 2⁰ = 4 + 0 + 1 = 5**\n\nWhen we left shift by 1 position, each bit moves to the next higher power:\n\n**10 = 1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰ = 8 + 0 + 2 + 0 = 10**\n\nEach term is now multiplied by 2 (from 2ⁿ to 2ⁿ⁺¹), and since we're summing these terms, the entire value is multiplied by 2. This is the fundamental algebraic identity:\n\n**x << k = x × 2^k** (when no overflow occurs)"},"type":"text"},{"data":{"items":["**Identity:** `x << 0 = x` — Shifting by zero positions leaves the value unchanged","**Associativity:** `(x << a) << b = x << (a + b)` — Multiple shifts can be combined into a single operation","**Distributivity over addition:** `(x + y) << k = (x << k) + (y << k)` — Left shift distributes over addition (within overflow bounds)","**Multiplication decomposition:** `x × 10 = x × (8 + 2) = (x << 3) + (x << 1)` — Any multiplication by a constant can be decomposed into shifts and adds","**Zero preservation:** `0 << k = 0` — Shifting zero always yields zero","**Power-of-two generation:** `1 << k = 2^k` — Left shifting 1 creates any power of 2"],"title":{"icon":"Lightbulb","text":"Key Mathematical Properties","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"The distributivity property is particularly powerful for compiler optimizations. A multiplication like `x × 6` can be computed as `(x << 2) + (x << 1)` (i.e., x × 4 + x × 2), potentially faster than a general multiplication instruction on some architectures."},"type":"text"},{"data":{"icon":"Info","title":"Why This Matters for Performance","content":"On most modern processors, bit shift operations complete in a single clock cycle and require minimal energy. The multiplication instruction, by contrast, may take 3-4 cycles even on high-performance CPUs. When you're processing billions of operations, this difference compounds significantly. Compilers often convert constant multiplications to shift-based equivalents automatically, but understanding this relationship helps you write inherently efficient algorithms.","variant":"note"},"type":"callout"}],"titleType":"number","titleNumber":2},{"id":"practical-applications","title":"Practical Applications of Left Shift","content":[{"data":{"content":"Left shifts appear throughout systems programming, embedded development, graphics processing, and algorithm implementation. Let's explore the most important use cases in depth."},"type":"text"},{"data":{"items":["**Fast multiplication by powers of 2** — When multiplying by 2, 4, 8, 16, etc., left shift is the optimal operation. Array doubling, buffer resizing, and geometric progressions all benefit.","**Creating bitmasks** — `1 << n` creates a mask with only bit n set, essential for bit manipulation idioms like setting, clearing, or testing individual bits.","**Packing multiple values** — When combining small values into a larger container (e.g., RGB colors into a 32-bit integer), left shift positions each component at the correct offset.","**Memory alignment calculations** — Aligning addresses to power-of-2 boundaries (required for SIMD, cache optimization, and many hardware interfaces) often involves shifts.","**Hash function construction** — Many hash functions use shifts to mix bits across different positions, creating avalanche effects where small input changes cascade through the output.","**Graphics and image processing** — Pixel coordinate calculations, texture addressing, and color channel manipulation all leverage shift operations extensively."],"title":{"icon":"Target","text":"Common Applications","type":"icon","color":"primary","variant":"outline-circle"},"variant":"glass"},"type":"list"},{"data":{"code":"$72","fileName":"left_shift_examples.py","languages":[{"label":"Python","value":"python"}],"showLineNumbers":true},"type":"code"},{"data":{"content":"These examples demonstrate why left shift is ubiquitous in systems code. The RGB packing example is particularly common—every pixel on your screen right now was likely constructed using shift operations. The alignment example shows how hardware requirements (cache lines, memory pages, SIMD vectors) translate directly into bit manipulation code."},"type":"text"}],"titleType":"number","titleNumber":3},{"id":"multiplication-decomposition","title":"Multiplication Decomposition Using Shifts","content":[{"data":{"content":"One of the most elegant applications of left shift is decomposing arbitrary multiplication into shift-and-add operations. Since any integer can be represented as a sum of powers of 2, any multiplication by a constant can be rewritten using only shifts and additions.