message stringlengths 2 28.7k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 21 109k | cluster float64 7 7 | __index_level_0__ int64 42 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n boxes with colored balls on the table. Colors are numbered from 1 to n. i-th box contains ai balls, all of which have color i. You have to write a program that will divide all balls into sets such that:
* each ball belongs to exactly one of the sets,
* there are no empty sets,
* there is no set containing two (or more) balls of different colors (each set contains only balls of one color),
* there are no two sets such that the difference between their sizes is greater than 1.
Print the minimum possible number of sets.
Input
The first line contains one integer number n (1 ≤ n ≤ 500).
The second line contains n integer numbers a1, a2, ... , an (1 ≤ ai ≤ 109).
Output
Print one integer number — the minimum possible number of sets.
Examples
Input
3
4 7 8
Output
5
Input
2
2 7
Output
4
Note
In the first example the balls can be divided into sets like that: one set with 4 balls of the first color, two sets with 3 and 4 balls, respectively, of the second color, and two sets with 4 balls of the third color.
Submitted Solution:
```
n = int(input())
a = input().split(" ")
min_color = int(1000000000)
for i in range(1,n):
if min(int(a[i]), int(a[i-1])) < min_color:
min_color = min(int(a[i]), int(a[i-1]))
all_figure = int(0)
for i in range(n):
all_figure += int(a[i])
if (all_figure % min_color + 1) == min_color and min_color != 2:
print(all_figure // min_color + 1)
else:
print(all_figure // min_color)
``` | instruction | 0 | 9,576 | 7 | 19,152 |
No | output | 1 | 9,576 | 7 | 19,153 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On one of the planets of Solar system, in Atmosphere University, many students are fans of bingo game.
It is well known that one month on this planet consists of n^2 days, so calendars, represented as square matrix n by n are extremely popular.
Weather conditions are even more unusual. Due to the unique composition of the atmosphere, when interacting with sunlight, every day sky takes one of three colors: blue, green or red.
To play the bingo, you need to observe the sky for one month — after each day, its cell is painted with the color of the sky in that day, that is, blue, green or red.
At the end of the month, students examine the calendar. If at least one row or column contains only cells of one color, that month is called lucky.
Let's call two colorings of calendar different, if at least one cell has different colors in them. It is easy to see that there are 3^{n ⋅ n} different colorings. How much of them are lucky? Since this number can be quite large, print it modulo 998244353.
Input
The first and only line of input contains a single integer n (1 ≤ n ≤ 1000 000) — the number of rows and columns in the calendar.
Output
Print one number — number of lucky colorings of the calendar modulo 998244353
Examples
Input
1
Output
3
Input
2
Output
63
Input
3
Output
9933
Note
In the first sample any coloring is lucky, since the only column contains cells of only one color.
In the second sample, there are a lot of lucky colorings, in particular, the following colorings are lucky:
<image>
While these colorings are not lucky:
<image>
Submitted Solution:
```
n = int(input())
if n==1: print(3)
elif n==2: print(63)
elif n==3: print(9933)
elif n==4: print(11213343)
elif n==5: print(149702586)
elif n==6: print(977299444)
elif n==7: print(184654847)
elif n==8: print(126441804)
elif n==9: print(858462679)
elif n==10: print(267328409)
elif n==100: print(485774850)
elif n==500: print(559588851)
elif n==1200: print(681471241)
elif n==10001: print(729761820)
elif n==100002: print(990446288)
elif n==1000000: print(733684421)
elif n==11: print(5647520983)
elif n==12: print(771756884)
elif n==13: print(138307135)
elif n==14: print(189544955)
elif n==15: print(695058759)
elif n==16: print(977073017)
elif n==17: print(49721264)
elif n==18: print(743995156)
elif n==19: print(133001100)
elif n==20: print(562961266)
elif n==21: print(476427482)
elif n==22: print(547105672)
elif n==23: print(92989454)
elif n==24: print(278945223)
elif n==25: print(883544047)
elif n==26: print(572019095)
elif n==27: print(39733884)
elif n==28: print(837323055)
elif n==29: print(475382551)
elif n==30: print(89507673)
elif n==1100: print(96619671)
elif n==10228: print(37159602)
elif n==401230: print(522040619)
elif n==591899: print(827652698)
elif n==791899: print(8092157)
elif n==999999: print(756184448)
``` | instruction | 0 | 10,543 | 7 | 21,086 |
No | output | 1 | 10,543 | 7 | 21,087 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
On one of the planets of Solar system, in Atmosphere University, many students are fans of bingo game.
It is well known that one month on this planet consists of n^2 days, so calendars, represented as square matrix n by n are extremely popular.
Weather conditions are even more unusual. Due to the unique composition of the atmosphere, when interacting with sunlight, every day sky takes one of three colors: blue, green or red.
To play the bingo, you need to observe the sky for one month — after each day, its cell is painted with the color of the sky in that day, that is, blue, green or red.
At the end of the month, students examine the calendar. If at least one row or column contains only cells of one color, that month is called lucky.
Let's call two colorings of calendar different, if at least one cell has different colors in them. It is easy to see that there are 3^{n ⋅ n} different colorings. How much of them are lucky? Since this number can be quite large, print it modulo 998244353.
Input
The first and only line of input contains a single integer n (1 ≤ n ≤ 1000 000) — the number of rows and columns in the calendar.
Output
Print one number — number of lucky colorings of the calendar modulo 998244353
Examples
Input
1
Output
3
Input
2
Output
63
Input
3
Output
9933
Note
In the first sample any coloring is lucky, since the only column contains cells of only one color.
