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Structures & Algorithms","topic":"Power of Two & Counting Bits","title":"Power of Two & Counting Bits","description":"Master the elegant bit manipulation techniques for detecting powers of two and counting set bits. Learn Brian Kernighan's algorithm, understand the mathematics behind n & (n-1), and discover how modern processors optimize bit counting operations.","difficulty":"INTERMEDIATE","estimatedMinutes":50,"pages":[{"id":"seed_5080c866ec2943802ed04ddc295b4263","title":"Check if n is a Power of Two: n & (n-1) == 0","order":0,"content":[{"id":"opening-hook","title":"The Elegance of Binary","content":[{"data":{"content":"Among the many elegant patterns in bit manipulation, few are as beautiful and frequently useful as detecting whether a number is a power of two. The expression `n & (n-1) == 0` appears deceptively simple—just five tokens—yet it encapsulates profound mathematical insight about binary representation.\n\nThis technique isn't merely academic. It appears constantly in systems programming, memory allocation, hash table sizing, graphics programming, and optimization of algorithms that benefit from power-of-two constraints. Understanding why this expression works transforms you from someone who memorizes tricks to someone who truly comprehends binary arithmetic."},"type":"text"},{"data":{"icon":"Target","title":"What You Will Master","content":"By the end of this page, you will understand exactly why `n & (n-1) == 0` works, be able to derive it from first principles, know all edge cases and variations, and recognize where this pattern applies in real-world software engineering.","variant":"info"},"type":"callout"}]},{"id":"powers-of-two-special","title":"What Makes Powers of Two Special in Binary?","content":[{"data":{"content":"Before understanding the detection technique, we must first appreciate what makes powers of two unique in binary representation.\n\n**The Fundamental Property:**\n\nEvery power of two has **exactly one bit set** in its binary representation. This is a direct consequence of how binary positional notation works:\n\n- 2⁰ = 1 → `0001`\n- 2¹ = 2 → `0010`\n- 2² = 4 → `0100`\n- 2³ = 8 → `1000`\n\nConversely, any number with exactly one bit set is, by definition, a power of two. The bit's position determines which power: bit position *k* (0-indexed from the right) represents 2ᵏ.\n\n**The Uniqueness:**\n\nNo other positive integers share this single-bit property. Any number that isn't a power of two requires multiple bits to represent:\n\n- 3 → `0011` (two bits: 2¹ + 2⁰)\n- 5 → `0101` (two bits: 2² + 2⁰)\n- 6 → `0110` (two bits: 2² + 2¹)\n- 7 → `0111` (three bits)\n- 9 → `1001` (two bits)\n\nThis property gives us our detection criterion: a number is a power of two if and only if it has exactly one set bit."},"type":"text"},{"data":{"rows":[["2⁰","1","00000001","Position 0"],["2¹","2","00000010","Position 1"],["2²","4","00000100","Position 2"],["2³","8","00001000","Position 3"],["2⁴","16","00010000","Position 4"],["2⁵","32","00100000","Position 5"],["2⁶","64","01000000","Position 6"],["2⁷","128","10000000","Position 7"]],"caption":"Powers of Two in Binary (First 16)","headers":["Power","Decimal","Binary (8-bit)","Set Bit Position"]},"type":"table"},{"data":{"icon":"Lightbulb","title":"The Binary Intuition","content":"Think of powers of two as the 'atoms' of binary representation. Every positive integer is a unique combination of these atoms (each used at most once). A power of two is, quite literally, a number composed of exactly one atom—hence exactly one bit.","variant":"tip"},"type":"callout"}],"titleType":"number","titleNumber":1},{"id":"understanding-n-minus-one","title":"Understanding n-1 in Binary: The Cascade Effect","content":[{"data":{"content":"The magic of `n & (n-1)` lies in understanding what happens when we subtract 1 from a binary number. This operation creates a **cascade effect** that propagates through the rightmost bits.