\n\nThis technique was crucial in early computing when multiplication hardware was expensive or slow. Today, compilers perform this optimization automatically, but understanding it reveals the deep connection between binary representation and arithmetic."},"type":"text"},{"data":{"rows":[["x × 3","11₂","(x << 1) + x","1 shift, 1 add"],["x × 5","101₂","(x << 2) + x","1 shift, 1 add"],["x × 6","110₂","(x << 2) + (x << 1)","2 shifts, 1 add"],["x × 7","111₂","(x << 3) - x","1 shift, 1 sub"],["x × 10","1010₂","(x << 3) + (x << 1)","2 shifts, 1 add"],["x × 12","1100₂","(x << 3) + (x << 2)","2 shifts, 1 add"],["x × 15","1111₂","(x << 4) - x","1 shift, 1 sub"],["x × 17","10001₂","(x << 4) + x","1 shift, 1 add"]],"caption":"Multiplication Decomposition Examples","headers":["Multiplication","Binary of Constant","Shift-Add Form","Operations"]},"type":"table"},{"data":{"content":"Notice the clever optimization for 7 and 15: instead of adding three or four shifted values, we use the identity `2^n - 1 = 2^(n-1) + 2^(n-2) + ... + 2 + 1`. Thus, `x × 7 = x × (8 - 1) = (x << 3) - x`. This reduces operations significantly for values with many consecutive 1-bits.\n\n**The trade-off:** While shift-add multiplication uses simpler operations, it's not always faster than the hardware multiplier on modern CPUs. The break-even point depends on:\n- The number of 1-bits in the constant (more bits = more additions)\n- CPU architecture (modern multipliers are highly optimized)\n- Whether the result is needed immediately (multiplication has higher latency but may pipeline better)\n\nCompilers make these decisions based on target architecture knowledge. Your role is understanding the underlying principle."},"type":"text"},{"data":{"code":"$73","fileName":"multiplication_decomposition.py","languages":[{"label":"Python","value":"python"}],"showLineNumbers":true},"type":"code"}],"titleType":"number","titleNumber":4},{"id":"understanding-shift-amounts","title":"Understanding Shift Amounts","content":[{"data":{"content":"A subtle but critical aspect of left shift is understanding what happens when the shift amount itself is problematic. While shifting by 1, 2, or 3 is straightforward, edge cases arise with larger or invalid shift amounts."},"type":"text"},{"data":{"items":["**Shift by 0:** `x << 0 = x` — The value is unchanged. This is well-defined and occasionally useful for code uniformity.","**Shift by negative amount:** Undefined behavior in C/C++. In Java, only the low bits of the shift amount are used. In Python, raises ValueError. Never assume this works.","**Shift amount ≥ bit width:** In C/C++, this is undefined behavior. In Java and JavaScript, the shift amount is masked (e.g., `x << 33` becomes `x << 1` for 32-bit integers). Python handles arbitrary precision correctly.","**Variable shift amounts:** When the shift amount is a variable, ensure bounds checking. An attacker-controlled shift could cause undefined behavior in low-level code.","**Shift of negative value:** For signed integers, left-shifting a negative value is undefined behavior in C/C++ (pre-C++20). Always use unsigned types for bit manipulation."],"title":{"icon":"AlertCircle","text":"Shift Amount Edge Cases","type":"icon","color":"destructive","variant":"outline-circle"},"variant":"glass"},"type":"list"},{"data":{"rows":[["1 << 31","INT_MIN or UB","-2147483648","2147483648","-2147483648"],["1 << 32","UB","1 (wraps)","4294967296","1 (wraps)"],["1 << -1","UB","1 << 31","Error","0"],["(-1) << 1","UB (pre-C++20)","-2","-2","-2"]],"caption":"Shift Behavior Across Languages (for 32-bit integers)","headers":["Scenario","C/C++","Java","Python","JavaScript"]},"type":"table"},{"data":{"icon":"AlertCircle","title":"Undefined Behavior is Dangerous","content":"In C and C++, undefined behavior doesn't just give a wrong result—it permits the compiler to do anything. Optimizers may eliminate code paths, assume conditions are true when they're not, or cause crashes. If you're writing systems code, always ensure shift amounts are within [0, bit_width - 1] for the type being shifted.","variant":"error"},"type":"callout"}],"titleType":"number","titleNumber":5},{"id":"left-shift-signed-integers","title":"Left Shift and Signed Integers","content":[{"data":{"content":"The interaction between left shift and signed integers deserves special attention. While bit manipulation is most natural with unsigned types, you'll inevitably encounter signed values in real code.