message stringlengths 2 45.8k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 254 108k | cluster float64 3 3 | __index_level_0__ int64 508 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations.
Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k.
The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal.
Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days.
The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day.
Output
Print a single integer k, such that
1. the shark was in each location the same number of days,
2. the number of locations is maximum possible satisfying the first condition,
3. k is smallest possible satisfying the first and second conditions.
Examples
Input
8
1 2 7 3 4 8 5 6
Output
7
Input
6
25 1 2 3 14 36
Output
2
Note
In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total.
In the second example the shark only moves inside a location on the 2-nd day, so there is only one location. | instruction | 0 | 40,169 | 3 | 80,338 |
Tags: brute force, data structures, dsu, trees
Correct Solution:
```
BigNum = 10 ** 10
n = int(input())
aa = [BigNum] + list(map(int, input().split(' '))) + [BigNum]
appear = sorted([(v, i) for i, v in enumerate(aa)])
ans = -1
maxLocations = 0
intervals = [(i, i) for i in range(len(aa))]
lengths = {}
def incCount(val):
global lengths
lengths[val] = lengths.get(val, 0) + 1
def decCount(val):
global lengths
if lengths[val] == 1:
del lengths[val]
else:
lengths[val] -= 1
def mergeIntervals(a, b):
return (min(a[0], b[0]), max(a[1], b[1]))
for v, i in appear:
if v == BigNum:
continue
inter = intervals[i]
if aa[i - 1] < aa[i]:
li = intervals[i - 1]
decCount(li[1] - li[0] + 1)
inter = mergeIntervals(li, inter)
if aa[i] > aa[i + 1]:
ri = intervals[i + 1]
decCount(ri[1] - ri[0] + 1)
inter = mergeIntervals(ri, inter)
intervals[inter[0]] = inter
intervals[inter[1]] = inter
incCount(inter[1] - inter[0] + 1)
if len(lengths) == 1:
count = list(lengths.values())[0]
if count > maxLocations:
maxLocations = count
ans = v + 1
#print(v + 1, count)
print(ans)
``` | output | 1 | 40,169 | 3 | 80,339 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations.
Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k.
The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal.
Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days.
The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day.
Output
Print a single integer k, such that
1. the shark was in each location the same number of days,
2. the number of locations is maximum possible satisfying the first condition,
3. k is smallest possible satisfying the first and second conditions.
Examples
Input
8
1 2 7 3 4 8 5 6
Output
7
Input
6
25 1 2 3 14 36
Output
2
Note
In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total.
In the second example the shark only moves inside a location on the 2-nd day, so there is only one location. | instruction | 0 | 40,170 | 3 | 80,340 |
Tags: brute force, data structures, dsu, trees
Correct Solution:
```
import bisect;
def getIntList():
return list(map(int, input().split()));
def getTransIntList(n):
first=getIntList();
m=len(first);
result=[[0]*n for _ in range(m)];
for i in range(m):
result[i][0]=first[i];
for j in range(1, n):
curr=getIntList();
for i in range(m):
result[i][j]=curr[i];
return result;
n=int(input());
a=getIntList();
anums=[(a[i], i) for i in range(n)];
anums.sort();
location=0;
length=0;
k=1;
pieces=[];
def upgrade(x):
curr=(x, x+1)
i=bisect.bisect(pieces, curr);
joinLeft=False;
joinRight=False;
if i>0 and pieces[i-1][1]==x:
joinLeft=True;
if i<len(pieces) and pieces[i][0]==x+1:
joinRight=True;
if joinLeft:
if joinRight:
pieces[i-1]=(pieces[i-1][0], pieces[i][1])
pieces.pop(i);
else:
pieces[i-1]=(pieces[i-1][0], x+1);
return pieces[i-1][1]-pieces[i-1][0];
else:
if joinRight:
pieces[i]=(x, pieces[i][1])
else:
pieces.insert(i, curr);
return pieces[i][1]-pieces[i][0];
currLength=0;
currSum=0;
for x in anums:
currSum+=1;
val, num=x;
l=upgrade(num);
#print(pieces);
currLength=max(currLength, l);
#print(currLength,"*",len(pieces),"==",currSum)
if currLength*len(pieces)==currSum:
currK=val+1;
currLocation=len(pieces);
if currLocation>location:
location=currLocation;
k=currK;
if (location+2)*currLength-1>n:
break;
print(k);
``` | output | 1 | 40,170 | 3 | 80,341 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations.
Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k.
The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal.
Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days.
The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day.
Output
Print a single integer k, such that
1. the shark was in each location the same number of days,
2. the number of locations is maximum possible satisfying the first condition,
3. k is smallest possible satisfying the first and second conditions.
Examples
Input
8
1 2 7 3 4 8 5 6
Output
7
Input
6
25 1 2 3 14 36
Output
2
Note
In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total.
In the second example the shark only moves inside a location on the 2-nd day, so there is only one location. | instruction | 0 | 40,171 | 3 | 80,342 |
Tags: brute force, data structures, dsu, trees
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
from types import GeneratorType
from collections import defaultdict
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def find(u):
if parent[u]==-1:
return -1
if parent[u] == u:
return u
parent[u] = find(parent[u])
return parent[u]
def union(a, b):
u = parent[a]
v = parent[b]
if size[u] > size[v]:
parent[v] = u
size[u] += size[v]
else:
parent[u] = v
size[v] += size[u]
n=int(input())
parent=[-1 for i in range(n+2)]
size = [1 for i in range(n + 2)]
b=list(map(int,input().split()))
c=[]
for i in range(n):
c.append([b[i],i+1])
c.sort()
ans=0
le=0
d=defaultdict(lambda:0)
cnt=0
for j in range(n):
val,ind=c[j]
lpar=find(ind-1)
rpar=find(ind+1)
parent[ind]=ind
if lpar!=-1:
sz1=size[find(lpar)]
d[sz1]+=-1
if d[sz1]==0:
cnt+=-1
union(ind-1,ind)
if rpar!=-1:
sz2=size[find(rpar)]
d[sz2]+=-1
if d[sz2]==0:
cnt+=-1
union(ind,ind+1)
sz=size[find(ind)]
d[sz]+=1
if d[sz]==1:
cnt+=1
if cnt == 1:
if d[sz] > le:
le = d[sz]
ans = val+1
print(ans)
``` | output | 1 | 40,171 | 3 | 80,343 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations.
Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k.
The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal.
Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days.
The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day.
Output
Print a single integer k, such that
1. the shark was in each location the same number of days,
2. the number of locations is maximum possible satisfying the first condition,
3. k is smallest possible satisfying the first and second conditions.
Examples
Input
8
1 2 7 3 4 8 5 6
Output
7
Input
6
25 1 2 3 14 36
Output
2
Note
In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total.
In the second example the shark only moves inside a location on the 2-nd day, so there is only one location. | instruction | 0 | 40,172 | 3 | 80,344 |
Tags: brute force, data structures, dsu, trees
Correct Solution:
```
class UnionFind():
def __init__(self, n):
self.n = n
self.parents = [-1] * (n)
def find(self, x):
if self.parents[x] < 0:
return x
else:
self.parents[x] = self.find(self.parents[x])
return self.parents[x]
def union(self, x, y):
x = self.find(x)
y = self.find(y)
if x == y:
return
if self.parents[x] > self.parents[y]:
x, y = y, x
self.parents[x] += self.parents[y]
self.parents[y] = x
def size(self, x):
return -self.parents[self.find(x)]
def same(self, x, y):
return self.find(x) == self.find(y)
n = int(input())
a = list(map(int, input().split()))
b = [(a[i], i) for i in range(n)]
b.sort(key=lambda x: x[0])
group_cnt = [0]*(n + 1)
ans = 0
uf = UnionFind(n)
segment_count = 0
for add_count,(value, index) in enumerate(b):
group_cnt[1] += 1
if index > 0:
if a[index - 1] < value:
if uf.same(index - 1, index) == False:
size_l, size_r = uf.size(index - 1), uf.size(index)
group_cnt[size_l] -= 1
group_cnt[size_r] -= 1
uf.union(index-1, index)
size_new = uf.size(index)
group_cnt[size_new] += 1
if index < n - 1:
if a[index + 1] < value:
if uf.same(index, index + 1) == False:
size_l, size_r = uf.size(index), uf.size(index + 1)
group_cnt[size_l] -= 1
group_cnt[size_r] -= 1
uf.union(index, index + 1)
size_new = uf.size(index)
group_cnt[size_new] += 1
size_new = uf.size(index)
#print(group_cnt[size_new],size_new,add_count + 1,value)
if group_cnt[size_new]*size_new == add_count + 1:
if segment_count < group_cnt[size_new]:
ans = value + 1
segment_count = group_cnt[size_new]
print(ans)
``` | output | 1 | 40,172 | 3 | 80,345 |
Provide tags and a correct Python 3 solution for this coding contest problem.
For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations.
Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k.
The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal.
Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days.
The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day.
Output
Print a single integer k, such that
1. the shark was in each location the same number of days,
2. the number of locations is maximum possible satisfying the first condition,
3. k is smallest possible satisfying the first and second conditions.