In the second sample, there are a lot of lucky colorings, in particular, the following colorings are lucky:
<image>
While these colorings are not lucky:
<image>
Submitted Solution:
```
def search(a):
s = None
flg = False
for i in range(len(a)):
if flg is True:
break
if a[i] == '2':
for j in range(len(a)):
if a[j] == '5':
s = '25'
flg = True
break
elif a[i] == '5':
for j in range(len(a)):
if a[j] == '2':
s = '25'
flg = True
break
elif a[j] == '7':
s = '75'
flg = True
break
elif a[j] == '0':
s = '50'
flg = True
break
elif a[i] == '7':
for j in range(len(a)):
if a[j] == '5':
s = '75'
flg = True
break
elif a[i] == '0':
for j in range(len(a)):
if a[j] == '5':
s = '50'
flg = True
break
elif a[j] == '0':
s = '00'
flg = True
break
if s is None:
print(-1)
exit()
return s
#def swap(a,b):
# a, b = b, a
# return b, a
def czero(a):
ctr = 0
index = None
for i in range(len(a)):
if a[i] != 0:
index = i
break
if index == 0:
return None
else:
cou = index
while a[0] == '0':
a[cou-1], a[cou] = a[cou], a[cou-1]
ctr+=1
cou-=1
return ctr
Counter = 0
a=input()[::-1]
Comb = search(a)
a = list(a)[::-1]
Nxt = a.index(Comb[1])
for i in range(Nxt+1, len(a)):
a[i-1], a[i] = a[i], a[i-1]
Counter+=1
Fst = a.index(Comb[0])
for i in range(Fst+1, len(a)-1):
a[i-1], a[i] = a[i], a[i-1]
Counter+=1
f = czero(a)
if f is None:
print(Counter)
else:
print(Counter+f)
``` | instruction | 0 | 10,544 | 7 | 21,088 |
No | output | 1 | 10,544 | 7 | 21,089 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3 | instruction | 0 | 11,051 | 7 | 22,102 |
Tags: implementation
Correct Solution:
```
s = sorted(list(map(int, input().split())))
d = 3
for i in range(3):
if(s[i] != s[i+1]):
d -= 1
print(d)
``` | output | 1 | 11,051 | 7 | 22,103 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3 | instruction | 0 | 11,052 | 7 | 22,104 |
Tags: implementation
Correct Solution:
```
arr = [int(i) for i in input().split()]
arr.sort()
c = 0
for i in range(3):
if arr[i]==arr[i+1]:
c += 1
print(c)
``` | output | 1 | 11,052 | 7 | 22,105 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3 | instruction | 0 | 11,053 | 7 | 22,106 |
Tags: implementation
Correct Solution:
```
l = [int(x) for x in input().split()]
l = set(l)
print(4-len(l))
``` | output | 1 | 11,053 | 7 | 22,107 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3 | instruction | 0 | 11,054 | 7 | 22,108 |
Tags: implementation
Correct Solution:
```
def s(a):
u=set()
u.update(a)
return 4-len(u)
a=map(int,input().split(" "))
print(s(a))
``` | output | 1 | 11,054 | 7 | 22,109 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3 | instruction | 0 | 11,055 | 7 | 22,110 |
Tags: implementation
Correct Solution:
```
colors = list(map(int, input().split(' ')))
print(4-len(list(set(colors))))
``` | output | 1 | 11,055 | 7 | 22,111 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3 | instruction | 0 | 11,056 | 7 | 22,112 |
Tags: implementation
Correct Solution:
```
shoes_coulur =list(map(int,input().split()))
uni_colur =[]
for i in shoes_coulur :
if i not in uni_colur :
uni_colur.append(i)
print(len(shoes_coulur)-len(uni_colur))
``` | output | 1 | 11,056 | 7 | 22,113 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3 | instruction | 0 | 11,057 | 7 | 22,114 |
Tags: implementation
Correct Solution:
```
s=list(map(int,input().split()))
print(len(s)-len(set(s)))
``` | output | 1 | 11,057 | 7 | 22,115 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3 | instruction | 0 | 11,058 | 7 | 22,116 |
Tags: implementation
Correct Solution:
```
a=input().split()
b=len(a)
c=len(set(a))
print(b-c)
``` | output | 1 | 11,058 | 7 | 22,117 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3
Submitted Solution:
```
s = list(map(int, input().split()))
b = set(s)
print(int(len(s)) - len(b))
``` | instruction | 0 | 11,059 | 7 | 22,118 |
Yes | output | 1 | 11,059 | 7 | 22,119 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3
Submitted Solution:
```
s = input().split(" ")
x = []
for i in s:
if i not in x:
x.append(i)
print(4-len(x))
``` | instruction | 0 | 11,060 | 7 | 22,120 |
Yes | output | 1 | 11,060 | 7 | 22,121 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3
Submitted Solution:
```
s = list(map(int, input().split()))
differList = []
for i in s:
if i not in differList:
differList.append(i)
result = 4 - len(differList)
print(result)
``` | instruction | 0 | 11,061 | 7 | 22,122 |
Yes | output | 1 | 11,061 | 7 | 22,123 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3
Submitted Solution:
```
x = list(map(int,input().split()))
q = len(set(x))
print(4-q)
``` | instruction | 0 | 11,062 | 7 | 22,124 |
Yes | output | 1 | 11,062 | 7 | 22,125 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3
Submitted Solution:
```
set1 = set(input())
print(5-len(set1))
``` | instruction | 0 | 11,063 | 7 | 22,126 |
No | output | 1 | 11,063 | 7 | 22,127 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3
Submitted Solution:
```
x = input().split()
d = {}
c = 0
for i in x:
if i in d.keys():
d[i] = d[i] + 1
else:
d[i] = 1
for j in d.values():
if j > 1:
c = c + j
elif j == 1:
c = c + 0
else:
pass
if c == 0:
print("0")
if c == 4:
print("2")
else:
print(c-1)
``` | instruction | 0 | 11,064 | 7 | 22,128 |
No | output | 1 | 11,064 | 7 | 22,129 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3
Submitted Solution:
```
arr = [int(i) for i in input().split()]
arr.sort()
c = 0
for i in range(2):
if arr[i]==arr[i+1]:
c += 1
print(c)
``` | instruction | 0 | 11,065 | 7 | 22,130 |
No | output | 1 | 11,065 | 7 | 22,131 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.
Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.
Input
The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has.
Consider all possible colors indexed with integers.
Output
Print a single integer — the minimum number of horseshoes Valera needs to buy.
Examples
Input
1 7 3 3
Output
1
Input
7 7 7 7
Output
3
Submitted Solution:
```
l = list(map(int,input().split()))
rs = 0
for i in range(len(l)):
if l.count(l[i]) > rs:
rs = l.count(l[i])
print(rs-1)
``` | instruction | 0 | 11,066 | 7 | 22,132 |
No | output | 1 | 11,066 | 7 | 22,133 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Innocentius has a problem — his computer monitor has broken. Now some of the pixels are "dead", that is, they are always black. As consequence, Innocentius can't play the usual computer games. He is recently playing the following game with his younger brother Polycarpus.
Innocentius is touch-typing a program that paints a white square one-pixel wide frame on the black screen. As the monitor is broken, some pixels that should be white remain black. Polycarpus should look at what the program displayed on the screen and guess the position and size of the frame Innocentius has painted. Polycarpus doesn't like the game but Innocentius persuaded brother to play as "the game is good for the imagination and attention".
Help Polycarpus, automatize his part in the gaming process. Write the code that finds such possible square frame that:
* the frame's width is 1 pixel,
* the frame doesn't go beyond the borders of the screen,
* all white pixels of the monitor are located on the frame,
* of all frames that satisfy the previous three conditions, the required frame must have the smallest size.
Formally, a square frame is represented by such pixels of the solid square, that are on the square's border, that is, are not fully surrounded by the other pixels of the square. For example, if the frame's size is d = 3, then it consists of 8 pixels, if its size is d = 2, then it contains 4 pixels and if d = 1, then the frame is reduced to a single pixel.
Input
The first line contains the resolution of the monitor as a pair of integers n, m (1 ≤ n, m ≤ 2000). The next n lines contain exactly m characters each — the state of the monitor pixels at the moment of the game. Character "." (period, ASCII code 46) corresponds to the black pixel, and character "w" (lowercase English letter w) corresponds to the white pixel. It is guaranteed that at least one pixel of the monitor is white.
Output
Print the monitor screen. Represent the sought frame by characters "+" (the "plus" character). The pixels that has become white during the game mustn't be changed. Print them as "w". If there are multiple possible ways to position the frame of the minimum size, print any of them.
If the required frame doesn't exist, then print a single line containing number -1.
Examples
Input
4 8
..w..w..
........
........
..w..w..
Output
..w++w..
..+..+..
..+..+..
..w++w..
Input
5 6
......
.w....
......
..w...
......
Output
......
+w+...
+.+...
++w...
......
Input
2 4
....
.w..
Output
....
.w..
Input
2 6
w..w.w
...w..
Output
-1
Note
In the first sample the required size of the optimal frame equals 4. In the second sample the size of the optimal frame equals 3. In the third sample, the size of the optimal frame is 1. In the fourth sample, the required frame doesn't exist. | instruction | 0 | 11,104 | 7 | 22,208 |
Tags: brute force, constructive algorithms, greedy, implementation
Correct Solution:
```
from itertools import chain
# To draw square: if point isn't 'w', draw '+'
def draw_square(scr, square_a, ymin, xmin):
for i in range(square_a + 1):
if scr[ymin][xmin + i] != 'w':
scr[ymin] = scr[ymin][:xmin + i] + '+' + scr[ymin][xmin + i + 1:]
if scr[ymin + square_a][xmin + i] != 'w':
scr[ymin + square_a] = scr[ymin + square_a][:xmin + i] + '+' + scr[ymin + square_a][xmin + i + 1:]
if scr[ymin + i][xmin] != 'w':
scr[ymin + i] = scr[ymin + i][:xmin] + '+' + scr[ymin + i][xmin + 1:]
if scr[ymin + i][xmin + square_a] != 'w':
scr[ymin + i] = scr[ymin + i][:xmin + square_a] + '+' + scr[ymin + i][xmin + square_a + 1:]
return scr
# To find the side length of a square, and if there is some point beside the edge of a square it'll print '-1'
def find_a(pixel, y, x):
ymax = xmax = 0
ymin = y
xmin = x
ymaxl = []
yminl = []
xmaxl = []
xminl = []
count_pixel = len(pixel) // 2
for i in range(count_pixel):
if ymax < pixel[2 * i]:
ymax = pixel[2 * i]
if ymin > pixel[2 * i]:
ymin = pixel[2 * i]
if xmax < pixel[2 * i + 1]:
xmax = pixel[2 * i + 1]
if xmin > pixel[2 * i + 1]:
xmin = pixel[2 * i + 1]
for i in range(count_pixel):
f = True
if pixel[2 * i] == ymax:
f = False
ymaxl.append(pixel[2 * i])
ymaxl.append(pixel[2 * i + 1])
if pixel[2 * i] == ymin:
f = False
yminl.append(pixel[2 * i])
yminl.append(pixel[2 * i + 1])
if pixel[2 * i + 1] == xmax:
f = False
xmaxl.append(pixel[2 * i])
xmaxl.append(pixel[2 * i + 1])
if pixel[2 * i + 1] == xmin:
f = False
xminl.append(pixel[2 * i])
xminl.append(pixel[2 * i + 1])
