Contest Python: ACSL › Unit 6 — What Does This Program Do? (Looping)
Exercises: Unit 6 — What Does This Program Do? (Looping)
Most exercises here are short-answer, just like the Junior What Does This Program Do? – Looping questions on an ACSL contest.
- Short-answer (marked short answer): a program is given, either in Python or in ACSL pseudocode.
Trace it by hand and write down exactly what it outputs.
For pseudocode, use ACSL's rules:
FORincludes its end value,WHILEtests at the top of each pass, andintrounds down, even below zero. Every program outputs exactly one line; when it outputs several values, they are separated by one space. - Predict, then verify (programming): a program is given in ACSL pseudocode.
First trace it on the sample input and write down your prediction.
Then translate it into a complete Python program that reads the input with
input(), run it on the sample, and compare. Save it as a.pyfile and run it from a terminal:python my_solution.py < assets/ex7/1.in.
Each exercise is marked with the lowest ACSL division it belongs to. This unit is the Junior Contest 2 category; Intermediate and Senior students can use it as loop-tracing drill. Exercises marked Challenge are extra practice for when you want more.
Exercise 1: Up in Threes
total = 0
FOR k = 2 TO 20 STEP 3
total = total + k
NEXT k
OUTPUT totalInput. None: the program reads no input.
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 2: Range Stops Early
total = 0
count = 0
for k in range(3, 30, 4):
if k % 3 == 0:
total = total + k
else:
count = count + 1
print(total, count)Input. None: the program reads no input.
What exactly does the program print? Work it out by hand first; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 3: Counting Down
n = 0
p = 1
FOR k = 15 TO 1 STEP -4
n = n + 1
p = p * 2 + k
NEXT k
OUTPUT n, pInput. None: the program reads no input.
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 4: Zero Passes or More?
x = 25
FOR k = 10 TO 4
x = x + k
NEXT k
y = 0
WHILE x > 20
x = x - 3
y = y + 1
END WHILE
OUTPUT x + yInput. None: the program reads no input.
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 5: Digits Backwards
n = int(input())
rev = 0
odd = 0
while n > 0:
d = n % 10
rev = rev * 10 + d
if d % 2 == 1:
odd = odd + 1
n = n // 10
print(rev, odd)Input
40721What exactly does the program print? Work it out by hand first; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 6: The Best Remainder
INPUT n
best = 0
where = 0
FOR k = 1 TO 8
v = (n * k) % 11
IF v > best THEN
best = v
where = k
END IF
NEXT k
OUTPUT best, whereInput. n = 7
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 7: Up and Down to One (predict, then verify)
This ACSL program starts from a whole number n.
While n is not 1, it halves n when n is even, and otherwise replaces n with 3 * n + 1.
It counts the steps and remembers the highest value n reaches, counting the starting value.
INPUT n
steps = 0
peak = n
WHILE n != 1
IF n % 2 == 0 THEN
n = int(n / 2)
ELSE
n = 3 * n + 1
END IF
steps = steps + 1
IF n > peak THEN
peak = n
END IF
END WHILE
OUTPUT steps, peak- Predict: trace the program by hand on the sample input and write down what it outputs, before you look at the sample output.
- Verify: translate the program into Python and run it on the sample input.
The input is one line holding the whole number n.
Print the number of steps and the peak, separated by one space.
Constraints
1 <= n <= 1000
Sample Input
6Sample Output
8 16How this is checked: Checked by running your program on 5 test inputs (1 sample, 4 hidden) and comparing its output line by line.
Exercise 8: Distance From the Line
a = 3
s = 0
FOR k = 1 TO 6
s = s + abs(a - k * 2)
a = a + 1
NEXT k
OUTPUT sInput. None: the program reads no input.
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 9: Floor Division Below Zero
x = 7
total = 0
for k in range(4):
x = x - 5
total = total + x // 2
print(x, total)Input. None: the program reads no input.
What exactly does the program print? Work it out by hand first; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 10: Halving Past Zero
Remember: ACSL's int(x) is the greatest integer less than or equal to x.
x = 45
c = 0
WHILE x > -20
x = int(x / 2) - 12
c = c + 1
END WHILE
OUTPUT x, cInput. None: the program reads no input.