Examples
Input
8
1 2 7 3 4 8 5 6
Output
7
Input
6
25 1 2 3 14 36
Output
2
Note
In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total.
In the second example the shark only moves inside a location on the 2-nd day, so there is only one location. | instruction | 0 | 40,173 | 3 | 80,346 |
Tags: brute force, data structures, dsu, trees
Correct Solution:
```
def main():
n = int(input())
ori_a = [int(x) for x in input().split()]
pos = {ori_a[i]: i for i in range(len(ori_a))}
seg = [dict(left=None, right=None) for i in range(len(ori_a))]
a = sorted(ori_a)
seg_size = 0
seg_num = 0
fi_k = a[0]
fi_seg_num = 0
for n_items, item in enumerate(a, 1):
i = pos[item]
seg[i]["left"], seg[i]["right"] = i, i
seg_num += 1
size = seg[i]["right"] - seg[i]["left"] + 1
if size > seg_size:
seg_size = size
li = pos[item] - 1
if 0 <= li:
if seg[li]["right"] == i - 1:
seg[i]["left"] = seg[li]["left"]
seg[li]["right"] = seg[i]["left"]
seg_num -= 1
size = seg[i]["right"] - seg[i]["left"] + 1
if size > seg_size:
seg_size = size
ri = pos[item] + 1
if ri < n:
if seg[ri]["left"] == i + 1:
seg[i]["right"] = seg[ri]["right"]
seg[ri]["left"] = seg[i]["left"]
seg_num -= 1
size = seg[i]["right"] - seg[i]["left"] + 1
if size > seg_size:
seg_size = size
if seg_size * seg_num == n_items and seg_num > fi_seg_num:
fi_seg_num = seg_num
fi_k = item + 1
print(fi_k)
if __name__ == '__main__':
main()
``` | output | 1 | 40,173 | 3 | 80,347 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations.
Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k.
The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal.
Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days.
The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day.
Output
Print a single integer k, such that
1. the shark was in each location the same number of days,
2. the number of locations is maximum possible satisfying the first condition,
3. k is smallest possible satisfying the first and second conditions.
Examples
Input
8
1 2 7 3 4 8 5 6
Output
7
Input
6
25 1 2 3 14 36
Output
2
Note
In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total.
In the second example the shark only moves inside a location on the 2-nd day, so there is only one location.
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
from types import GeneratorType
from collections import defaultdict
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def find(u):
if parent[u]==-1:
return -1
if parent[u] == u:
return u
parent[u] = find(parent[u])
return parent[u]
def union(a, b):
u = parent[a]
v = parent[b]
if size[u] > size[v]:
parent[v] = u
size[u] += size[v]
else:
parent[u] = v
size[v] += size[u]
n=int(input())
parent=[-1 for i in range(n+2)]
size = [1 for i in range(n + 2)]
b=list(map(int,input().split()))
c=[]
for i in range(n):
c.append([b[i],i+1])
c.sort()
ans=0
le=0
curr=0
d=defaultdict(lambda:0)
cnt=0
for j in range(n):
val,ind=c[j]
if cnt==1:
if d[curr]>le:
le=d[curr]
ans=val
lpar=find(ind-1)
rpar=find(ind+1)
parent[ind]=ind
if lpar!=-1:
sz1=size[find(lpar)]
d[sz1]+=-1
if d[sz1]==0:
cnt+=-1
union(ind-1,ind)
if rpar!=-1:
sz2=size[find(rpar)]
d[sz2]+=-1
if d[sz2]==0:
cnt+=-1
union(ind,ind+1)
sz=size[find(ind)]
d[sz]+=1
if d[sz]==1:
cnt+=1
if cnt==1:
curr=sz
print(ans)
``` | instruction | 0 | 40,174 | 3 | 80,348 |
No | output | 1 | 40,174 | 3 | 80,349 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations.
Max is a young biologist. For n days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer k that if the shark in some day traveled the distance strictly less than k, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to k; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least k.
The shark never returned to the same location after it has moved from it. Thus, in the sequence of n days we can find consecutive nonempty segments when the shark traveled the distance less than k in each of the days: each such segment corresponds to one location. Max wants to choose such k that the lengths of all such segments are equal.
Find such integer k, that the number of locations is as large as possible. If there are several such k, print the smallest one.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of days.
The second line contains n distinct positive integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the distance traveled in each of the day.
Output
Print a single integer k, such that
1. the shark was in each location the same number of days,
2. the number of locations is maximum possible satisfying the first condition,
3. k is smallest possible satisfying the first and second conditions.
Examples
Input
8
1 2 7 3 4 8 5 6
Output
7
Input
6
25 1 2 3 14 36
Output
2
Note
In the first example the shark travels inside a location on days 1 and 2 (first location), then on 4-th and 5-th days (second location), then on 7-th and 8-th days (third location). There are three locations in total.
In the second example the shark only moves inside a location on the 2-nd day, so there is only one location.
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
from types import GeneratorType
from collections import defaultdict
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def find(u):
if parent[u] == u:
return u
parent[u] = find(parent[u])
return parent[u]
def union(a, b):
u = parent[a]
v = parent[b]
if size[u] > size[v]:
parent[v] = u
size[u] += size[v]
else:
parent[u] = v
size[v] += size[u]
n=int(input())
parent=[-1 for i in range(n+2)]
size = [1 for i in range(n + 2)]
b=list(map(int,input().split()))
c=[]
for i in range(n):
c.append([b[i],i+1])
c.sort()
ans=0
le=0
curr=0
d=defaultdict(lambda:0)
cnt=0
for j in range(n):
val,ind=c[j]
if cnt==1:
if d[curr]>le:
le=d[curr]
ans=val
lpar=find(ind-1)
rpar=find(ind+1)
parent[ind]=ind
if lpar!=-1:
sz1=size[find(lpar)]
d[sz1]+=-1
if d[sz1]==0:
cnt+=-1
union(ind-1,ind)
if rpar!=-1:
sz2=size[find(rpar)]
d[sz2]+=-1
if d[sz2]==0:
cnt+=-1
union(ind,ind+1)
sz=size[find(ind)]
d[sz]+=1
if d[sz]==1:
cnt+=1
if cnt==1:
curr=sz
print(ans)
``` | instruction | 0 | 40,175 | 3 | 80,350 |
No | output | 1 | 40,175 | 3 | 80,351 |
Provide a correct Python 3 solution for this coding contest problem.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000 | instruction | 0 | 40,310 | 3 | 80,620 |
"Correct Solution:
```
import math
x1, y1, x2, y2 = [int(i) for i in input().split()]
n = int(input())
xy = [[x1, y1, 0]]
for _ in range(n):
xy.append([int(i) for i in input().split()])
xy.append([x2, y2, 0])
def dif(x, y):
return max(0, math.sqrt((x[0] - y[0]) ** 2 + (x[1] - y[1]) ** 2) - x[2] - y[2])
q = set([i for i in range(n + 2)])
mi = [10 ** 16] * (n + 2)
mi[0] = 0
while q:
u = -1
mm = 10**16
for i in q:
if mm > mi[i]:
mm = mi[i]
u = i
q.remove(u)
for i in q:
mi[i] = min(mi[i], mi[u] + dif(xy[i], xy[u]))
print(mi[-1])
``` | output | 1 | 40,310 | 3 | 80,621 |
Provide a correct Python 3 solution for this coding contest problem.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000 | instruction | 0 | 40,311 | 3 | 80,622 |
"Correct Solution:
```
xs,ys,xt,yt = map(int,input().split())
n = int(input())
v = [(xs,ys,0),(xt,yt,0)]
for i in range(n):
x,y,r = map(int,input().split())
v.append((x,y,r))
path = [[] for i in range(n+2)]
for i in range(n+1):
for j in range(i+1,n+2):
l = max(0, ((v[i][0] - v[j][0])**2 + (v[i][1] - v[j][1])**2)**0.5 - v[i][2] - v[j][2])
path[i].append((j,l))
path[j].append((i,l))
import heapq