# if some point beside the edge of a square: like the 'x'
# 5 7
# .......
# .+++...
# .+x+...
# .www...
# .......
if f:
print('-1')
exit()
return ymax, ymin, xmax, xmin, ymaxl, yminl, xmaxl, xminl
def main():
y, x = map(int, input().split())
scr = []
for i in range(y):
scr.append(input())
pixel = []
# To collect the point info
for i in range(y):
for j in range(x):
if scr[i][j] == 'w':
pixel.append(i)
pixel.append(j)
ymax, ymin, xmax, xmin, ymaxl, yminl, xmaxl, xminl = find_a(pixel, y, x)
count_ymax = len(ymaxl) / 2
count_ymin = len(yminl) / 2
count_xmax = len(xmaxl) / 2
count_xmin = len(xminl) / 2
countx_ymax = ymaxl[1::2].count(xmax) + ymaxl[1::2].count(xmin)
countx_ymin = yminl[1::2].count(xmax) + yminl[1::2].count(xmin)
county_xmax = xmaxl[::2].count(ymax) + xmaxl[::2].count(ymin)
county_xmin = xminl[::2].count(ymax) + xminl[::2].count(ymin)
#print('ymax:%d,ymin:%d,xmax:%d,xmin:%d'%(ymax,ymin,xmax,xmin))
#print(f'ymaxl:\n{ymaxl}\nyminl:\n{yminl}\nxmaxl:\n{xmaxl}\nxminl:\n{xminl}\ncounty_xmax:{county_xmax}\ncounty_xmin:{county_xmin}\ncountx_ymax:{countx_ymax}\ncountx_ymin:{countx_ymin}')
# There are three conditions:
# 1.height > width 2.height < width 3.height == width
# eg: 1.height > width:
# so square_a = height
if ymax - ymin > xmax - xmin:
square_a = ymax - ymin
# if the point form a rectangle:
# 5 7
# .......
# .ww....
# .wx....
# .ww....
# .......
# or
# 5 7
# .......
# .w.....
# .w.....
# .w.....
# .......
if county_xmax < count_xmax and county_xmin < count_xmin:
# 5 7
# .......
# .w++...
# .w.+...
# .w++...
# .......
if xmax == xmin:
if xmin + square_a < x:
xmax = xmin + square_a
elif xmax - square_a >= 0:
xmin = xmax - square_a
else:
print('-1')
exit()
else:
print('-1')
exit()
# if the point from the shape of [ like:
# 5 7
# .......
# .www...
# .w.....
# .www...
# .......
elif county_xmax < count_xmax and county_xmin == count_xmin:
xmin = xmax - square_a
if xmin < 0:
print('-1')
exit()
# if the point from the shape of ] like:
# 5 7
# .......
# .www...
# ...w...
# .www...
# .......
elif county_xmax == count_xmax and county_xmin < count_xmin:
xmax = xmin + square_a
if xmax >= x:
print('-1')
exit()
# if there is some point to make county_xmax == count_xmax and county_xmin == count_xmin like:
# 5 7
# .......
# .w.....
# .......
# ..w....
# .......
elif county_xmax == count_xmax and county_xmin == count_xmin:
if square_a < x:
if xmin + square_a < x:
xmax = xmin + square_a
elif xmax - square_a >= 0:
xmin = xmax - square_a
# sp:
# 5 5
# .w...
# .....
# .....
# .....
# ..w..
else:
xmin = 0
xmax = xmin + square_a
else:
print('-1')
exit()
elif ymax - ymin < xmax - xmin:
square_a = xmax - xmin
if countx_ymax < count_ymax and countx_ymin < count_ymin:
if ymax == ymin:
if ymin + square_a < y:
ymax = ymin + square_a
elif ymax - square_a >= 0:
ymin = ymax - square_a
else:
print('-1')
exit()
else:
print('-1')
exit()
elif countx_ymax < count_ymax and countx_ymin == count_ymin:
ymin = ymax - square_a
if ymin < 0:
print('-1')
exit()
elif countx_ymax == count_ymax and countx_ymin < count_ymin:
ymax = ymin + square_a
if ymax >= y:
print('-1')
exit()
elif countx_ymax == count_ymax and countx_ymin == count_ymin:
if square_a < y:
if ymin + square_a < y:
ymax = ymin + square_a
elif ymax - square_a >= 0:
ymin = ymax -square_a
else:
ymin = 0
ymax = ymin + square_a
else:
print('-1')
exit()
elif ymax - ymin == xmax - xmin:
square_a = xmax - xmin
#print('ymax:%d,ymin:%d,xmax:%d,xmin:%d,a:%d'%(ymax,ymin,xmax,xmin,square_a))
scr = draw_square(scr, square_a, ymin, xmin)
for i in range(y):
print(scr[i])
if __name__ == '__main__':
main()
#while True:
# main()
``` | output | 1 | 11,104 | 7 | 22,209 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Innocentius has a problem — his computer monitor has broken. Now some of the pixels are "dead", that is, they are always black. As consequence, Innocentius can't play the usual computer games. He is recently playing the following game with his younger brother Polycarpus.
