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45
| contest_id
stringlengths 10
10
| contest_date
timestamp[s]date 1011-01-01 00:00:00
2098-01-01 00:00:00
| starter_code
stringclasses 1
value | difficulty
stringclasses 3
values | public_test_cases
stringlengths 160
7.6M
| private_test_cases
stringlengths 172
35.8M
| metadata
stringlengths 86
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Good Bitstrings
|
For any two positive integers $a$ and $b$, define the function
$\texttt{gen_string}(a,b)$ by the following Python code:
def gen_string(a: int, b: int):
res = ""
ia, ib = 0, 0
while ia + ib < a + b:
if ia * b <= ib * a:
res += '0'
ia += 1
else:
res += '1'
ib += 1
return res
Equivalent C++ code:
string gen_string(int64_t a, int64_t b) {
string res;
int ia = 0, ib = 0;
while (ia + ib < a + b) {
if ((__int128)ia * b <= (__int128)ib * a) {
res += '0';
ia++;
} else {
res += '1';
ib++;
}
}
return res;
}
$ia$ will equal $a$ and $ib$ will equal $b$ when the loop terminates, so this
function returns a bitstring of length $a+b$ with exactly $a$ zeroes and $b$
ones. For example, $\texttt{gen_string}(4,10)=01110110111011$.
Call a bitstring $s$ $\textbf{good}$ if there exist positive integers $x$ and
$y$ such that $s=\texttt{gen_string}(x,y)$. Given two positive integers $A$ and
$B$ ($1\le A,B\le 10^{18}$), your job is to compute the number of good prefixes
of $\texttt{gen_string}(A,B)$. For example, there are $6$ good prefixes of
$\texttt{gen_string}(4,10)$:
x = 1 | y = 1 | gen_string(x, y) = 01
x = 1 | y = 2 | gen_string(x, y) = 011
x = 1 | y = 3 | gen_string(x, y) = 0111
x = 2 | y = 5 | gen_string(x, y) = 0111011
x = 3 | y = 7 | gen_string(x, y) = 0111011011
x = 4 | y = 10 | gen_string(x, y) = 01110110111011
INPUT FORMAT (input arrives from the terminal / stdin):
The first line contains $T$ ($1\le T\le 10$), the number of independent test
cases.
Each of the next $T$ lines contains two integers $A$ and $B$.
OUTPUT FORMAT (print output to the terminal / stdout):
The answer for each test case on a new line.
|
codeforces
|
1333_platinum_good_bitstrings
|
usaco_1333
| 1333-01-01T00:00:00 |
# Read input and solve the problem
|
hard
|
[{"input": "6\n1 1\n3 5\n4 7\n8 20\n4 10\n27 21", "output": "1\n5\n7\n10\n6\n13", "testtype": "stdin"}, {"input": "10\n85 13\n71 66\n28 66\n29 71\n96 63\n38 31\n17 68\n36 58\n36 4\n63 33", "output": "20\n32\n12\n15\n27\n16\n36\n12\n15\n17", "testtype": "stdin"}, {"input": "10\n906 527\n608 244\n263 174\n839 281\n153 492\n987 849\n701 390\n195 518\n410 59\n48 971", "output": "23\n42\n50\n80\n19\n31\n28\n32\n30\n34", "testtype": "stdin"}]
|
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
|
{"problem_level": "platinum", "contest_year": 1333, "original_problem_id": "1333_platinum_good_bitstrings"}