def Dijkstra(edge,start,v):
d = [float('inf')]*v
d[start] = 0
pq = [(0,start)]
heapq.heapify(pq)
while pq:
dist,p = heapq.heappop(pq)
if dist > d[p]:continue
for to,cost in edge[p]:
if d[to] <= dist + cost:continue
d[to] = dist + cost
heapq.heappush(pq, (d[to], to))
return d
d = Dijkstra(path, 0, n+2)
print(d[1])
``` | output | 1 | 40,311 | 3 | 80,623 |
Provide a correct Python 3 solution for this coding contest problem.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000 | instruction | 0 | 40,312 | 3 | 80,624 |
"Correct Solution:
```
from heapq import*
def Dijkstra(G: list, source=0):
INF = float("inf")
V = len(G)
D = [INF] * V
D[source] = 0
vis = [False] * V
H = [(0, source)]
while H:
dist, cur = heappop(H)
if vis[cur]:
continue
vis[cur] = True
for nxt, cost in G[cur]:
t = dist + cost
if D[nxt] > t:
D[nxt] = t
heappush(H, (t, nxt))
return D
import sys
input = sys.stdin.buffer.readline
from math import hypot
sx,sy,gx,gy=map(int,input().split())
n=int(input())
v=[(sx,sy,0),(gx,gy,0)]
for _ in range(n):
v.append(tuple(map(int,input().split())))
con=[[] for _ in range(n+2)]
for i,p1 in enumerate(v):
for j,p2 in enumerate(v[i+1:]):
t=max(0,hypot(p1[0]-p2[0],p1[1]-p2[1])-p1[2]-p2[2])
con[i].append((i+j+1,t))
con[i+j+1].append((i,t))
print(Dijkstra(con)[1])
``` | output | 1 | 40,312 | 3 | 80,625 |
Provide a correct Python 3 solution for this coding contest problem.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000 | instruction | 0 | 40,313 | 3 | 80,626 |
"Correct Solution:
```
from heapq import heappush, heappop
sx,sy,gx,gy=map(int,input().split())
n=int(input())
g = [[] for i in range(n+2)]
data=[(sx+sy*1j,0)]
for i in range(n):
a,b,c=map(int,input().split())
data.append((a+b*1j,c))
data.append((gx+gy*1j,0))
for i in range(n+2):
for j in range(i+1,n+2):
tmp=abs(data[i][0]-data[j][0])-data[i][1]-data[j][1]
g[i].append((tmp,j))
g[j].append((tmp,i))
dist=[2828427127 for i in range(n+2)]
visited=[False for i in range(n+2)]
dist[0]=0
que=[]
heappush(que,(0,0))
while que:
c,v=heappop(que)
if visited[v]:
continue
visited[v]=True
for x in g[v]:
if visited[x[1]]:
continue
tmp=x[0]+c if not x[0]<0 else c
if tmp<dist[x[1]]:
dist[x[1]]=tmp
heappush(que,(tmp,x[1]))
print(dist[n+1])
``` | output | 1 | 40,313 | 3 | 80,627 |
Provide a correct Python 3 solution for this coding contest problem.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000 | instruction | 0 | 40,314 | 3 | 80,628 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
from collections import defaultdict,deque
from itertools import combinations
from heapq import heappush, heappop
xs,ys,xt,yt = map(int,input().split())
N = int(input())
xyr = [list(map(int,input().split())) for i in range(N)]
#import random
#N = 1000
#xs,ys = (-10**9,-10**9)
#xt,yt = (10**9, 10**9)
#xyr = [[random.randint(-10**9, 10**9),random.randint(-10**9, 10**9),random.randint(1,10)] for i in range(N)]
#xyr = [[2*i,2*i,1] for i in range(N)]
xyr = [[xs,ys,0]] + xyr + [[xt,yt,0]]
cost = {}
for s in range(0,N+1):
for t in range(s+1,N+2):
x1,y1,r1 = xyr[s]
x2,y2,r2 = xyr[t]
R = pow((x2-x1)**2+(y2-y1)**2,0.5)
c = max(0, R-r1-r2)
cost[(s,t)] = c
cost[(t,s)] = c
h = [(0,0)]
dist = [10**15] * (N+2)
dist[0] = 0
while h:
d,v = heappop(h)
if dist[v] < d:
continue
for nv in range(N+2):
if v == nv:
continue
temp = d + cost[(v,nv)]
if temp < dist[nv]:
dist[nv] = temp
heappush(h, (temp,nv))
print(dist[N+1])
``` | output | 1 | 40,314 | 3 | 80,629 |
Provide a correct Python 3 solution for this coding contest problem.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000 | instruction | 0 | 40,315 | 3 | 80,630 |
"Correct Solution:
```
import sys
from collections import deque, defaultdict
import copy
import bisect
sys.setrecursionlimit(10 ** 9)
import math
import heapq
from itertools import product, permutations,combinations
import fractions
from operator import itemgetter
import sys
def input():
return sys.stdin.readline().strip()
xs, ys, xt, yt = list(map(int, input().split()))
N = int(input())
circle = [(xs, ys, 0)]
for i in range(N):
circle.append(tuple(map(int, input().split())))
circle.append((xt, yt, 0))
graph = [[0]*(N + 2) for _ in range(N + 2)]
for i in range(N + 2):
for j in range(i):
dist = ((circle[i][0] - circle[j][0])**2 + (circle[i][1] - circle[j][1])**2)**0.5 - circle[i][2] - circle[j][2]
dist = max(0, dist)
graph[i][j] = dist
graph[j][i] = dist
dist = [10**13]*(N + 2)
dist[0] = 0
node_list = []
heapq.heappush(node_list, (0, 0))
while len(node_list) > 0:
node = heapq.heappop(node_list)
if dist[node[1]] == node[0]:
for i in range(N + 2):
if i != node[1] and dist[i] > node[0] + graph[node[1]][i]:
dist[i] = node[0] + graph[node[1]][i]
heapq.heappush(node_list, (dist[i], i))
print(dist[-1])
``` | output | 1 | 40,315 | 3 | 80,631 |
Provide a correct Python 3 solution for this coding contest problem.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000 | instruction | 0 | 40,316 | 3 | 80,632 |
"Correct Solution:
```
#from collections import deque,defaultdict
printn = lambda x: print(x,end='')
inn = lambda : int(input())
inl = lambda: list(map(int, input().split()))
inm = lambda: map(int, input().split())
ins = lambda : input().strip()
DBG = True # and False
BIG = 10**18
R = 10**9 + 7
#R = 998244353
def ddprint(x):
if DBG:
print(x)
#import math,heapq
from math import sqrt
from heapq import heappush,heappop
def pdist(x1,y1,x2,y2):
return sqrt((x2-x1)**2+(y2-y1)**2)
xs,ys,xt,yt = inm()
n = inn()
cir = []
for i in range(n):
x,y,r = inm()
cir.append((x,y,r))
dst = [[0]*(n+2) for i in range(n+2)]
dst[n][n+1] = dst[n+1][n] = pdist(xs,ys,xt,yt)
for i in range(n):
x,y,r = cir[i]
dst[n][i] = dst[i][n] = max(0.0,pdist(xs,ys,x,y)-r)
dst[n+1][i] = dst[i][n+1] = max(0.0,pdist(xt,yt,x,y)-r)
for j in range(i+1,n):
xx,yy,rr = cir[j]
dst[j][i] = dst[i][j] = \
max(0.0,pdist(xx,yy,x,y)-rr-r)
if False and DBG:
for i in range(n+2):
ddprint(dst[i])
cost = [float(BIG)]*(n+2)
q = [(0.0,n)]
while len(q)>0:
d,p = heappop(q)
#ddprint(f"{d=} {p=}")
if cost[p]<=d:
continue
cost[p] = d
for v in range(n+2):
newdist = d+dst[p][v]
if v!=p and newdist<cost[v]:
heappush(q,(newdist, v))
print(cost[n+1])
``` | output | 1 | 40,316 | 3 | 80,633 |
Provide a correct Python 3 solution for this coding contest problem.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000 | instruction | 0 | 40,317 | 3 | 80,634 |
"Correct Solution:
```
import sys
import heapq as h
stdin = sys.stdin
ni = lambda: int(ns())
nl = lambda: list(map(int, stdin.readline().split()))
nm = lambda: map(int, stdin.readline().split())
ns = lambda: stdin.readline().rstrip()
def dist(p,q):
px,py,pr = p
qx,qy,qr = q
d = ((px-qx)**2 + (py-qy)**2)**.5
return max(d-(pr+qr),0)
xs,ys,xt,yt = nm()
n = ni()
pl = [(xs,ys,0)] + [tuple(nm()) for _ in range(n)] + [(xt,yt,0)]
gr = [dict() for _ in range(n+2)]
for i in range(n+1):
for j in range(i+1,n+2):
gr[i][j] = dist(pl[i],pl[j])
gr[j][i] = gr[i][j]
dis = [float("inf")]*(n+2)
q = [(0,0)]
while q:
d,v = h.heappop(q)
if dis[v] <= d:
continue
dis[v] = d
for x in gr[v]:
if dis[x] > dis[v]+gr[v][x]:
h.heappush(q,(dis[v]+gr[v][x],x))
print(dis[-1])
``` | output | 1 | 40,317 | 3 | 80,635 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000
Submitted Solution:
```
import sys
input = sys.stdin.readline
def dijkstra(edge_adj: list, node: int, start: int) -> list:
# graph[node] = [(cost, to)]
inf = 3 * 10 ** 9
dist = [inf] * node
used = [False] * node
dist[start] = 0