\n\n**The Borrow Propagation:**\n\nWhen you subtract 1 from a number, you attempt to reduce the rightmost bit. If that bit is 1, it simply becomes 0. But if it's 0, you must borrow from the next position—which triggers a cascade:\n\n```\n n = 12: 1100\n n-1 = 11: 1011\n ^^^^--- Everything changes from the rightmost 1 onward\n```\n\n**The Critical Observation:**\n\nSubtracting 1 from any number:\n1. Finds the rightmost set bit\n2. Clears that bit (turns it to 0)\n3. Sets all bits to its right to 1\n4. Leaves all bits to its left unchanged\n\nThis is precisely what binary subtraction does—borrows propagate until they find a 1, clearing that 1 and leaving a trail of 1s in their wake."},"type":"text"},{"data":{"rows":[["8","1000","0111","Single 1 cleared, all zeros became ones"],["12","1100","1011","Rightmost 1 cleared, its right became 1"],["6","0110","0101","Rightmost 1 cleared, its right became 1"],["10","1010","1001","Rightmost 1 cleared, zero became one"],["16","10000","01111","Single 1 cleared, all zeros became ones"],["7","0111","0110","Rightmost 1 simply cleared"],["15","1111","1110","Rightmost 1 simply cleared"]],"caption":"Example: How n-1 Transforms Various Numbers","headers":["n (decimal)","n (binary)","n-1 (binary)","What Changed"]},"type":"table"},{"data":{"icon":"Info","title":"The Pattern Emerges","content":"Notice how n and n-1 always differ in at least two bit positions (except when n's rightmost bit is 1, where they differ in exactly one position). The rightmost 1 in n is always cleared in n-1, and all bits to its right flip. This relationship is the foundation of `n & (n-1)`.","variant":"note"},"type":"callout"}],"titleType":"number","titleNumber":2},{"id":"why-formula-works","title":"Why n & (n-1) == 0 Works","content":[{"data":{"content":"Now we can understand the complete formula. When we compute `n & (n-1)`, we're performing a bitwise AND between:\n- **n**: the original number\n- **n-1**: the number with its rightmost 1 cleared and all bits to its right flipped\n\n**For a power of two (single set bit):**\n\n```\nn = 8: 1000\nn-1 = 7: 0111\n ----\nn & (n-1): 0000 ✓ Result is 0!\n```\n\nBecause n has only one bit set, and n-1 has that bit cleared (with all other bits to its right set), the AND produces zero. The only 1 in n aligns with a 0 in n-1.\n\n**For a non-power of two (multiple set bits):**\n\n```\nn = 12: 1100\nn-1 = 11: 1011\n ----\nn & (n-1): 1000 ✗ Result is NOT 0!\n```\n\nBecause n has multiple 1s, clearing the rightmost one still leaves other 1s intact. The bits to the left of the rightmost 1 remain unchanged in both n and n-1, so the AND preserves them."},"type":"text"},{"data":{"left":[{"data":{"items":["**1 (2⁰)**: 0001 & 0000 = 0000 ✓","**2 (2¹)**: 0010 & 0001 = 0000 ✓","**4 (2²)**: 0100 & 0011 = 0000 ✓","**8 (2³)**: 1000 & 0111 = 0000 ✓","**16 (2⁴)**: 10000 & 01111 = 00000 ✓","**32 (2⁵)**: 100000 & 011111 = 000000 ✓"],"title":{"icon":"CheckCircle","text":"Powers of Two: n & (n-1) == 0","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"}],"right":[{"data":{"items":["**3**: 0011 & 0010 = 0010 ✗","**5**: 0101 & 0100 = 0100 ✗","**6**: 0110 & 0101 = 0100 ✗","**7**: 0111 & 0110 = 0110 ✗","**9**: 1001 & 1000 = 1000 ✗","**10**: 1010 & 1001 = 1000 ✗"],"title":{"icon":"XCircle","text":"Non-Powers: n & (n-1) != 0","type":"icon","color":"destructive","variant":"outline-circle"},"variant":"accent"},"type":"list"}]},"type":"two-column"},{"data":{"icon":"Lightbulb","title":"The Mathematical Proof","content":"Formally: If n = 2ᵏ, then n has exactly bit k set. n-1 = 2ᵏ - 1 has all bits from 0 to k-1 set (it's a sequence of k ones). Since these bit patterns have no overlapping 1s, their AND is 0. Conversely, if n has multiple set bits, the leftmost ones survive the AND since n-1 only affects bits from the rightmost 1 onward.","variant":"tip"},"type":"callout"}],"titleType":"number","titleNumber":3},{"id":"edge-case-zero","title":"The Critical Edge Case: Zero","content":[{"data":{"content":"Here's where many developers get caught: **zero is not a power of two**, but `0 & (-1) == 0` is true!\n\n```\nn = 0: 00000000\nn - 1: 11111111 (in two's complement, this wraps around to all 1s)\nn & (n-1): 00000000\n```\n\nThe AND of all zeros with anything is zero. So the expression `n & (n-1) == 0` incorrectly returns true for n = 0.