|
Pareidolia
| "\nPareidolia is the phenomenon where your eyes tend to see familiar patterns in\nimages where none (...TRUNCATED) |
codeforces
|
1330_gold_pareidolia
|
usaco_1330
| 1330-01-01T00:00:00 |
# Read input and solve the problem
|
hard
| "[{\"input\": \"besssie\\n1 1 5 4 6 1 1\", \"output\": \"1\\n4\", \"testtype\": \"stdin\"}, {\"input(...TRUNCATED) | "eJzsvcuO80qTteeBL6TQQ+MflM6Sb8C3YMD/hEkmqSTFY5IUJcOAr8VX6vVE1jYMAzbsidHdH6P72/t9qyQyMzJixYoDuf/X//Z(...TRUNCATED) | "{\"problem_level\": \"gold\", \"contest_year\": 1330, \"original_problem_id\": \"1330_gold_pareidol(...TRUNCATED) |
Milk Sum
| "\n**Note: The time limit for this problem is 4s, 2x the default.**\nFarmer John's $N$ cows ($1\\le (...TRUNCATED) |
codeforces
|
1326_silver_milk_sum
|
usaco_1326
| 1326-01-01T00:00:00 |
# Read input and solve the problem
|
medium
| "[{\"input\": \"5\\n1 10 4 2 6\\n3\\n2 1\\n2 8\\n4 5\", \"output\": \"55\\n81\\n98\", \"testtype\": (...TRUNCATED) | "eJxMnUmubUmTlSXEQLainQ2vC0aCRDTJRnaClPLPBkJIDIKBMSTWt8z8RCLgj/fevefs7W7FsmXV//nP//X//fP//U//7X/98S9(...TRUNCATED) | "{\"problem_level\": \"silver\", \"contest_year\": 1326, \"original_problem_id\": \"1326_silver_milk(...TRUNCATED) |
Field Day
| "\n**Note: The time limit for this problem in Python is 15s. Other languages have the default time (...TRUNCATED) |
codeforces
|
1327_silver_field_day
|
usaco_1327
| 1327-01-01T00:00:00 |
# Read input and solve the problem
|
medium
| "[{\"input\": \"5 3\\nGHGGH\\nGHHHH\\nHGHHG\", \"output\": \"5\\n3\\n5\", \"testtype\": \"stdin\"}, (...TRUNCATED) | "eJx8+UGuLcuubIlBgBqSyBZkVtUBsq6KAN0OqJJQIVVSRV1RT5XvbbdhgzHX130fH3HmjvCgk2aDDF//n//z/+3/+3/93/9P//f(...TRUNCATED) | "{\"problem_level\": \"silver\", \"contest_year\": 1327, \"original_problem_id\": \"1327_silver_fiel(...TRUNCATED) |
Pareidolia
| "\n**Note: The time limit for this problem is 4s, 2x the default.**\nPareidolia is the phenomenon wh(...TRUNCATED) |
codeforces
|
1328_silver_pareidolia
|
usaco_1328
| 1328-01-01T00:00:00 |
# Read input and solve the problem
|
medium
| "[{\"input\": \"bessiebessie\", \"output\": \"14\", \"testtype\": \"stdin\"}, {\"input\": \"abcdefgh(...TRUNCATED) | "eJyMvcmOJD20HuaFH+TirrWRrmQNTyLAK85zcB4NA350f4zMqu7/ygsDjc6qzMgI8vCcb2CQUf/P//4//8e//cv/9n/+X/9qntT(...TRUNCATED) | "{\"problem_level\": \"silver\", \"contest_year\": 1328, \"original_problem_id\": \"1328_silver_pare(...TRUNCATED) |
Rotate and Shift
| "\n**Note: The time limit for this problem is 4s, 2x the default.**\nTo celebrate the start of sprin(...TRUNCATED) |
codeforces
|
1325_bronze_rotate_and_shift
|
usaco_1325
| 1325-01-01T00:00:00 |
# Read input and solve the problem
|
easy