while True:
v = -1
for i in range(node):
if not used[i] and (v == -1 or dist[v] > dist[i]):
v = i
if v == -1:
break
used[v] = True
for i in range(node):
if dist[i] > dist[v] + edge_adj[v][i]:
dist[i] = dist[v] + edge_adj[v][i]
return dist
# dist = [costs to nodes]
xs, ys, xt, yt = map(int, input().split())
n = int(input())
circles = [(xs, ys, 0), (xt, yt, 0)]
for i in range(n):
circles.append(tuple(map(int, input().split())))
n += 2
edges = [[0] * n for i in range(n)]
for i in range(n):
for j in range(i+1, n):
dist = ((circles[i][0] - circles[j][0]) ** 2 + (circles[i][1] - circles[j][1]) ** 2) ** 0.5
cost = max(0, dist - circles[i][2] - circles[j][2])
edges[i][j] = cost
edges[j][i] = cost
dist = dijkstra(edges, n, 0)
print(dist[1])
``` | instruction | 0 | 40,318 | 3 | 80,636 |
Yes | output | 1 | 40,318 | 3 | 80,637 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000
Submitted Solution:
```
import sys
import heapq
my_input = sys.stdin.readline
def main():
xs, ys, xt, yt = map(int, my_input().split())
N = int(my_input())
C = [(xs, ys, 0), (xt, yt, 0)]
C += [tuple(map(int, my_input().split())) for i in range(N)]
G = [[] for i in range(N+2)]
for i in range(N + 2):
for j in range(i + 1, N + 2):
cost = max(0, ((C[i][0] - C[j][0]) ** 2 + (C[i][1] - C[j][1]) ** 2) ** 0.5 - (C[i][2] + C[j][2]))
G[i].append((j, cost))
G[j].append((i, cost))
def dijkstra(graph, start, inf=float('inf')):
import heapq
n = len(graph)
distances = [inf] * n
distances[start] = 0
visited = [False] * n
# 距離・頂点
hq = [(0, start)]
while hq:
dist, fr = heapq.heappop(hq)
visited[fr] = True
if distances[fr] < dist:
continue
if fr == 1:
return distances
for to, cost in graph[fr]:
new_dist = distances[fr] + cost
if (visited[to]) or (distances[to] <= new_dist):
continue
distances[to] = new_dist
heapq.heappush(hq, (new_dist, to))
return distances
dist = dijkstra(G, 0)
print(dist[1])
if __name__ == '__main__':
main()
``` | instruction | 0 | 40,319 | 3 | 80,638 |
Yes | output | 1 | 40,319 | 3 | 80,639 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000
Submitted Solution:
```
import sys
input = sys.stdin.readline
from collections import defaultdict
from heapq import heappop, heappush
class Graph(object):
def __init__(self):
self.graph = defaultdict(list)
def add_edge(self, a, b, w):
self.graph[a].append((b, w))
class Dijkstra(object):
def __init__(self, graph, s):
self.g = graph.graph
self.dist = defaultdict(lambda: float('inf'))
self.dist[s] = 0
self.Q = []
heappush(self.Q, (self.dist[s], s))
while self.Q:
dist_u, u = heappop(self.Q)
if self.dist[u] < dist_u:
continue
for v, w in self.g[u]:
alt = dist_u + w
if self.dist[v] > alt:
self.dist[v] = alt
heappush(self.Q, (alt, v))
def s_d(self, goal):
return self.dist[goal]
xs, ys, xg, yg = list(map(int, input().split()))
xyr = []
xyr.append([xs, ys, 0])
N = int(input())
for i in range(N):
xyr.append(list(map(int, input().split())))
xyr.append([xg, yg, 0])
g_a = Graph()
for i in range(N + 1):
for j in range(i + 1, N + 2):
R = ((xyr[i][0] - xyr[j][0]) * (xyr[i][0] - xyr[j][0]) + (xyr[i][1] - xyr[j][1]) * (xyr[i][1] - xyr[j][1]))
R = R ** 0.5
if R > xyr[i][2] + xyr[j][2]:
r = R - xyr[i][2] - xyr[j][2]
else:
r = 0
g_a.add_edge(i, j, r)
g_a.add_edge(j, i, r)
d_a = Dijkstra(g_a, 0)
print(d_a.s_d(N + 1))
``` | instruction | 0 | 40,320 | 3 | 80,640 |
Yes | output | 1 | 40,320 | 3 | 80,641 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000
Submitted Solution:
```
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline
xs,ys,xt,yt = map(int,readline().split())
n, = map(int,readline().split())
xyr = [tuple(map(int,readline().split())) for _ in range(n)] + [(xs,ys,0),(xt,yt,0)]
"""
d: 隣接行列に対する Dijkstra
O(N^2)
"""
def Dijkstra_matrix(d,start):
n = len(d)
#INF = 1<<61
INF = float("inf")
dist = d[start][:] #startからの最短距離
used = [0]*n # 最短距離が決まった頂点
used[start] = 1
for _ in range(n-1):
d0 = INF
idx = -1
for i in range(n):
if not used[i] and dist[i] < d0:
idx = i
d0 = dist[i]
if idx == -1:
return dist
else:
used[idx] = 1
for j in range(n):
if not used[j] and dist[j] > dist[idx]+d[idx][j]:
dist[j] = dist[idx]+d[idx][j]
return dist
from math import hypot
d = [[max(0.0,hypot((xi-xj),(yi-yj))-ri-rj) for xj,yj,rj in xyr] for xi,yi,ri in xyr]
#print(d)
dist = Dijkstra_matrix(d,n)
print(dist[-1])
#print(dist)
``` | instruction | 0 | 40,321 | 3 | 80,642 |
Yes | output | 1 | 40,321 | 3 | 80,643 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000
Submitted Solution:
```
from math import hypot
def dijkstra(matrix):
from heapq import heappush, heappop
n = len(matrix)
inf = 10**10
hq = []
ans = [inf]*n
ans[0] = 0
heappush(hq, (0, 0))
while hq:
d, p = heappop(hq)
for i in range(n):
if ans[p] == d and p != i and d + matrix[p][i] < ans[i]:
ans[i] = d + matrix[p][i]
heappush(hq, (ans[i], i))
return ans[n-1]
x_s, y_s, x_t, y_t = map(int, input().split())
N = int(input())
xyr = []
xyr.append((x_s,y_s,0))
for i in range(N):
x_i, y_i, r_i = map(int, input().split())
xyr.append((x_i, y_i, r_i))
xyr.append((x_t,y_t,0))
graph = [[0]*(N+2) for j in range(N+2)]
for i in range(N+2):
for j in range(i,N+2):
graph[i][j] = max(hypot((xyr[i][1]-xyr[j][1]), (xyr[i][0]-xyr[j][0])) - xyr[i][2] - xyr[j][2], 0)
graph[j][i] = graph[i][j]
print(dijkstra(graph))
``` | instruction | 0 | 40,322 | 3 | 80,644 |
No | output | 1 | 40,322 | 3 | 80,645 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000
Submitted Solution:
```
import math
from heapq import heapify, heappush as hpush, heappop as hpop
xs, ys, xt, yt = map(int, input().split())
N = int(input())
X = [(xs, ys, 0), (xt, yt, 0)]
for _ in range(N):
x, y, r = map(int, input().split())
X.append((x, y, r))
N += 2
DD = [[0] * N for _ in range(N)]
for i in range(N):
xi, yi, ri = X[i]
for j in range(N):
xj, yj, rj = X[j]
DD[i][j] = max(math.sqrt((xi-xj)**2 + (yi-yj)**2) - (ri+rj), 0)
def dijkstra(n, E, i0=0):
h = [[0, i0]]
D = [1<<100] * n
done = [0] * n
D[i0] = 0
while h:
d, i = hpop(h)
done[i] = 1
for j in range(N):
if j == i: continue
w = DD[i][j]
nd = d + w
if D[j] > nd:
if done[j] == 0:
hpush(h, [nd, j])
D[j] = nd
return D
print(dijkstra(N, X)[1])
``` | instruction | 0 | 40,323 | 3 | 80,646 |
No | output | 1 | 40,323 | 3 | 80,647 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000
Submitted Solution:
```
import heapq
xs,ys,xt,yt=map(int,input().split())
n=int(input())
l=[list(map(int,input().split())) for _ in range(n)]
f,g=float("inf"),float("inf")
start,end=0,0
v=0
for i,(x,y,r) in enumerate(l):
v1=(x-xs)**2+(y-ys)**2
v2=(x-xt)**2+(y-yt)**2
if v1<f:
f=v1
start=i
if v2<g:
g=v2
end=i
G=[[0]*n for _ in range(n)]
for i in range(n):
x1,y1,r1=l[i]
for j in range(n):
x2,y2,r2=l[j]
G[i][j]=max(0,((x1-x2)**2+(y1-y2)**2)**0.5-r1-r2)
x1,y1,r1=l[start]
x2,y2,r2=l[end]
v+=max(0,((xs-x1)**2+(ys-y1)**2)**0.5-r1)
v+=max(0,((xt-x2)**2+(yt-y2)**2)**0.5-r2)
d=[float("inf")]*(n+1)
q=[]
d[start]=0
heapq.heappush(q,(0,start))
while q:
dist,pos=q.pop()
if d[pos]<dist:continue
for to,cost in enumerate(G[pos]):
if d[to]>d[pos]+cost:
d[to]=d[pos]+cost
heapq.heappush(q,(d[to],to))
v+=d[end]
print("{:.10f}".format(v))
``` | instruction | 0 | 40,324 | 3 | 80,648 |
No | output | 1 | 40,324 | 3 | 80,649 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On the xy-plane, Snuke is going to travel from the point (x_s, y_s) to the point (x_t, y_t). He can move in arbitrary directions with speed 1. Here, we will consider him as a point without size.