\n\n**The Complete Solution:**\n\nTo correctly check for powers of two, you must also verify that n is positive:\n\n```\nn > 0 && (n & (n-1)) == 0\n```\n\nOr equivalently:\n\n```\nn != 0 && (n & (n-1)) == 0\n```\n\nThis additional check ensures we exclude zero from being classified as a power of two."},"type":"text"},{"data":{"icon":"AlertCircle","title":"Common Bug Alert","content":"Forgetting, to handle zero is one of the most common bugs when implementing power-of-two checks. In interviews and production code alike, always include the `n > 0` or `n != 0` guard. Many have failed technical interviews by presenting an incomplete solution.","variant":"warning"},"type":"callout"},{"data":{"content":"**What About Negative Numbers?**\n\nIn signed integer representations (two's complement), negative numbers have a very specific property: they always have the sign bit set (the leftmost bit). This means:\n\n- Negative powers of two like -2, -4, -8 exist mathematically but their binary representation has multiple bits set\n- For example, -8 in 8-bit two's complement is `11111000`, not a single bit\n\nSince we typically consider powers of two as positive integers (which aligns with most use cases like array sizing, memory allocation), the `n > 0` check correctly excludes negative numbers.\n\nIf your domain specifically requires checking if |n| is a power of two, you'd need:\n\n```\nMath.abs(n) > 0 && (Math.abs(n) & (Math.abs(n) - 1)) == 0\n```"},"type":"text"}],"titleType":"number","titleNumber":4},{"id":"implementation","title":"Implementation in Multiple Languages","content":[{"data":{"content":"Let's see how this translates into clean, production-ready code across different programming languages. Note the consistency of the core logic while accommodating language-specific considerations."},"type":"text"},{"data":{"fileName":"power_of_two.py","languages":[{"code":"$72","label":"Python","value":"python"},{"code":"/**\n * Check if n is a power of two using bit manipulation.\n * \n * @param n - The number to check\n * @returns true if n is a positive power of two\n * \n * Time Complexity: O(1)\n * Space Complexity: O(1)\n */\nfunction isPowerOfTwo(n: number): boolean {\n // JavaScript bitwise operations convert to 32-bit integers\n // This naturally handles floating point by truncating\n return n > 0 && (n & (n - 1)) === 0;\n}\n\n// For handling larger numbers (beyond 32-bit safe bitwise)\nfunction isPowerOfTwoBigInt(n: bigint): boolean {\n return n > 0n && (n & (n - 1n)) === 0n;\n}\n\n// Test cases\nconsole.log(isPowerOfTwo(1)); // true (2^0)\nconsole.log(isPowerOfTwo(2)); // true (2^1)\nconsole.log(isPowerOfTwo(256)); // true (2^8)\nconsole.log(isPowerOfTwo(0)); // false\nconsole.log(isPowerOfTwo(6)); // false\nconsole.log(isPowerOfTwo(-4)); // false","label":"TypeScript","value":"typescript"},{"code":"public class PowerOfTwo {\n \n /**\n * Check if n is a power of two using bit manipulation.\n * \n * @param n the number to check\n * @return true if n is a positive power of two\n * \n * Time Complexity: O(1)\n * Space Complexity: O(1)\n */\n public static boolean isPowerOfTwo(int n) {\n return n > 0 && (n & (n - 1)) == 0;\n }\n \n /**\n * For long integers (handles larger range).\n */\n public static boolean isPowerOfTwo(long n) {\n return n > 0 && (n & (n - 1)) == 0;\n }\n \n /**\n * Alternative using Integer utility (Java 8+).\n * Uses population count - powers of two have exactly one bit set.\n */\n public static boolean isPowerOfTwoAlt(int n) {\n return n > 0 && Integer.bitCount(n) == 1;\n }\n \n public static void main(String[] args) {\n // Test cases\n int[] tests = {1, 2, 4, 8, 16, 0, 3, 6, -8};\n for (int n : tests) {\n System.out.println(n + \": \" + isPowerOfTwo(n));\n }\n }\n}","label":"Java","value":"java"},{"code":"$73","label":"C++","value":"cpp"}],"showLineNumbers":true},"type":"code"},{"data":{"icon":"Info","title":"Language Considerations","content":"Note that C++20 provides std::has_single_bit() which does exactly this check. Java provides Integer.bitCount(). When these built-ins are available and readable, prefer them for maintenance—but understand the underlying bit manipulation for interviews and when built-ins aren't available.","variant":"note"},"type":"callout"}],"titleType":"number","titleNumber":5},{"id":"alternative-approaches","title":"Alternative Approaches and Their Trade-offs","content":[{"data":{"content":"While `n & (n-1) == 0` is the canonical solution, there are other valid approaches. Understanding alternatives deepens your comprehension and prepares you for variations in interviews."