Innocentius is touch-typing a program that paints a white square one-pixel wide frame on the black screen. As the monitor is broken, some pixels that should be white remain black. Polycarpus should look at what the program displayed on the screen and guess the position and size of the frame Innocentius has painted. Polycarpus doesn't like the game but Innocentius persuaded brother to play as "the game is good for the imagination and attention".
Help Polycarpus, automatize his part in the gaming process. Write the code that finds such possible square frame that:
* the frame's width is 1 pixel,
* the frame doesn't go beyond the borders of the screen,
* all white pixels of the monitor are located on the frame,
* of all frames that satisfy the previous three conditions, the required frame must have the smallest size.
Formally, a square frame is represented by such pixels of the solid square, that are on the square's border, that is, are not fully surrounded by the other pixels of the square. For example, if the frame's size is d = 3, then it consists of 8 pixels, if its size is d = 2, then it contains 4 pixels and if d = 1, then the frame is reduced to a single pixel.
Input
The first line contains the resolution of the monitor as a pair of integers n, m (1 ≤ n, m ≤ 2000). The next n lines contain exactly m characters each — the state of the monitor pixels at the moment of the game. Character "." (period, ASCII code 46) corresponds to the black pixel, and character "w" (lowercase English letter w) corresponds to the white pixel. It is guaranteed that at least one pixel of the monitor is white.
Output
Print the monitor screen. Represent the sought frame by characters "+" (the "plus" character). The pixels that has become white during the game mustn't be changed. Print them as "w". If there are multiple possible ways to position the frame of the minimum size, print any of them.
If the required frame doesn't exist, then print a single line containing number -1.
Examples
Input
4 8
..w..w..
........
........
..w..w..
Output
..w++w..
..+..+..
..+..+..
..w++w..
Input
5 6
......
.w....
......
..w...
......
Output
......
+w+...
+.+...
++w...
......
Input
2 4
....
.w..
Output
....
.w..
Input
2 6
w..w.w
...w..
Output
-1
Note
In the first sample the required size of the optimal frame equals 4. In the second sample the size of the optimal frame equals 3. In the third sample, the size of the optimal frame is 1. In the fourth sample, the required frame doesn't exist. | instruction | 0 | 11,105 | 7 | 22,210 |
Tags: brute force, constructive algorithms, greedy, implementation
Correct Solution:
```
#!/usr/bin/python3
def readln(): return list(map(int, input().split()))
import sys
def exit():
print(-1)
sys.exit()
n, m = readln()
mon = [list(input()) for _ in range(n)]
hor = [i for i in range(n) if mon[i] != ['.'] * m]
rmon = list(zip(*mon))
ver = [j for j in range(m) if rmon[j] != ('.',) * n]
mini = hor[0]
maxi = hor[-1]
minj = ver[0]
maxj = ver[-1]
cnt_in = len([1 for i in range(mini + 1, maxi) for j in range(minj + 1, maxj) if mon[i][j] == 'w'])
cnt_l = len([1 for i in range(mini + 1, maxi) if mon[i][minj] == 'w'])
cnt_r = len([1 for i in range(mini + 1, maxi) if mon[i][maxj] == 'w'])
cnt_d = len([1 for j in range(minj + 1, maxj) if mon[mini][j] == 'w'])
cnt_u = len([1 for j in range(minj + 1, maxj) if mon[maxi][j] == 'w'])
if cnt_in:
exit()
if maxi - mini < maxj - minj:
k = maxj - minj + 1
if maxi == mini and cnt_d:
if mini >= k - 1:
mini -= k - 1
elif maxi + k - 1 < n:
maxi += k - 1
else:
exit()
else:
if not cnt_d:
mini = max(0, maxi - k + 1)
if maxi - maxi + 1 != k and not cnt_u:
maxi = min(mini + k - 1, n - 1)
if maxi - mini + 1 != k:
exit()
else:
k = maxi - mini + 1
if maxj == minj and cnt_l:
if minj >= k - 1:
minj -= k - 1
elif maxj + k - 1 < m:
maxj += k - 1
else:
exit()
else:
if not cnt_l:
minj = max(0, maxj - k + 1)
if maxj - minj + 1 != k and not cnt_r:
maxj = min(minj + k - 1, m - 1)
if maxj - minj + 1 != k:
exit()
for i in range(mini, maxi + 1):
if mon[i][minj] == '.':
mon[i][minj] = '+'
for i in range(mini, maxi + 1):
if mon[i][maxj] == '.':
mon[i][maxj] = '+'
for j in range(minj, maxj + 1):
if mon[mini][j] == '.':
mon[mini][j] = '+'
for j in range(minj, maxj + 1):
if mon[maxi][j] == '.':
mon[maxi][j] = '+'
print('\n'.join([''.join(row) for row in mon]))
``` | output | 1 | 11,105 | 7 | 22,211 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1. | instruction | 0 | 11,205 | 7 | 22,410 |
Tags: dp
Correct Solution:
```
import sys
from math import *
def input():
return sys.stdin.readline().strip()
def inputy():
return int(input())
def input_l():
return map(int, input().split())
n = inputy()
c = list(input_l())
dp = [[1e9]*n for i in range(n)]
for i in range(n):
dp[i][i] = 1
for i in range(n-1):
dp[i][i+1] = 1 if c[i] == c[i+1] else 2
for i in range(2,n):
for j in range(n-i):
z = dp[j+1][j+i]+1
if c[j] == c[j+1]:
z = min(z, dp[j+2][j+i] + 1)
for k in range(j+2,j+i):
if c[j] == c[k]:
z = min(z, dp[j][k] + dp[k+1][j+i])
if c[j] == c[j+i]:
z = min(z, dp[j+1][j+i-1])
dp[j][j+i] = z
print(dp[0][n-1])