There are N circular barriers deployed on the plane. The center and the radius of the i-th barrier are (x_i, y_i) and r_i, respectively. The barriers may overlap or contain each other.
A point on the plane is exposed to cosmic rays if the point is not within any of the barriers.
Snuke wants to avoid exposure to cosmic rays as much as possible during the travel. Find the minimum possible duration of time he is exposed to cosmic rays during the travel.
Constraints
* All input values are integers.
* -10^9 ≤ x_s, y_s, x_t, y_t ≤ 10^9
* (x_s, y_s) ≠ (x_t, y_t)
* 1≤N≤1,000
* -10^9 ≤ x_i, y_i ≤ 10^9
* 1 ≤ r_i ≤ 10^9
Input
The input is given from Standard Input in the following format:
x_s y_s x_t y_t
N
x_1 y_1 r_1
x_2 y_2 r_2
:
x_N y_N r_N
Output
Print the minimum possible duration of time Snuke is exposed to cosmic rays during the travel. The output is considered correct if the absolute or relative error is at most 10^{-9}.
Examples
Input
-2 -2 2 2
1
0 0 1
Output
3.6568542495
Input
-2 0 2 0
2
-1 0 2
1 0 2
Output
0.0000000000
Input
4 -2 -2 4
3
0 0 2
4 0 1
0 4 1
Output
4.0000000000
Submitted Solution:
```
import heapq
import sys
input = sys.stdin.buffer.readline
def dijkstra(adj, start):
# adj: [[to, cost] * vertices], 0th index must be empty
dist = [float('inf')] * len(adj)
dist[start] = 0
q = []
heapq.heappush(q, [0, start])
while q:
min_dist, v_from = heapq.heappop(q)
if min_dist > dist[v_from]:
continue
v_tos = adj[v_from]
for v_to_info in v_tos:
v_to, cost = v_to_info
if min_dist + cost < dist[v_to]:
dist[v_to] = min_dist + cost
heapq.heappush(q, [dist[v_to], v_to])
return dist
def main():
xs, ys, xt, yt = map(int, input().split())
N = int(input())
br = [[xs, ys, 0], [xt, yt, 0]]
for _ in range(N):
br.append(list(map(int, input().split())))
adj = [[] for _ in range(N+3)]
for i in range(N+2):
for j in range(i+1, N+2):
dij = max(((br[i][0] - br[j][0])**2 + (br[i][1] - br[j][1])**2) ** (1/2) - (br[i][2] + br[j][2]), 0)
adj[i+1].append([j+1, dij])
adj[j+1].append([i+1, dij])
print(dijkstra(adj, 1)[2])
if __name__ == '__main__':
main()
``` | instruction | 0 | 40,325 | 3 | 80,650 |
No | output | 1 | 40,325 | 3 | 80,651 |
Provide a correct Python 3 solution for this coding contest problem.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000 | instruction | 0 | 40,342 | 3 | 80,684 |
"Correct Solution:
```
import math
def loop(a, x, m):
count = 0
while 1:
count += 1
x = (a * x) % m
if x == 1: break
return count
while 1:
a1, m1, a2, m2, a3, m3 = map(int, input().split())
if a1 == 0: break
x = y = z = 1
x = loop(a1, x, m1)
y = loop(a2, y, m2)
z = loop(a3, z, m3)
xy = int(x * y / math.gcd(x, y))
xyz = int(xy * z / math.gcd(xy, z))
print(xyz)
``` | output | 1 | 40,342 | 3 | 80,685 |
Provide a correct Python 3 solution for this coding contest problem.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000 | instruction | 0 | 40,343 | 3 | 80,686 |
"Correct Solution:
```
from fractions import gcd
while True:
a = list(map(int, input().split()))
if a.count(0) == 6:
break
x = a[0] % a[1]
ix = 1
while x != 1:
x = a[0] * x % a[1]
ix += 1
y = a[2] % a[3]
iy = 1
while y != 1:
y = a[2] * y % a[3]
iy += 1
z = a[4] % a[5]
iz = 1
while z != 1:
z = a[4] * z % a[5]
iz += 1
ixy = ix * iy // gcd(ix, iy)
print(ixy * iz // gcd(ixy, iz))
``` | output | 1 | 40,343 | 3 | 80,687 |
Provide a correct Python 3 solution for this coding contest problem.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000 | instruction | 0 | 40,344 | 3 | 80,688 |
"Correct Solution:
```
import math
def get_input():
while True:
try:
yield ''.join(input())
except EOFError:
break
def lcm(a,b):
d = math.gcd(a,b)
aa = int(a/d)
bb = int(b/d)
return aa*bb*d
while True:
a1,m1,a2,m2,a3,m3 = [int(i) for i in input().split()]
if a1 == 0 and m1 == 0 and a2 == 0 and m2 == 0 and a3 == 0 and m3 == 0:
break
x = 1
y = 1
z = 1
cnt1 = 0
cnt2 = 0
cnt3 = 0
while True:
x = a1*x % m1
cnt1 += 1
if x == 1:
break
while True:
y = a2*y % m2
cnt2 += 1
if y == 1:
break
while True:
z = a3*z % m3
cnt3 += 1
if z == 1:
break
print(lcm(lcm(cnt1,cnt2),cnt3))
``` | output | 1 | 40,344 | 3 | 80,689 |
Provide a correct Python 3 solution for this coding contest problem.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000 | instruction | 0 | 40,345 | 3 | 80,690 |
"Correct Solution:
```
# 0114
def gcd(a, b):
if b == 0: return a
return gcd(b, a % b)
def lcm(a, b):
return a * b / gcd(a, b)
def times(a, m):
c = 1
x = a * 1 % m
while x != 1:
x = a * x % m
c += 1
return c
while True:
x, y, z = 1, 1, 1
c1, c2 ,c3 = 0, 0, 0
a1, m1, a2, m2, a3, m3 = map(int, input().split())
if sum([a1, m1, a2, m2, a3, m3]) == 0:
break
c1 = times(a1, m1)
c2 = times(a2, m2)
c3 = times(a3, m3)
print(int(lcm(c1, lcm(c2, c3))))
``` | output | 1 | 40,345 | 3 | 80,691 |
Provide a correct Python 3 solution for this coding contest problem.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000 | instruction | 0 | 40,346 | 3 | 80,692 |
"Correct Solution:
```
def gcd(a, b):
if a < b: a, b = b, a
while b > 0:
r = a % b
a, b = b, r
return a
def lcm(a,b):
return ((a*b) // gcd(a,b))
def getCnt(a,m):
cnt = 0
n = 1
while(1):
n = (a * n) % m
cnt += 1
if n == 1:
return cnt
while(1):
a1,m1,a2,m2,a3,m3 = (int(x) for x in input().split())
if a1 == 0:
break
x = y = z = 1
cnt1 = getCnt(a1,m1)
cnt2 = getCnt(a2,m2)
cnt3 = getCnt(a3,m3)
ans = lcm(cnt1,cnt2)
ans = lcm(ans,cnt3)
print(ans)
``` | output | 1 | 40,346 | 3 | 80,693 |
Provide a correct Python 3 solution for this coding contest problem.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000 | instruction | 0 | 40,347 | 3 | 80,694 |
"Correct Solution:
```
from math import gcd
def get_loop(a, m):
count = 1
acc = a
while acc != 1:
count += 1
acc *= a
acc %= m
return count
while True:
a1, m1, a2, m2, a3, m3 = map(int, input().split())
if not a1:
break
loop_a = get_loop(a1, m1)
loop_b = get_loop(a2, m2)
loop_c = get_loop(a3, m3)
loop_ab = loop_a * loop_b // gcd(loop_a, loop_b)
loop_abc = loop_ab * loop_c // gcd(loop_ab, loop_c)
print(loop_abc)
``` | output | 1 | 40,347 | 3 | 80,695 |
Provide a correct Python 3 solution for this coding contest problem.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000 | instruction | 0 | 40,348 | 3 | 80,696 |
"Correct Solution:
```
# 0114
def gcd(a, b):
if b == 0: return a
return gcd(b, a % b)
def lcm(a, b):
return a * b / gcd(a, b)
def times(a, m):
c = 1
x = a * 1 % m
while x != 1:
x = a * x % m
c += 1
return c
while True:
try:
x, y, z = 1, 1, 1
c1, c2 ,c3 = 0, 0, 0
a1, m1, a2, m2, a3, m3 = map(int, input().split())
if sum([a1, m1, a2, m2, a3, m3]) == 0:
break
c1 = times(a1, m1)
c2 = times(a2, m2)
c3 = times(a3, m3)
print(int(lcm(c1, lcm(c2, c3))))
except EOFError:
break
``` | output | 1 | 40,348 | 3 | 80,697 |
Provide a correct Python 3 solution for this coding contest problem.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000 | instruction | 0 | 40,349 | 3 | 80,698 |
"Correct Solution:
```
def gcd(a, b):
if b == 0: return a
return gcd(b, a % b)
while True:
a = list(map(int, input().split()))
