Chapter quiz · Greedy & Bit Manipulation

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8 questions on Greedy & Bit Manipulation. Pass 70% to clear the chapter.

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Greedy Algorithms & Bit Manipulation — Chapter Quiz

Eight questions on interval scheduling, Huffman coding, JS bitwise int32 coercion, bit tricks, popcount, and BigInt.

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Question 1
1
The interval scheduling maximisation problem (select the maximum number of non-overlapping intervals) is solved greedily by:
ASorting intervals by start time and always picking the one that starts earliestBSorting intervals by end time (earliest end first) and greedily selecting non-overlapping intervalsCSorting by duration (shortest first)DUsing dynamic programming on overlapping intervals
Earliest-end-time greedy leaves the most room for subsequent intervals. It is provably optimal by an exchange argument. O(n log n) to sort, then O(n) to sweep.
Question 2
2
Huffman coding produces an optimal prefix-free code by:
AAssigning fixed-length codes based on alphabetical orderBRepeatedly merging the two lowest-frequency symbols into a new node, building the code tree bottom-up with a min-heapCSorting symbols by frequency and assigning 1 bit to the most frequentDUsing a trie where depth equals the symbol frequency
Huffman greedily merges the two smallest frequency nodes. A min- heap keeps the process O(n log n). The result is a code where high-frequency symbols get shorter codes, minimising average code length.
Question 3
3
What happens when you apply a bitwise operator (e.g., |, &, ^, ~) to a JavaScript number?
AJavaScript operates on 64-bit floating-point bits directlyBThe number is first converted to a 32-bit signed integer (truncating), the operation is performed, then the result is converted back to a 64-bit floatCBitwise operators only work on integers already; no conversion happensDThe operation is performed on the mantissa bits of the IEEE 754 representation
Per the ECMAScript spec, bitwise operators use ToInt32 to convert operands to 32-bit signed integers. Numbers outside the int32 range are silently truncated. This is a common gotcha for large numbers.
Question 4
4
How do you check whether the k-th bit (0-indexed from LSB) of an integer n is set?
An % (2 ** k) === 1B(n >> k) & 1Cn & kDn ^ (1 << k)
Right-shifting n by k positions moves the k-th bit to position 0. ANDing with 1 isolates it. The result is 1 if the bit is set and 0 otherwise.
Question 5
5
The expression n & (n - 1) is useful for:
ASetting the lowest set bit of nBClearing the lowest set bit of n — used to count set bits (popcount) in a loopCChecking if n is divisible by 4DComputing n modulo a power of 2
n - 1 flips all bits below the lowest set bit and clears that bit. ANDing with n removes the lowest set bit. Repeating until n = 0 counts the number of set bits in O(popcount) iterations.
Question 6
6
JavaScript's Number type can exactly represent all integers up to 2⁵³ − 1 (Number.MAX_SAFE_INTEGER).
TTrueFFalse
IEEE 754 double-precision has a 53-bit mantissa. All integers up to 2⁵³ − 1 are representable without loss. Beyond that, not every integer has a unique representation — use BigInt for larger values.
Question 7
7
To perform safe integer arithmetic on values larger than Number.MAX_SAFE_INTEGER in JavaScript, you should use the ___ type.
BigInt (e.g., 9007199254740992n) supports arbitrary-precision integers. Note that BigInt and Number cannot be mixed in arithmetic — explicit conversion is required.
Question 8
8
Which of the following are valid bit manipulation tricks in JavaScript? (Select all that apply)
Select all that apply.
An & 1 checks if n is oddBn << 1 multiplies n by 2 (for 32-bit int range)Cn ^ n always equals 0D~n computes the bitwise NOT and equals -(n + 1) for 32-bit signed integers
All four are correct. n & 1 isolates the LSB. n << 1 is a left shift doubling the value. n ^ n cancels all bits to 0. ~n flips all 32 bits, which for signed int32 equals -(n + 1) by two's complement.