},"type":"text"},{"data":{"tabs":[{"id":"approach-loop","label":"Iterative Division","content":[{"data":{"content":"**Approach: Repeatedly divide by 2**\n\nKeep dividing n by 2 as long as it's even. If you end up with 1, it was a power of two.\n\n**Logic:**\n- A power of two divided by 2 repeatedly eventually becomes 1\n- A non-power of two will have an odd factor > 1 at some point"},"type":"text"},{"data":{"languages":[{"code":"def is_power_of_two_iterative(n: int) -> bool:\n \"\"\"\n O(log n) time - loops log₂(n) times.\n O(1) space.\n \"\"\"\n if n <= 0:\n return False\n \n while n % 2 == 0: # While n is even\n n //= 2\n \n return n == 1 # Should reduce to exactly 1\n\n\n# Example trace for n = 16:\n# n = 16 → 8 → 4 → 2 → 1 ✓ (power of two)\n\n# Example trace for n = 12:\n# n = 12 → 6 → 3 (odd, loop stops) ✗ (not power of two)","label":"Python","value":"python"}]},"type":"code"},{"data":{"icon":"AlertCircle","title":"Complexity Comparison","content":"This approach is O(log n) time vs O(1) for the bit manipulation method. For large numbers, this is significantly slower. However, it's useful when bit operations aren't available or for educational purposes.","variant":"warning"},"type":"callout"}],"titleIcon":"Code2"},{"id":"approach-bit-count","label":"Count Set Bits","content":[{"data":{"content":"**Approach: Count the number of 1 bits**\n\nA power of two has exactly one bit set. Count the bits and check if count equals 1."},"type":"text"},{"data":{"languages":[{"code":"def is_power_of_two_popcount(n: int) -> bool:\n \"\"\"\n Uses Python's built-in bit_count() (Python 3.10+).\n \n Time: O(1) - modern CPUs have native popcount instruction\n Space: O(1)\n \"\"\"\n return n > 0 and n.bit_count() == 1\n\n\n# For older Python or manual implementation:\ndef is_power_of_two_manual_count(n: int) -> bool:\n \"\"\"\n Manual bit counting - O(number of set bits).\n \"\"\"\n if n <= 0:\n return False\n \n count = 0\n while n:\n count += n & 1 # Add rightmost bit\n n >>= 1 # Shift right\n if count > 1: # Early termination\n return False\n \n return count == 1","label":"Python","value":"python"}]},"type":"code"},{"data":{"icon":"Lightbulb","title":"Built-in Advantage","content":"Modern languages offer built-in bit counting (Python's bit_count(), Java's Integer.bitCount(), C++20's std::popcount). These typically compile to single CPU instructions and are O(1). Using them makes code more readable while maintaining performance.","variant":"tip"},"type":"callout"}],"titleIcon":"Code2"},{"id":"approach-log","label":"Logarithm Method","content":[{"data":{"content":"**Approach: Use logarithm**\n\nIf n is a power of 2, then log₂(n) is an integer. Check if 2^(log₂(n)) equals n.\n\n**Warning: Floating-point precision issues!**"},"type":"text"},{"data":{"languages":[{"code":"import math\n\ndef is_power_of_two_log(n: int) -> bool:\n \"\"\"\n CAUTION: Floating-point precision can cause incorrect results\n for very large numbers.\n \n Not recommended for production use.\n \"\"\"\n if n <= 0:\n return False\n \n log_value = math.log2(n)\n \n # Check if log is (approximately) an integer\n return log_value == int(log_value)\n\n\n# Better version using integer logarithm (Python 3.9+):\ndef is_power_of_two_log_safe(n: int) -> bool:\n \"\"\"\n Uses integer bit_length to avoid floating-point issues.\n \n bit_length() returns position of highest bit + 1.\n For power of 2, 2^(bit_length - 1) should equal n.