if a.count(0) == 6:
break
x = a[0] % a[1]
ix = 1
while x != 1:
x = a[0] * x % a[1]
ix += 1
y = a[2] % a[3]
iy = 1
while y != 1:
y = a[2] * y % a[3]
iy += 1
z = a[4] % a[5]
iz = 1
while z != 1:
z = a[4] * z % a[5]
iz += 1
ixy = ix * iy // gcd(ix, iy)
print(ixy * iz // gcd(ixy, iz))
``` | output | 1 | 40,349 | 3 | 80,699 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Submitted Solution:
```
# 0114
def gcd(a, b):
if b == 0: return a
return gcd(b, a % b)
def lcm(a, b):
return a * b / gcd(a, b)
while True:
try:
x, y, z = 1, 1, 1
c1, c2 ,c3 = 0, 0, 0
a1, m1, a2, m2, a3, m3 = map(int, input().split())
if sum([a1, m1, a2, m2, a3, m3]) == 0:
break
while True:
x = a1 * x % m1
c1 += 1
if x == 1:
break
while True:
y = a2 * y % m2
c2 += 1
if y == 1:
break
while True:
z = a3 * z % m3
c3 += 1
if z == 1:
break
print(int(lcm(c1, lcm(c2, c3))))
except EOFError:
break
``` | instruction | 0 | 40,350 | 3 | 80,700 |
Yes | output | 1 | 40,350 | 3 | 80,701 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Submitted Solution:
```
import itertools as I,math;
def lcm(x,y):return x*y//math.gcd(x,y);
while 1:
a,b,c,d,e,f=map(int,input().split());
if a==0:break;
A=I.dropwhile(lambda x:1<pow(a,x,b),range(1,b));
B=I.dropwhile(lambda x:1<pow(c,x,d),range(1,d));
C=I.dropwhile(lambda x:1<pow(e,x,f),range(1,f));
x,y,z=map(lambda u:list(u)[0],[A,B,C]);
print(lcm(x,lcm(y,z)))
``` | instruction | 0 | 40,351 | 3 | 80,702 |
Yes | output | 1 | 40,351 | 3 | 80,703 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Submitted Solution:
```
from decimal import *
class Fry:
def __init__(self,a1,m1,a2,m2,a3,m3):
self.a1 = a1
self.m1 = m1
self.a2 = a2
self.m2 = m2
self.a3 = a3
self.m3 = m3
def euc(self,m,n):
if n==0:
return(m)
else:
r = m % n
return(self.euc(n,r))
def test(self,a,m):
n = 0
x = 1
while True:
x1 = (a * x) % m
n += 1
if x1 == 1:
break
else:
x = x1
return(n)
def mv(self):
n1 = Decimal(self.test(self.a1,self.m1))
n2 = Decimal(self.test(self.a2,self.m2))
n3 = Decimal(self.test(self.a3,self.m3))
m1 = n1*n2/self.euc(n1,n2)
m2 = m1*n3/self.euc(m1,n3)
return(m2)
while True:
a1,m1,a2,m2,a3,m3 = list(map(int, input().strip().split()))
if a1==m1==a2==m2==a3==m3==0:
break
fry = Fry(a1,m1,a2,m2,a3,m3)
print(fry.mv())
``` | instruction | 0 | 40,352 | 3 | 80,704 |
Yes | output | 1 | 40,352 | 3 | 80,705 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0114
"""
import sys
def lcm(x, y):
return x*y//gcd(x, y)
def gcd(x, y):
if x < y:
temp = x
x = y
y = temp
while y > 0:
r = x % y
x = y
y = r
return x
def calc_cycle(a, m):
x = 1
cycle = 0
while True:
x = (a * x) % m
cycle += 1
if x == 1:
break
return cycle
def solve(data):
a1, m1, a2, m2, a3, m3 = data
x_cycle = calc_cycle(a1, m1)
y_cycle = calc_cycle(a2, m2)
z_cycle = calc_cycle(a3, m3)
return lcm(lcm(x_cycle, y_cycle), z_cycle)
def main(args):
# data = [2, 5, 3, 7, 6, 13]
#data = [517, 1024, 746, 6561, 4303, 3125]
while True:
data = [int(x) for x in input().split(' ')]
if data.count(0) == 6:
break
result = solve(data)
print(result)
if __name__ == '__main__':
main(sys.argv[1:])
``` | instruction | 0 | 40,353 | 3 | 80,706 |
Yes | output | 1 | 40,353 | 3 | 80,707 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Submitted Solution:
```
# -*- coding: utf-8 -*-
import sys
import os
import math
def lcm(a, b):
return (a * b) // math.gcd(a, b)
def interval(a, m):
cnt = 0
x = 1
while True:
x = (a * x) % m
cnt += 1
if x == 1:
return cnt
for s in sys.stdin:
a1, m1, a2, m2, a3, m3 = map(int, s.split())
if sum([a1, m1, a2, m2, a3, m3]) == 0:
break
x_num = interval(a1, m1)
y_num = interval(a2, m2)
z_num = interval(a3, m3)
a = lcm(x_num, y_num)
b = lcm(a, z_num)
print(b)
``` | instruction | 0 | 40,354 | 3 | 80,708 |
No | output | 1 | 40,354 | 3 | 80,709 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Submitted Solution:
```
# -*- coding: utf-8 -*-
import sys
import os
import math
def lcm(a, b):
return (a * b) // math.gcd(a, b)
for s in sys.stdin:
a1, m1, a2, m2, a3, m3 = map(int, s.split())
if a1 == m1 == a2 == m2 == a3 == m3 == 0:
break
x = 1
y = 1
z = 1
x_num = 0
while True:
x = (a1 * x) % m1
x_num += 1
if x == 1:
break
y_num = 0
while True:
y = (a2 * y) % m2
y_num += 1
if y == 1:
break
z_num = 0
while True:
z = (a3 * z) % m3
z_num += 1
if z == 1:
break
a = lcm(x_num, y_num)
b = lcm(a, z_num)
print(b)
``` | instruction | 0 | 40,355 | 3 | 80,710 |
No | output | 1 | 40,355 | 3 | 80,711 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Submitted Solution:
```
from math import gcd
while True:
a = list(map(int, input().split()))
if a.count(0) == 6:
break
x = a[0] % a[1]
ix = 1
while x != 1:
x = a[0] * x % a[1]
ix += 1
y = a[2] % a[3]
iy = 1
while y != 1:
y = a[2] * y % a[3]
iy += 1
z = a[4] % a[5]
iz = 1
while z != 1:
z = a[4] * z % a[5]
iz += 1
ixy = ix * iy // gcd(ix, iy)
print(ixy * iz // gcd(ixy, iz))
``` | instruction | 0 | 40,356 | 3 | 80,712 |
No | output | 1 | 40,356 | 3 | 80,713 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A calculator scholar has discovered a strange life form called an electronic fly that lives in electronic space. While observing the behavior of the electronic flies, the electronic flies at the (x, y, z) point in this space then move to (x', y', z') indicated by the following rules. I found out.
<image>
However, a1, m1, a2, m2, a3, m3 are positive integers determined for each individual electronic fly. A mod B is the remainder of the positive integer A divided by the positive integer B.
Further observation revealed that some electronic flies always return to (1,1,1) shortly after being placed at (1,1,1). Such flies were named return flies (1).
Create a program that takes the data of the return fly as input and outputs the minimum number of movements (> 0) that return to (1,1,1). Note that 1 <a1, m1, a2, m2, a3, m3 <215.
(1) Returns when a1 and m1, a2 and m2, a3 and m3 are relatively prime (common divisor 1), respectively.
Input
Given multiple datasets. Each dataset is given in the following format:
a1 m1 a2 m2 a3 m3
The input ends with a line containing 6 0s. The number of datasets does not exceed 50.
Output
For each dataset, output the minimum number of moves (integer) that return to (1,1,1) on one line.
Example
Input
2 5 3 7 6 13
517 1024 746 6561 4303 3125
0 0 0 0 0 0
Output
12
116640000
Submitted Solution:
```
from math import gcd
def get_loop(a, m):
count = 1
acc = a
while acc % m != 1:
count += 1
acc *= a
return count
while True:
a1, m1, a2, m2, a3, m3 = map(int, input().split())
if not a1:
break
loop_a = get_loop(a1, m1)
loop_b = get_loop(a2, m2)
loop_c = get_loop(a3, m3)
loop_ab = loop_a * loop_b // gcd(loop_a, loop_b)
loop_abc = loop_ab * loop_c // gcd(loop_ab, loop_c)
print(loop_abc)
``` | instruction | 0 | 40,357 | 3 | 80,714 |
No | output | 1 | 40,357 | 3 | 80,715 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People like to be fit. That's why many of them are ready to wake up at dawn, go to the stadium and run. In this problem your task is to help a company design a new stadium.