``` | output | 1 | 11,205 | 7 | 22,411 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1. | instruction | 0 | 11,207 | 7 | 22,414 |
Tags: dp
Correct Solution:
```
def main():
n, l = int(input()), list(map(int, input().split()))
dp = [[0] * n for _ in range(n)]
for i in range(n):
dp[i][i] = 1
for i in range(n - 1, 0, -1):
ci, row = l[i - 1], dp[i]
for j in range(i, n):
tmp = [1 + row[j]]
if ci == l[i]:
tmp.append(1 + dp[i + 1][j] if i + 1 < n else 1)
for k in range(i + 1, j):
if ci == l[k]:
tmp.append(row[k - 1] + dp[k + 1][j])
if ci == l[j] and j > i:
tmp.append(row[j - 1])
dp[i - 1][j] = min(tmp)
print(dp[0][n - 1])
if __name__ == '__main__':
main()
``` | output | 1 | 11,207 | 7 | 22,415 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1. | instruction | 0 | 11,208 | 7 | 22,416 |
Tags: dp
Correct Solution:
```
n = int(input())
C = list(map(int, input().split()))
dp = [[0]*n for _ in range(n)]
for i in range(n) :
dp[i][i] = 1
for i in range(n-2, -1, -1) :
for j in range(i+1, n) :
dp[i][j] = 1 + dp[i+1][j]
if C[i] == C[i+1] : dp[i][j] = min( dp[i][j], 1 + (dp[i+2][j] if i+2 < n else 0) )
for k in range(i+2, j) :
if C[i] == C[k] : dp[i][j] = min( dp[i][j], dp[i+1][k-1] + dp[k+1][j] )
if C[i] == C[j] and j-i > 1:
dp[i][j] = min( dp[i][j], dp[i+1][j-1] )
print( dp[0][n-1] )
``` | output | 1 | 11,208 | 7 | 22,417 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1. | instruction | 0 | 11,209 | 7 | 22,418 |
Tags: dp
Correct Solution:
```
# ---------------------------iye ha aam zindegi---------------------------------------------
import math
import random
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
import threading
from collections import defaultdict
# threading.stack_size(10**8)
mod = 10 ** 9 + 7
mod1 = 998244353
# ------------------------------warmup----------------------------
import os
import sys
from io import BytesIO, IOBase
# sys.setrecursionlimit(300000)
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")
# -------------------game starts now----------------------------------------------------import math
class TreeNode:
def __init__(self, k, v):
self.key = k
self.value = v
self.left = None
self.right = None
self.parent = None
self.height = 1
self.num_left = 1
self.num_total = 1
class AvlTree:
def __init__(self):
self._tree = None
def add(self, k, v):
if not self._tree:
self._tree = TreeNode(k, v)
return
node = self._add(k, v)
if node:
self._rebalance(node)
def _add(self, k, v):
node = self._tree
while node:
if k < node.key:
if node.left:
node = node.left
else:
node.left = TreeNode(k, v)
node.left.parent = node
return node.left
elif node.key < k:
if node.right:
node = node.right
else:
node.right = TreeNode(k, v)
node.right.parent = node
return node.right
else:
node.value = v
return
@staticmethod
def get_height(x):
return x.height if x else 0
@staticmethod
def get_num_total(x):
return x.num_total if x else 0
def _rebalance(self, node):
n = node
while n:
lh = self.get_height(n.left)
rh = self.get_height(n.right)
n.height = max(lh, rh) + 1
balance_factor = lh - rh
n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right)
n.num_left = 1 + self.get_num_total(n.left)
if balance_factor > 1:
if self.get_height(n.left.left) < self.get_height(n.left.right):
self._rotate_left(n.left)
self._rotate_right(n)
elif balance_factor < -1:
if self.get_height(n.right.right) < self.get_height(n.right.left):
self._rotate_right(n.right)
self._rotate_left(n)
else:
n = n.parent
def _remove_one(self, node):
"""
Side effect!!! Changes node. Node should have exactly one child
"""
replacement = node.left or node.right
if node.parent:
if AvlTree._is_left(node):
node.parent.left = replacement
else:
node.parent.right = replacement
replacement.parent = node.parent
node.parent = None
else:
self._tree = replacement
replacement.parent = None
node.left = None
node.right = None
node.parent = None
self._rebalance(replacement)
def _remove_leaf(self, node):
if node.parent:
if AvlTree._is_left(node):
node.parent.left = None
else:
node.parent.right = None
self._rebalance(node.parent)
else:
self._tree = None
node.parent = None
node.left = None
node.right = None
def remove(self, k):
node = self._get_node(k)
if not node:
return
if AvlTree._is_leaf(node):
self._remove_leaf(node)
return
if node.left and node.right:
nxt = AvlTree._get_next(node)
node.key = nxt.key
node.value = nxt.value
if self._is_leaf(nxt):
self._remove_leaf(nxt)
else:
self._remove_one(nxt)
self._rebalance(node)
else:
self._remove_one(node)
def get(self, k):
node = self._get_node(k)
return node.value if node else -1
def _get_node(self, k):
if not self._tree:
return None
node = self._tree
while node:
if k < node.key:
node = node.left
elif node.key < k:
node = node.right
else:
return node
return None
def get_at(self, pos):
x = pos + 1
node = self._tree
while node:
if x < node.num_left:
node = node.left
elif node.num_left < x:
x -= node.num_left
node = node.right
else:
return (node.key, node.value)
raise IndexError("Out of ranges")
@staticmethod
def _is_left(node):
return node.parent.left and node.parent.left == node
@staticmethod
def _is_leaf(node):
return node.left is None and node.right is None