\n \"\"\"\n if n <= 0:\n return False\n \n # n.bit_length() gives the number of bits needed\n # For n = 8 (1000), bit_length = 4\n # 2^(4-1) = 8 = n ✓\n return 2 ** (n.bit_length() - 1) == n","label":"Python","value":"python"}]},"type":"code"},{"data":{"icon":"AlertCircle","title":"Precision Warning","content":"The logarithm method suffers from floating-point precision issues. For example, log₂(2⁵³) might not compute exactly to 53.0 due to IEEE 754 limitations. Always prefer integer-based methods (bit manipulation) for reliability.","variant":"error"},"type":"callout"}],"titleIcon":"Code2"}]},"type":"tabs"}],"titleType":"number","titleNumber":6},{"id":"real-world-applications","title":"Real-World Applications","content":[{"data":{"content":"The power-of-two check appears constantly in systems programming and algorithm design. Understanding these applications reveals why this \"simple trick\" is actually foundational knowledge."},"type":"text"},{"data":{"items":["**Hash Table Sizing** — Hash tables often use power-of-two sizes because `index = hash & (size - 1)` replaces expensive modulo with cheap AND. This only works when size is a power of two.","**Memory Allocation** — Memory allocators (malloc, jemalloc) often align allocations to power-of-two boundaries. The allocator must detect and validate these constraints.","**Graphics Programming** — Texture dimensions are commonly required to be powers of two for efficient mipmapping and GPU memory access patterns.","**FFT (Fast Fourier Transform)** — The Cooley-Tukey FFT algorithm requires input sizes to be powers of two (or related composite sizes).","**Binary Tree Properties** — A complete binary tree with n nodes has heights and level sizes that relate to powers of two. Many tree algorithms use this check.","**Ring Buffers** — Circular buffer implementations often use power-of-two sizes so wrap-around can use AND instead of modulo.","**Data Compression** — Huffman coding and other compression algorithms often work with power-of-two alphabet sizes.","**Network Protocols** — Many protocol specifications require power-of-two field sizes for efficient parsing and alignment."],"title":{"icon":"Zap","text":"Where Power-of-Two Checks Appear","type":"icon","color":"primary","variant":"outline-circle"},"variant":"glass"},"type":"list"},{"data":{"content":"**Example: Efficient Modulo in Hash Tables**\n\nWhen a hash table size is a power of two, we can replace:\n```\nindex = hash % table_size // Division is slow\n```\n\nWith:\n```\nindex = hash & (table_size - 1) // Bitwise AND is fast\n```\n\nThis works because `table_size - 1` creates a bitmask of all 1s in the lower bits. For example, if `table_size = 16 (10000)`, then `table_size - 1 = 15 (01111)`. ANDing with this mask extracts exactly the lower 4 bits, which is equivalent to mod 16."},"type":"text"},{"data":{"fileName":"hash_table_optimization.py","languages":[{"code":"$74","label":"Python","value":"python"}],"showLineNumbers":true},"type":"code"}],"titleType":"number","titleNumber":7},{"id":"related-patterns","title":"Related Bit Manipulation Patterns","content":[{"data":{"content":"The `n & (n-1)` pattern is a gateway to several related techniques. Understanding these connections builds a cohesive mental model of bit manipulation."},"type":"text"},{"data":{"rows":[["Clear rightmost set bit","n & (n-1)","Removes the lowest 1 bit","12 (1100) → 8 (1000)"],["Isolate rightmost set bit","n & (-n)","Extracts just the lowest 1 bit","12 (1100) → 4 (0100)"],["Set rightmost zero bit","n | (n+1)","Sets the lowest 0 bit to 1","12 (1100) → 13 (1101)"],["Clear rightmost consecutive 1s","n & (n+1)","Clears trailing 1s","7 (0111) → 0 (0000)"],["Count trailing zeros","log₂(n & -n)","Position of rightmost 1 bit","12 (1100) → 2"]],"caption":"Related Bit Manipulation Patterns","headers":["Pattern","Expression","What It Does","Example"]},"type":"table"},{"data":{"icon":"Lightbulb","title":"Building Block Patterns","content":"These patterns form building blocks for more complex bit manipulation algorithms. Brian Kernighan's bit counting algorithm (covered in the next page) is built directly on the `n & (n-1)` pattern. Master these fundamentals, and advanced techniques become natural extensions.","variant":"tip"},"type":"callout"}],"titleType":"number","titleNumber":8},{"id":"summary","title":"Summary and Key Takeaways","content":[{"data":{"content":"We've thoroughly explored one of the most elegant expressions in bit manipulation. Let's consolidate the key insights:"},"type":"text"},{"data":{"type":"ordered","items":["**Powers