The city of N has a shabby old stadium. Many people like it and every morning thousands of people come out to this stadium to run. The stadium can be represented as a circle, its length is exactly l meters with a marked start line. However, there can't be simultaneous start in the morning, so exactly at 7, each runner goes to his favorite spot on the stadium and starts running from there. Note that not everybody runs in the same manner as everybody else. Some people run in the clockwise direction, some of them run in the counter-clockwise direction. It mostly depends on the runner's mood in the morning, so you can assume that each running direction is equiprobable for each runner in any fixed morning.
The stadium is tiny and is in need of major repair, for right now there only is one running track! You can't get too playful on a single track, that's why all runners keep the same running speed — exactly 1 meter per a time unit. Nevertheless, the runners that choose different directions bump into each other as they meet.
The company wants to design a new stadium, but they first need to know how bad the old one is. For that they need the expectation of the number of bumpings by t time units after the running has begun. Help the company count the required expectation. Note that each runner chooses a direction equiprobably, independently from the others and then all runners start running simultaneously at 7 a.m. Assume that each runner runs for t time units without stopping. Consider the runners to bump at a certain moment if at that moment they found themselves at the same point in the stadium. A pair of runners can bump more than once.
Input
The first line of the input contains three integers n, l, t (1 ≤ n ≤ 106, 1 ≤ l ≤ 109, 1 ≤ t ≤ 109). The next line contains n distinct integers a1, a2, ..., an (0 ≤ a1 < a2 < ... < an < l), here ai is the clockwise distance from the start line to the i-th runner's starting position.
Output
Print a single real number — the answer to the problem with absolute or relative error of at most 10 - 6.
Examples
Input
2 5 1
0 2
Output
0.2500000000
Input
3 7 3
0 1 6
Output
1.5000000000
Note
There are two runners in the first example. If the first runner run clockwise direction, then in 1 time unit he will be 1m away from the start line. If the second runner run counter-clockwise direction then in 1 time unit he will be also 1m away from the start line. And it is the only possible way to meet. We assume that each running direction is equiprobable, so the answer for the example is equal to 0.5·0.5 = 0.25.
Submitted Solution:
```
def sol():
n, l, t = list(map(int, input().split(" ")))
b = list(map(int, input().split(" ")))
ans_a = (t // l) * (n * (n - 1) // 2)
c = t - ((2*t) // l) * l*2
e = 0
for i in range(0, n - 1):
for j in range(i + 1, n):
if b[j] - b[i] <= 2 * c:
e += 1
if b[j] - b[i] > 2 * c:
break
for i in range(0, n - 1):
for j in range(i + 1, n):
if b[j] - b[i] >= l - 2 * c:
e += n - j
break
ans_b = e * 0.25
ans = ans_a + ans_b
print(ans)
sol()
``` | instruction | 0 | 40,740 | 3 | 81,480 |
No | output | 1 | 40,740 | 3 | 81,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People like to be fit. That's why many of them are ready to wake up at dawn, go to the stadium and run. In this problem your task is to help a company design a new stadium.
The city of N has a shabby old stadium. Many people like it and every morning thousands of people come out to this stadium to run. The stadium can be represented as a circle, its length is exactly l meters with a marked start line. However, there can't be simultaneous start in the morning, so exactly at 7, each runner goes to his favorite spot on the stadium and starts running from there. Note that not everybody runs in the same manner as everybody else. Some people run in the clockwise direction, some of them run in the counter-clockwise direction. It mostly depends on the runner's mood in the morning, so you can assume that each running direction is equiprobable for each runner in any fixed morning.
The stadium is tiny and is in need of major repair, for right now there only is one running track! You can't get too playful on a single track, that's why all runners keep the same running speed — exactly 1 meter per a time unit. Nevertheless, the runners that choose different directions bump into each other as they meet.
The company wants to design a new stadium, but they first need to know how bad the old one is. For that they need the expectation of the number of bumpings by t time units after the running has begun. Help the company count the required expectation. Note that each runner chooses a direction equiprobably, independently from the others and then all runners start running simultaneously at 7 a.m. Assume that each runner runs for t time units without stopping. Consider the runners to bump at a certain moment if at that moment they found themselves at the same point in the stadium. A pair of runners can bump more than once.
Input
The first line of the input contains three integers n, l, t (1 ≤ n ≤ 106, 1 ≤ l ≤ 109, 1 ≤ t ≤ 109). The next line contains n distinct integers a1, a2, ..., an (0 ≤ a1 < a2 < ... < an < l), here ai is the clockwise distance from the start line to the i-th runner's starting position.
Output
Print a single real number — the answer to the problem with absolute or relative error of at most 10 - 6.
Examples
Input
2 5 1
0 2
Output
0.2500000000
Input
3 7 3
0 1 6
Output
1.5000000000
Note
There are two runners in the first example. If the first runner run clockwise direction, then in 1 time unit he will be 1m away from the start line. If the second runner run counter-clockwise direction then in 1 time unit he will be also 1m away from the start line. And it is the only possible way to meet. We assume that each running direction is equiprobable, so the answer for the example is equal to 0.5·0.5 = 0.25.
Submitted Solution:
```
def sol():
n, l, t = list(map(int, input().split(" ")))
b = list(map(int, input().split(" ")))
ans_a = (t//l)*(n*(n-1)//2)*0.5
c = t-(t//l)*l
e = 0
for i in range(0, n-1):
for j in range(i+1, n):
if b[j]-b[i] <= 2*c:
e += 1
if b[j]-b[i] > 2*c:
break
for i in range(0, n - 1):
for j in range(i+1, n):
if b[j] - b[i] >= l - 2 * c:
e += n-j
break
ans_b = e*0.25
ans = ans_a+ans_b
print (ans)
sol()
``` | instruction | 0 | 40,741 | 3 | 81,482 |
No | output | 1 | 40,741 | 3 | 81,483 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People like to be fit. That's why many of them are ready to wake up at dawn, go to the stadium and run. In this problem your task is to help a company design a new stadium.
The city of N has a shabby old stadium. Many people like it and every morning thousands of people come out to this stadium to run. The stadium can be represented as a circle, its length is exactly l meters with a marked start line. However, there can't be simultaneous start in the morning, so exactly at 7, each runner goes to his favorite spot on the stadium and starts running from there. Note that not everybody runs in the same manner as everybody else. Some people run in the clockwise direction, some of them run in the counter-clockwise direction. It mostly depends on the runner's mood in the morning, so you can assume that each running direction is equiprobable for each runner in any fixed morning.
The stadium is tiny and is in need of major repair, for right now there only is one running track! You can't get too playful on a single track, that's why all runners keep the same running speed — exactly 1 meter per a time unit. Nevertheless, the runners that choose different directions bump into each other as they meet.
The company wants to design a new stadium, but they first need to know how bad the old one is. For that they need the expectation of the number of bumpings by t time units after the running has begun. Help the company count the required expectation. Note that each runner chooses a direction equiprobably, independently from the others and then all runners start running simultaneously at 7 a.m. Assume that each runner runs for t time units without stopping. Consider the runners to bump at a certain moment if at that moment they found themselves at the same point in the stadium. A pair of runners can bump more than once.
Input
The first line of the input contains three integers n, l, t (1 ≤ n ≤ 106, 1 ≤ l ≤ 109, 1 ≤ t ≤ 109). The next line contains n distinct integers a1, a2, ..., an (0 ≤ a1 < a2 < ... < an < l), here ai is the clockwise distance from the start line to the i-th runner's starting position.
Output
Print a single real number — the answer to the problem with absolute or relative error of at most 10 - 6.
Examples
Input
2 5 1
0 2
Output
0.2500000000
Input
3 7 3
0 1 6
Output
1.5000000000
Note
There are two runners in the first example. If the first runner run clockwise direction, then in 1 time unit he will be 1m away from the start line. If the second runner run counter-clockwise direction then in 1 time unit he will be also 1m away from the start line. And it is the only possible way to meet. We assume that each running direction is equiprobable, so the answer for the example is equal to 0.5·0.5 = 0.25.
Submitted Solution:
```
def sol():
n, l, t = list(map(int, input().split(" ")))
b = list(map(int, input().split(" ")))
ans_a = (t//l)*(n*(n-1)//2)
c = t-(t//l)*l
e = 0
f = 0
for i in range(0, n-1):
for j in range(i+1, n):
if b[j]-b[i] <= 2*c:
e += 1
if b[j]-b[i] > 2*c:
break
for i in range(0, n - 1):
for j in range(i+1, n):
if b[j] - b[i] >= l - 2 * c:
f += 1
ans_b = (e+f)*0.5
ans = ans_a+ans_b
print (ans)
sol()
``` | instruction | 0 | 40,742 | 3 | 81,484 |
No | output | 1 | 40,742 | 3 | 81,485 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
People like to be fit. That's why many of them are ready to wake up at dawn, go to the stadium and run. In this problem your task is to help a company design a new stadium.
The city of N has a shabby old stadium. Many people like it and every morning thousands of people come out to this stadium to run. The stadium can be represented as a circle, its length is exactly l meters with a marked start line. However, there can't be simultaneous start in the morning, so exactly at 7, each runner goes to his favorite spot on the stadium and starts running from there. Note that not everybody runs in the same manner as everybody else. Some people run in the clockwise direction, some of them run in the counter-clockwise direction. It mostly depends on the runner's mood in the morning, so you can assume that each running direction is equiprobable for each runner in any fixed morning.