def _rotate_right(self, node):
if not node.parent:
self._tree = node.left
node.left.parent = None
elif AvlTree._is_left(node):
node.parent.left = node.left
node.left.parent = node.parent
else:
node.parent.right = node.left
node.left.parent = node.parent
bk = node.left.right
node.left.right = node
node.parent = node.left
node.left = bk
if bk:
bk.parent = node
node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
node.num_left = 1 + self.get_num_total(node.left)
def _rotate_left(self, node):
if not node.parent:
self._tree = node.right
node.right.parent = None
elif AvlTree._is_left(node):
node.parent.left = node.right
node.right.parent = node.parent
else:
node.parent.right = node.right
node.right.parent = node.parent
bk = node.right.left
node.right.left = node
node.parent = node.right
node.right = bk
if bk:
bk.parent = node
node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
node.num_left = 1 + self.get_num_total(node.left)
@staticmethod
def _get_next(node):
if not node.right:
return node.parent
n = node.right
while n.left:
n = n.left
return n
# -----------------------------------------------binary seacrh tree---------------------------------------
class SegmentTree1:
def __init__(self, data, default=2 ** 30, func=lambda a, b: min(a, b)):
"""initialize the segment tree with data"""
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
if start == stop:
return self.__getitem__(start)
stop += 1
start += self._size
stop += self._size
res = self._default
while start < stop:
if start & 1:
res = self._func(res, self.data[start])
start += 1
if stop & 1:
stop -= 1
res = self._func(res, self.data[stop])
start >>= 1
stop >>= 1
return res
def __repr__(self):
return "SegmentTree({0})".format(self.data)
# -------------------game starts now----------------------------------------------------import math
class SegmentTree:
def __init__(self, data, default=0, func=lambda a, b: a + b):
"""initialize the segment tree with data"""
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
if start == stop:
return self.__getitem__(start)
stop += 1
start += self._size
stop += self._size
res = self._default
while start < stop:
if start & 1:
res = self._func(res, self.data[start])
start += 1
if stop & 1:
stop -= 1
res = self._func(res, self.data[stop])
start >>= 1
stop >>= 1
return res
def __repr__(self):
return "SegmentTree({0})".format(self.data)
# -------------------------------iye ha chutiya zindegi-------------------------------------
class Factorial:
def __init__(self, MOD):
self.MOD = MOD
self.factorials = [1, 1]
self.invModulos = [0, 1]
self.invFactorial_ = [1, 1]
def calc(self, n):
if n <= -1:
print("Invalid argument to calculate n!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.factorials):
return self.factorials[n]
nextArr = [0] * (n + 1 - len(self.factorials))
initialI = len(self.factorials)
prev = self.factorials[-1]
m = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = prev * i % m
self.factorials += nextArr
return self.factorials[n]
def inv(self, n):
if n <= -1:
print("Invalid argument to calculate n^(-1)")
print("n must be non-negative value. But the argument was " + str(n))
exit()
p = self.MOD
pi = n % p
if pi < len(self.invModulos):
return self.invModulos[pi]
nextArr = [0] * (n + 1 - len(self.invModulos))
initialI = len(self.invModulos)
for i in range(initialI, min(p, n + 1)):
next = -self.invModulos[p % i] * (p // i) % p
self.invModulos.append(next)
return self.invModulos[pi]
def invFactorial(self, n):
if n <= -1:
print("Invalid argument to calculate (n^(-1))!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.invFactorial_):
return self.invFactorial_[n]
self.inv(n) # To make sure already calculated n^-1
nextArr = [0] * (n + 1 - len(self.invFactorial_))
initialI = len(self.invFactorial_)
prev = self.invFactorial_[-1]
p = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p
self.invFactorial_ += nextArr
return self.invFactorial_[n]
class Combination:
def __init__(self, MOD):
self.MOD = MOD
self.factorial = Factorial(MOD)
def ncr(self, n, k):
if k < 0 or n < k:
return 0
k = min(k, n - k)
f = self.factorial
return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD
# --------------------------------------iye ha combinations ka zindegi---------------------------------
def powm(a, n, m):
if a == 1 or n == 0:
return 1
if n % 2 == 0:
s = powm(a, n // 2, m)
return s * s % m
else:
return a * powm(a, n - 1, m) % m
# --------------------------------------iye ha power ka zindegi---------------------------------
def sort_list(list1, list2):
zipped_pairs = zip(list2, list1)
z = [x for _, x in sorted(zipped_pairs)]
return z
# --------------------------------------------------product----------------------------------------
def product(l):
por = 1
for i in range(len(l)):
por *= l[i]
return por
# --------------------------------------------------binary----------------------------------------
def binarySearchCount(arr, n, key):
left = 0
right = n - 1
count = 0
while (left <= right):
mid = int((right + left) / 2)
# Check if middle element is
# less than or equal to key
if (arr[mid] < key):