\n\n**The core issue:** In two's complement representation (used by virtually all modern systems), the most significant bit (MSB) indicates the sign. When left shifting, this bit can change, causing unexpected sign flips."},"type":"text"},{"data":{"rows":[["8","00001000","00010000","16","Correct"],["32","00100000","01000000","64","Correct"],["64","01000000","10000000","-128","Sign flip!"],["-1","11111111","11111110","-2","Correct"],["-64","11000000","10000000","-128","Correct"],["-65","10111111","01111110","126","Sign flip!"]],"caption":"Left Shifting Signed 8-bit Values","headers":["Decimal","Binary (8-bit)","After << 1","New Decimal","Issue?"]},"type":"table"},{"data":{"content":"These sign flips occur when significant bits shift into or out of the MSB position. For positive numbers, shifting too much makes the MSB become 1 (interpreting as negative). For negative numbers, shifting can push the original sign bit out, leaving a 0 in the MSB position (interpreting as positive).\n\n**The safe approach in C/C++:**\n1. Cast to an unsigned type before shifting\n2. Perform the shift\n3. Cast back to signed if needed (with awareness of implementation-defined behavior)\n\nOr better yet: use unsigned types for all bit manipulation and convert only at program boundaries."},"type":"text"},{"data":{"code":"$74","fileName":"safe_left_shift.c","languages":[{"label":"C","value":"c"}],"showLineNumbers":true},"type":"code"},{"data":{"icon":"Lightbulb","title":"Modern C++ Standard (C++20+)","content":"As of C++20, left shift of signed integers is well-defined even when it changes the sign bit. The result is the mathematical value taken modulo 2^n (where n is the bit width). However, for maximum portability and clarity, the unsigned-type approach remains recommended for new code.","variant":"tip"},"type":"callout"}],"titleType":"number","titleNumber":6},{"id":"performance-characteristics","title":"Performance Characteristics","content":[{"data":{"content":"Understanding the performance profile of left shift helps you make informed decisions about when to use it and when the complexity isn't worth the gain."},"type":"text"},{"data":{"items":["**Latency:** 1 CPU cycle on virtually all modern processors (x86, ARM, RISC-V). This is as fast as any operation can be.","**Throughput:** Multiple shift operations can often execute simultaneously due to superscalar execution and multiple execution units.","**No memory access:** Shifts operate entirely in registers, avoiding cache latency entirely.","**Constant shifts are free:** When the shift amount is a compile-time constant, the instruction encoding is typically smaller and may be fused with adjacent operations.","**Variable shifts:** Slightly more expensive on some older architectures but still 1 cycle on modern CPUs. The shift amount typically comes from the CL register on x86.","**Comparison with multiplication:** Modern x86 multiplication has 3-4 cycle latency but high throughput. For single operations, the difference is often unnoticeable. For tight loops, shift is measurably faster."],"title":{"icon":"Zap","text":"Performance Facts","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**When does this matter?**\n\nIn most application code, replacing `x * 2` with `x << 1` is unnecessary—the compiler does this automatically. However, understanding shift performance becomes crucial for:\n\n- **Hot loops** processing millions of elements where every nanosecond counts\n- **Embedded systems** with slower processors or without hardware multipliers\n- **Cryptographic code** where timing side-channels are a concern (shifts have constant-time behavior)\n- **SIMD programming** where shift operations apply to multiple elements simultaneously"},"type":"text"},{"data":{"icon":"Info","title":"Trust Your Compiler","content":"Modern optimizing compilers (GCC, Clang, MSVC) are excellent at converting multiplications by powers of 2 into shifts. They also perform sophisticated strength reduction for other constant multipliers. Unless you're working in a performance-critical section with verified assembly output, write clear code with * and let the compiler optimize.","variant":"note"},"type":"callout"}],"titleType":"number","titleNumber":7},{"id":"summary","title":"Summary: Mastering Left Shift","content":[{"data":{"content":"We've explored the left shift operator from first principles to advanced applications. Let's consolidate the essential knowledge:"},"type":"text"},{"data":{"type":"ordered","items":["**Left shift moves bits leftward, filling with zeros.** The operation `x << n` is equivalent to `x × 2^n` when no overflow occurs.","**The mathematical equivalence comes from positional notation.