The stadium is tiny and is in need of major repair, for right now there only is one running track! You can't get too playful on a single track, that's why all runners keep the same running speed — exactly 1 meter per a time unit. Nevertheless, the runners that choose different directions bump into each other as they meet.
The company wants to design a new stadium, but they first need to know how bad the old one is. For that they need the expectation of the number of bumpings by t time units after the running has begun. Help the company count the required expectation. Note that each runner chooses a direction equiprobably, independently from the others and then all runners start running simultaneously at 7 a.m. Assume that each runner runs for t time units without stopping. Consider the runners to bump at a certain moment if at that moment they found themselves at the same point in the stadium. A pair of runners can bump more than once.
Input
The first line of the input contains three integers n, l, t (1 ≤ n ≤ 106, 1 ≤ l ≤ 109, 1 ≤ t ≤ 109). The next line contains n distinct integers a1, a2, ..., an (0 ≤ a1 < a2 < ... < an < l), here ai is the clockwise distance from the start line to the i-th runner's starting position.
Output
Print a single real number — the answer to the problem with absolute or relative error of at most 10 - 6.
Examples
Input
2 5 1
0 2
Output
0.2500000000
Input
3 7 3
0 1 6
Output
1.5000000000
Note
There are two runners in the first example. If the first runner run clockwise direction, then in 1 time unit he will be 1m away from the start line. If the second runner run counter-clockwise direction then in 1 time unit he will be also 1m away from the start line. And it is the only possible way to meet. We assume that each running direction is equiprobable, so the answer for the example is equal to 0.5·0.5 = 0.25.
Submitted Solution:
```
def sol():
n, l, t = list(map(int, input().split(" ")))
b = list(map(int, input().split(" ")))
ans_a = (t//l)*(n*(n-1)//2)*0.5*2
c = t-(t//l)*l
e = 0
for i in range(0, n-1):
for j in range(i+1, n):
if b[j]-b[i] <= 2*c:
e += 1
if b[j]-b[i] > 2*c:
break
for i in range(0, n - 1):
for j in range(i+1, n):
if b[j] - b[i] >= l - 2 * c:
e += n-j
break
ans_b = e*0.25
ans = ans_a+ans_b
print (ans)
sol()
``` | instruction | 0 | 40,743 | 3 | 81,486 |
No | output | 1 | 40,743 | 3 | 81,487 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently Luba bought a monitor. Monitor is a rectangular matrix of size n × m. But then she started to notice that some pixels cease to work properly. Luba thinks that the monitor will become broken the first moment when it contains a square k × k consisting entirely of broken pixels. She knows that q pixels are already broken, and for each of them she knows the moment when it stopped working. Help Luba to determine when the monitor became broken (or tell that it's still not broken even after all q pixels stopped working).
Input
The first line contains four integer numbers n, m, k, q (1 ≤ n, m ≤ 500, 1 ≤ k ≤ min(n, m), 0 ≤ q ≤ n·m) — the length and width of the monitor, the size of a rectangle such that the monitor is broken if there is a broken rectangle with this size, and the number of broken pixels.
Each of next q lines contain three integer numbers xi, yi, ti (1 ≤ xi ≤ n, 1 ≤ yi ≤ m, 0 ≤ t ≤ 109) — coordinates of i-th broken pixel (its row and column in matrix) and the moment it stopped working. Each pixel is listed at most once.
We consider that pixel is already broken at moment ti.
Output
Print one number — the minimum moment the monitor became broken, or "-1" if it's still not broken after these q pixels stopped working.
Examples
Input
2 3 2 5
2 1 8
2 2 8
1 2 1
1 3 4
2 3 2
Output
8
Input
3 3 2 5
1 2 2
2 2 1
2 3 5
3 2 10
2 1 100
Output
-1
Submitted Solution:
```
n, m, k, q = map(int, input().split())
def sort(x):
return x[2]
def check(matrix):
sas = matrix.copy()
for i in range(n + 1):
for j in range(m + 1):
sas[i][j] = matrix[i][j]
if i:
sas[i][j] += sas[i - 1][j]
if j:
sas[i][j] += sas[i][j - 1]
if i and j:
sas[i][j] -= sas[i - 1][j - 1]
for i in range(k, n + 1):
for j in range(k, m + 1):
if (sas[i][j] - sas[i - k][j] - sas[i][j - k] + sas[i - k][j - k]) == (k * k):
return True
return False
h = sorted([list(map(int, input().split())) for _ in range(q)], key=sort)
matrix = [[0 for _ in range(m + 1)] for __ in range(n + 1)]
for i in h:
matrix[i[0]][i[1]] = 1
if not check(matrix):
print(-1)
exit()
l, r = -1, len(h)
while l < r:
mid = (l + r) // 2
matrix = [[0 for _ in range(m + 1)] for __ in range(n + 1)]
for i in h[:mid]:
matrix[i[0]][i[1]] = 1
parasha = check(matrix)
if parasha:
r = mid - 1
else:
l = mid + 1
mid = (l + r) // 2
if mid < 0:
mid = 0
if mid >= len(h):
mid = len(h) - 1
print(h[mid][2])
``` | instruction | 0 | 40,908 | 3 | 81,816 |
No | output | 1 | 40,908 | 3 | 81,817 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.
Input
The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].
Output
Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.
Examples
Input
2 2 5 3
Output
4
Input
5 4 11 8
Output
20 | instruction | 0 | 41,498 | 3 | 82,996 |
Tags: brute force, math
Correct Solution:
```
n, d, m, l = [int(i) for i in input().split()]
x = 0
if m % d == 0:
x = ((n-1)*m+l) // d * d + d
elif (m - l) > d:
x = l // d * d + d
else:
for k in range(1, n+1):
r = k*m % d
if r < (m-l) and r != 0:
x = k*m - r
x = ((k-1)*m+l) // d * d + d
break
if x==0:
x = ((n-1)*m+l) // d * d + d
print(x)
``` | output | 1 | 41,498 | 3 | 82,997 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.
Input
The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].
Output
Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.
Examples
Input
2 2 5 3
Output
4
Input
5 4 11 8
Output
20 | instruction | 0 | 41,499 | 3 | 82,998 |
Tags: brute force, math
Correct Solution:
```
import sys
input = sys.stdin.readline
n, d, m, l = map(int, input().split())
res = 0
for i in range(n):
z = m * i + l + d; res = z - z % d
if m * (i+1) > z - z % d: break
print(res)
``` | output | 1 | 41,499 | 3 | 82,999 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.
Input
The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].
Output
Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.
Examples
Input
2 2 5 3
Output
4
Input
5 4 11 8
Output
20 | instruction | 0 | 41,500 | 3 | 83,000 |
Tags: brute force, math
Correct Solution:
```
#coding gbk
while True:
try:
n,d,m,l=map(int,input().strip().split())
mi = 0
mx = 0
step = 0
for i in range(n):
mi = i*m+l
mx = (i+1)*m
step = (mi+d)//d
if step*d<mx:
break
print(step*d)
except EOFError:
break
``` | output | 1 | 41,500 | 3 | 83,001 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.
Input
The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].
Output
Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.
Examples
Input
2 2 5 3
Output
4
Input
5 4 11 8
Output
20 | instruction | 0 | 41,501 | 3 | 83,002 |
Tags: brute force, math
Correct Solution:
```
n, d, m, l = [int(i) for i in input().split()]
x = 0
for k in range(1, n+1):
r = k*m % d
if r < (m-l) and r != 0:
x = k*m - r
x = ((k-1)*m+l) // d * d + d
break
if x==0:
x = ((n-1)*m+l) // d * d + d
print(x)
``` | output | 1 | 41,501 | 3 | 83,003 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.
Input
The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].
Output
Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.
Examples
Input
2 2 5 3
Output
4
Input
5 4 11 8
Output
20 | instruction | 0 | 41,502 | 3 | 83,004 |
Tags: brute force, math
Correct Solution:
```
n,d,m,l = [int(x) for x in input().split()]
c = 0
counter = 0
fall = False
while counter <= m:
c += d
counter += 1
if c%m > l:
print(c)
fall = True
break
if not fall:
print(((m*(n-1)+l)//d)*d +d)
``` | output | 1 | 41,502 | 3 | 83,005 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.
Input
The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 106, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].
Output
Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.
Examples
Input
2 2 5 3
Output
4
Input
5 4 11 8
Output
20 | instruction | 0 | 41,503 | 3 | 83,006 |
Tags: brute force, math
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
from typing import Text
from collections import*
'''
2 2 5 3
1 : 0,3
2 : 5,
'''
def main():
n,d,m,l = map(int,input().split())
Coordinate = 0
for i in range(n):
left = i*m
right = i*m + l
if(Coordinate < left):
print(Coordinate)
exit(0)
NumberOfMoves = ((right - Coordinate) // d) + 1
Coordinate += NumberOfMoves * d
# print(i , Coordinate)
pass
print(Coordinate)
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
if __name__ == "__main__":
main()
``` | output | 1 | 41,503 | 3 | 83,007 |
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