| "[{\"input\": \"5 3 4\\n0 2 3\", \"output\": \"1 2 3 4 0\", \"testtype\": \"stdin\"}, {\"input\": \"(...TRUNCATED) | "eJzMvc2OJbuSXqlBP0jgjmvgpPG3H6GfQED3sDXQpFRAXQ0EQYDmPelHlq1F3xE7dkZk5jn3VEGD+HInnU53J52k2WfmZv/z//i(...TRUNCATED) | "{\"problem_level\": \"bronze\", \"contest_year\": 1325, \"original_problem_id\": \"1325_bronze_rota(...TRUNCATED) |
Bakery
| "\nBessie has opened a bakery!\n\nIn her bakery, Bessie has an oven that can produce a cookie in $t_(...TRUNCATED) |
codeforces
|
1302_silver_bakery
|
usaco_1302
| 1302-01-01T00:00:00 |
# Read input and solve the problem
|
medium
| "[{\"input\": \"2\\n\\n3 7 9\\n4 3 18\\n2 4 19\\n1 1 6\\n\\n5 7 3\\n5 9 45\\n5 2 31\\n6 4 28\\n4 1 8(...TRUNCATED) | "eJxk3UvOLEuSJGYOuAQuwFHjHvjT3JwrIcAcsgc9STbQ1QOCaIAL4yq4IsonFn82AVYVsm7eEyfC3R76EBUV/b/+x//l//5//qf(...TRUNCATED) | "{\"problem_level\": \"silver\", \"contest_year\": 1302, \"original_problem_id\": \"1302_silver_bake(...TRUNCATED) |
Cow-libi
| "\n**Note: The time limit for this problem is 4s, two times the default.**\n\nSomebody has been graz(...TRUNCATED) |
codeforces
|
1303_silver_cow-libi
|
usaco_1303
| 1303-01-01T00:00:00 |
# Read input and solve the problem
|
medium
| "[{\"input\": \"2 4\\n0 0 100\\n50 0 200\\n0 50 50\\n1000 1000 0\\n50 0 200\\n10 0 170\", \"output\"(...TRUNCATED) | "eJxsfUuOdsmSlIRYSKrGpBTvBytBoof0oCeXlvr2AKGW2BQbYwW4+cM8TtUV4lL8mfl950R4+MPc3OL//Of/9n//33/8p//+v//(...TRUNCATED) | "{\"problem_level\": \"silver\", \"contest_year\": 1303, \"original_problem_id\": \"1303_silver_cow-(...TRUNCATED) |
Hungry Cow
| "\nBessie is a hungry cow. Each day, for dinner, if there is a haybale in the barn,\nshe will eat on(...TRUNCATED) |
codeforces
|
1299_bronze_hungry_cow
|
usaco_1299
| 1299-01-01T00:00:00 |
# Read input and solve the problem
|
easy
| "[{\"input\": \"1 5\\n1 2\", \"output\": \"2\", \"testtype\": \"stdin\"}, {\"input\": \"2 5\\n1 2\\n(...TRUNCATED) | "eJxMvbuxLTuznHsFGjLiWNB4A9cBusAIHgeonKBASlRoES2kQHyZibn/LeyFnqPRjcajUKjKyvrf/+m//Of/83//v//6v/7tv/3(...TRUNCATED) | "{\"problem_level\": \"bronze\", \"contest_year\": 1299, \"original_problem_id\": \"1299_bronze_hung(...TRUNCATED) |
Stamp Grid
| "\nA stamp painting is a black and white painting on an $N \\times N$ canvas,\nwhere certain cells a(...TRUNCATED) |
codeforces
|
1300_bronze_stamp_grid
|
usaco_1300
| 1300-01-01T00:00:00 |
# Read input and solve the problem
|
easy
| "[{\"input\": \"4\\n\\n2\\n**\\n*.\\n1\\n*\\n\\n3\\n.**\\n.**\\n***\\n2\\n.*\\n**\\n\\n3\\n...\\n.*.(...TRUNCATED) | "eJzsvc3OLMltLXoHF7ivIfSQEIje+pfnntoDT45xemgNNGkLUGtgGAbOkx9c7crg4lokIzLr21u2GuhSa39VTCaDwZ9FRmRW1v/(...TRUNCATED) | "{\"problem_level\": \"bronze\", \"contest_year\": 1300, \"original_problem_id\": \"1300_bronze_stam(...TRUNCATED) |
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