** Each bit position represents a power of 2; shifting moves each bit to the next higher power.","**Overflow silently discards high-order bits.** Always ensure results fit within your data type's range, or expect wraparound behavior.","**Applications are ubiquitous:** bitmask creation, color packing, alignment, hash functions, and fast arithmetic all leverage left shift.","**Signed integer shifts require caution.** Use unsigned types for bit manipulation to avoid undefined behavior in C/C++.","**Performance is exceptional.** Left shift completes in 1 cycle and is the fastest arithmetic operation available.","**Compilers are smart.** Write clear code; let the optimizer convert to shifts when beneficial."],"title":{"icon":"CheckCircle","text":"Key Takeaways","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**Next up:** We'll explore the complementary operation—right shift. While left shift multiplies, right shift divides. But there's a crucial distinction between logical and arithmetic shifts that affects signed values differently. Understanding both operations gives you complete mastery over bit-level arithmetic."},"type":"text"},{"data":{"icon":"CheckCircle","title":"Page Complete","content":"You now have a comprehensive understanding of the left shift operator. You can use it for fast multiplication, bitmask creation, value packing, and countless other low-level operations. Next, we'll complete the picture with right shift and the critical distinction between logical and arithmetic variants.","variant":"success"},"type":"callout"}],"titleType":"number","titleNumber":8}],"isLocked":false},{"id":"seed_aacab455ee64e5f5e3831048d20e5366","title":"Right Shift — Divide by 2","order":1,"content":null,"isLocked":true},{"id":"seed_04b5a41807a95fe37141a2290fb44959","title":"Logical vs Arithmetic Right Shift","order":2,"content":null,"isLocked":true},{"id":"seed_758697df565a250c724aff928542c2b8","title":"Shift Overflow and Loss of Bits","order":3,"content":null,"isLocked":true}]}},"dataUpdateCount":1,"dataUpdatedAt":1792292111997,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getModule"],{"input":{"slug":"bit-shifting"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getModule\"],{\"input\":{\"slug\":\"bit-shifting\"},\"type\":\"query\"}]"},{"dehydratedAt":1792292112108,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792292111998,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getProgress"],{"input":{"moduleId":"seed_f3ea30c32ff9385746452ec79dcbe45c"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getProgress\"],{\"input\":{\"moduleId\":\"seed_f3ea30c32ff9385746452ec79dcbe45c\"},\"type\":\"query\"}]"},{"dehydratedAt":1792292112108,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792292111998,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["feedback","get"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_04b5a41807a95fe37141a2290fb44959"},"type":"query"}],"queryHash":"[[\"feedback\",\"get\"],{\"input\":{\"contentId\":\"seed_04b5a41807a95fe37141a2290fb44959\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792292112108,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792292111998,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["feedback","getUserLike"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_04b5a41807a95fe37141a2290fb44959"},"type":"query"}],"queryHash":"[[\"feedback\",\"getUserLike\"],{\"input\":{\"contentId\":\"seed_04b5a41807a95fe37141a2290fb44959\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792292112108,"state":{"data":{"json":[]},"dataUpdateCount":1,"dataUpdatedAt":1792292111998,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["highlights","getHighlights"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_04b5a41807a95fe37141a2290fb44959"},"type":"query"}],"queryHash":"[[\"highlights\",\"getHighlights\"],{\"input\":{\"contentId\":\"seed_04b5a41807a95fe37141a2290fb44959\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792292112108,"state":{"data":"$undefined","dataUpdateCount":0,"dataUpdatedAt":0,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"pending","fetchStatus":"fetching"},"queryKey":[["highlights","getPopularHighlights"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_04b5a41807a95fe37141a2290fb44959","minCount":2},"type":"query"}],"queryHash":"[[\"highlights\",\"getPopularHighlights\"],{\"input\":{\"contentId\":\"seed_04b5a41807a95fe37141a2290fb44959\",\"contentType\":\"LEARNING_PAGE\",\"minCount\":2},\"type\":\"query\"}]","promise":"$@75"}]},"children":"$L76"}]