of two have exactly one bit set** — This unique property makes them detectable via bit patterns.","**n-1 transforms the rightmost 1** — Subtracting 1 clears the rightmost 1 and sets all bits to its right.","**n & (n-1) clears the rightmost 1** — For powers of two (single bit), this produces zero.","**Always handle zero explicitly** — The expression returns true for zero, which isn't a power of two.","**The complete check is: n > 0 && (n & (n-1)) == 0** — Both conditions are necessary for correctness.","**Real applications abound** — Hash tables, memory allocation, graphics, and more rely on this technique.","**This pattern extends to related operations** — Isolating bits, counting bits, and other manipulations build on the same foundations."],"title":{"icon":"CheckCircle","text":"Key Takeaways","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**What's Next:**\n\nNow that you understand the power-of-two check, we're ready to explore counting set bits (popcount). The next page covers multiple approaches to counting how many 1 bits exist in a number, culminating in Brian Kernighan's elegant algorithm—which uses exactly the `n & (n-1)` pattern we've mastered here."},"type":"text"},{"data":{"icon":"CheckCircle","title":"Page Complete","content":"You now deeply understand one of the most fundamental bit manipulation patterns. The expression `n > 0 && (n & (n-1)) == 0` will serve you in countless scenarios—from interview problems to systems programming. Next, we'll extend this foundation to count all set bits in a number.","variant":"success"},"type":"callout"}],"titleType":"number","titleNumber":9}],"isLocked":false},{"id":"seed_6f01f8b222d80e61a965825b5f5e2a2e","title":"Count Set Bits (Popcount)","order":1,"content":null,"isLocked":true},{"id":"seed_8176aa881eb36b5b44cfc59747584b22","title":"Brian Kernighan's Algorithm","order":2,"content":null,"isLocked":true},{"id":"seed_7ce0cce3eb68b3e7bdf95edc99d0f006","title":"Built-in Functions for Counting Bits","order":3,"content":null,"isLocked":true}]}},"dataUpdateCount":1,"dataUpdatedAt":1792299156881,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getModule"],{"input":{"slug":"power-of-two-and-counting-bits"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getModule\"],{\"input\":{\"slug\":\"power-of-two-and-counting-bits\"},\"type\":\"query\"}]"},{"dehydratedAt":1792299156968,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792299156881,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getProgress"],{"input":{"moduleId":"seed_4930e56c7ab26494ee2e476fb7740632"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getProgress\"],{\"input\":{\"moduleId\":\"seed_4930e56c7ab26494ee2e476fb7740632\"},\"type\":\"query\"}]"},{"dehydratedAt":1792299156968,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792299156881,"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_6f01f8b222d80e61a965825b5f5e2a2e"},"type":"query"}],"queryHash":"[[\"feedback\",\"get\"],{\"input\":{\"contentId\":\"seed_6f01f8b222d80e61a965825b5f5e2a2e\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792299156968,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792299156881,"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_6f01f8b222d80e61a965825b5f5e2a2e"},"type":"query"}],"queryHash":"[[\"feedback\",\"getUserLike\"],{\"input\":{\"contentId\":\"seed_6f01f8b222d80e61a965825b5f5e2a2e\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792299156968,"state":{"data":{"json":[]},"dataUpdateCount":1,"dataUpdatedAt":1792299156881,"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_6f01f8b222d80e61a965825b5f5e2a2e"},"type":"query"}],"queryHash":"[[\"highlights\",\"getHighlights\"],{\"input\":{\"contentId\":\"seed_6f01f8b222d80e61a965825b5f5e2a2e\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792299156968,"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_6f01f8b222d80e61a965825b5f5e2a2e","minCount":2},"type":"query"}],"queryHash":"[[\"highlights\",\"getPopularHighlights\"],{\"input\":{\"contentId\":\"seed_6f01f8b222d80e61a965825b5f5e2a2e\",\"contentType\":\"LEARNING_PAGE\",\"minCount\":2},\"type\":\"query\"}]","promise":"$@75"}]},"children":"$L76"}]