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 11: Biggest Leftover (predict, then verify)
This ACSL program divides m by every whole number from n down to 1.
It finds the largest remainder, and the divisor that first gives it.
INPUT n, m
best = -1
at = 0
FOR k = n TO 1 STEP -1
r = m % k
IF r > best THEN
best = r
at = k
END IF
NEXT k
OUTPUT best, at- Predict: trace the program by hand on the sample input and write down what it outputs, before you look at the sample output.
- Verify: translate the program into Python and run it on the sample input.
The input is one line holding n and m, separated by one space.
Print the largest remainder and its divisor, separated by one space.
Constraints
1 <= n <= 1001 <= m <= 1000
Sample Input
7 20Sample Output
6 7How this is checked: Checked by running your program on 5 test inputs (1 sample, 4 hidden) and comparing its output line by line.
Exercise 12: Pairs That Add to Threes
c = 0
t = 0
FOR i = 1 TO 5
FOR j = i TO 5
c = c + 1
IF (i + j) % 3 == 0 THEN
t = t + i * j
END IF
NEXT j
NEXT i
OUTPUT c, tInput. None: the program reads no input.
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 13: Stepping Down Inside
n = int(input())
total = 0
for i in range(1, n + 1):
for j in range(i, 0, -2):
total = total + j
print(total)Input
6What exactly does the program print? Work it out by hand first; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 14: Powers of Three
INPUT n
p = 1
k = 0
s = 0
WHILE p * 3 <= n
p = p * 3
k = k + 1
s = s + n % p
END WHILE
OUTPUT k, sInput. n = 100
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 15: Biggest Jump
prev = 5
biggest = 0
where = 0
for k in range(1, 8):
cur = (prev * 7 + k) % 23
gap = abs(cur - prev)
if gap >= biggest:
biggest = gap
where = k
prev = cur
print(biggest, where)Input. None: the program reads no input.
What exactly does the program print? Work it out by hand first; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 16: Doubling and Shrinking
a = 1
b = 100
n = 0
WHILE a < b
a = a * 2
b = b - a
n = n + 1
END WHILE
OUTPUT a, b, nInput. None: the program reads no input.
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.
Exercise 17: Pairs With a Multiple (predict, then verify)
This ACSL program counts the pairs of different whole numbers i and j, with 1 <= i < j <= n, whose product i * j is a multiple of m.
INPUT n, m
count = 0
FOR i = 1 TO n - 1
FOR j = i + 1 TO n
IF (i * j) % m == 0 THEN
count = count + 1
END IF
NEXT j
NEXT i
OUTPUT count- Predict: trace the program by hand on the sample input and write down what it outputs, before you look at the sample output.
- Verify: translate the program into Python and run it on the sample input.
The input is one line holding n and m, separated by one space.
Print the count.
Constraints
2 <= n <= 2001 <= m <= 1000
Sample Input
6 4Sample Output
6How this is checked: Checked by running your program on 6 test inputs (1 sample, 5 hidden) and comparing its output line by line.
Exercise 18: Divisors Counted Down
INPUT n
total = 0
FOR i = n TO 1 STEP -2
FOR j = 1 TO int(i / 2)
IF i % j == 0 THEN
total = total + j
ELSE
total = total - 1
END IF
NEXT j
NEXT i
OUTPUT totalInput. n = 11
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: a number
Exercise 19: Odd Digit Sums
count = 0
best = 0
FOR k = 100 TO 60 STEP -7
m = k
s = 0
WHILE m > 0
s = s + m % 10
m = int(m / 10)
END WHILE
IF s % 2 == 1 THEN
count = count + 1
END IF
IF s > best THEN
best = s
END IF
NEXT k
OUTPUT count, bestInput. None: the program reads no input.
What exactly is output? Trace it by hand, using ACSL's rules; write the output exactly as it appears.
How this is checked: Checked by comparing your answer with the expected answer.
Answer format: Exactly the one line the program outputs: values separated by one space, strings without quotation marks, and letters in the case the program prints them.