Math — Reasoning Check

Apply the module invariants, traces, and boundary conditions.

Get every question correct to pass this checkpoint. You can review feedback, revise your answers, and submit again.

1. How many trailing decimal zeroes does 130! contain? Enter one integer.

2. Given that 46340 squared is 2147395600, what must the integer-floor Sqrt(x) return for x=2147395599? Enter one integer.

3. A caller keeps a reference to the input slice [9,9,9] and calls the supplied PlusOne implementation. Which input and returned contents should it observe?

Select one answer.

The original slice becomes [0,0,0], and the returned larger slice is [1,0,0,0]. The original slice stays [9,9,9], and the returned slice is [1,0,0,0]. The original slice becomes [0,0,0], and the returned slice is also [0,0,0]. The original slice grows in place to length four with contents [1,0,0,0].

4. Half-reversal palindrome checking on 1234321 stops with remaining x=123 and reversed half rev=1234. Which comparison accepts this odd-length palindrome?

Select one answer.

x == rev/10 using integer division, which removes the middle digit 4. x == rev, because odd-length halves always have equal digit counts. x/10 == rev, which removes a digit from the shorter half. x == rev%10, which compares the remaining half with only its middle digit.

5. A port of fast exponentiation stores n in a signed 32-bit type. For n=-2147483648, which operation order safely creates the positive exponent magnitude?

Select one answer.

Apply a 32-bit absolute-value operation, because absolute values cannot overflow. Convert n to a wider signed type first, then negate that widened value. Leave n negative and repeatedly divide it by two while the loop requires n>0. Negate n in 32 bits first, then convert the result to a wider type.

6. For points [(1,1),(1,1),(2,3),(3,5),(0,-1),(2,2)], counting repeated coordinates as separate input points, what is the maximum number lying on one line? Enter one integer.

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