count = mid + 1
left = mid + 1
# If key is smaller, ignore right half
else:
right = mid - 1
return count
# --------------------------------------------------binary----------------------------------------
def countdig(n):
c = 0
while (n > 0):
n //= 10
c += 1
return c
def binary(x, length):
y = bin(x)[2:]
return y if len(y) >= length else "0" * (length - len(y)) + y
def countGreater(arr,n, k):
l = 0
r = n - 1
# Stores the index of the left most element
# from the array which is greater than k
leftGreater = n
# Finds number of elements greater than k
while (l <= r):
m = int(l + (r - l) / 2)
if (arr[m] > k):
leftGreater = m
r = m - 1
# If mid element is less than
# or equal to k update l
else:
l = m + 1
# Return the count of elements
# greater than k
return (n - leftGreater)
# --------------------------------------------------binary------------------------------------
class TrieNode:
def __init__(self):
self.children = [None] * 26
self.isEndOfWord = False
class Trie:
def __init__(self):
self.root = self.getNode()
def getNode(self):
return TrieNode()
def _charToIndex(self, ch):
return ord(ch) - ord('a')
def insert(self, key):
pCrawl = self.root
length = len(key)
for level in range(length):
index = self._charToIndex(key[level])
if not pCrawl.children[index]:
pCrawl.children[index] = self.getNode()
pCrawl = pCrawl.children[index]
pCrawl.isEndOfWord = True
def search(self, key):
pCrawl = self.root
length = len(key)
for level in range(length):
index = self._charToIndex(key[level])
if not pCrawl.children[index]:
return False
pCrawl = pCrawl.children[index]
return pCrawl != None and pCrawl.isEndOfWord
# -----------------------------------------trie---------------------------------
def merge(arr, temp, left, mid, right):
inv_count = 0
i = left # i is index for left subarray*/
j = mid # i is index for right subarray*/
k = left # i is index for resultant merged subarray*/
while ((i <= mid - 1) and (j <= right)):
if (arr[i] <= arr[j]):
temp[k] = arr[i]
k += 1
i += 1
else:
temp[k] = arr[j]
k += 1
j += 1
inv_count = inv_count + (mid - i)
while (i <= mid - 1):
temp[k] = arr[i]
k += 1
i += 1
while (j <= right):
temp[k] = arr[j]
k += 1
j += 1
# Copy back the merged elements to original array*/
for i in range(left, right + 1, 1):
arr[i] = temp[i]
return inv_count
def _mergeSort(arr, temp, left, right):
inv_count = 0
if (right > left):
mid = int((right + left) / 2)
inv_count = _mergeSort(arr, temp, left, mid)
inv_count += _mergeSort(arr, temp, mid + 1, right)
inv_count += merge(arr, temp, left, mid + 1, right)
return inv_count
def countSwaps(arr, n):
temp = [0 for i in range(n)]
return _mergeSort(arr, temp, 0, n - 1)
#-----------------------------------------adjcent swap required------------------------------
def minSwaps(arr):
n = len(arr)
arrpos = [*enumerate(arr)]
arrpos.sort(key=lambda it: it[1])
vis = {k: False for k in range(n)}
ans = 0
for i in range(n):
if vis[i] or arrpos[i][0] == i:
continue
cycle_size = 0
j = i
while not vis[j]:
vis[j] = True
j = arrpos[j][0]
cycle_size += 1
if cycle_size > 0:
ans += (cycle_size - 1)
return ans
#----------------------swaps required----------------------------
class Node:
def __init__(self, data):
self.data = data
self.count = 0
self.left = None # left node for 0
self.right = None # right node for 1
class BinaryTrie:
def __init__(self):
self.root = Node(0)
def insert(self, pre_xor):
self.temp = self.root
for i in range(31, -1, -1):
val = pre_xor & (1 << i)
if val:
if not self.temp.right:
self.temp.right = Node(0)
self.temp = self.temp.right
self.temp.count += 1
if not val:
if not self.temp.left:
self.temp.left = Node(0)
self.temp = self.temp.left
self.temp.count += 1
self.temp.data = pre_xor
def query(self, xor):
self.temp = self.root
for i in range(31, -1, -1):
val = xor & (1 << i)
if not val:
if self.temp.left and self.temp.left.count > 0:
self.temp = self.temp.left
elif self.temp.right:
self.temp = self.temp.right
else:
if self.temp.right and self.temp.right.count > 0:
self.temp = self.temp.right
elif self.temp.left:
self.temp = self.temp.left
self.temp.count -= 1
return xor ^ self.temp.data
# -------------------------bin trie-------------------------------------------
n=int(input())
l=list(map(int,input().split()))
dp=[[9999999999999 for i in range(n+1)]for j in range(n+1)]
for i in range(n+1):
dp[i][i]=1
for j in range(i):
dp[i][j]=0
for i in range(n):
for j in range(i-1,-1,-1):
if j!=i-1 and l[j]==l[i]:
dp[j][i]=min(dp[j][i],dp[j+1][i-1])
if l[j]==l[j+1]:
dp[j][i]=min(1+dp[j+2][i],dp[j][i])
dp[j][i]=min(dp[j][i],dp[j][i-1]+1,dp[j+1][i]+1)
for k in range(j+2,i):
if l[j]==l[k]:
dp[j][i]=min(dp[j][i],dp[j+1][k-1]+dp[k+1][i])
print(dp[0][n-1])
``` | output | 1 | 11,209 | 7 | 22,419 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1. | instruction | 0 | 11,211 | 7 | 22,422 |
Tags: dp
Correct Solution:
```
def main():
n, l = int(input()), list(map(int, input().split()))
dp = [[0] * n for _ in range(n + 1)]
for le in range(1, n + 1):
for lo, hi in zip(range(n), range(le - 1, n)):
row, c = dp[lo], l[lo]
if le == 1:
row[hi] = 1
else:
tmp = [1 + dp[lo + 1][hi]]
if c == l[lo + 1]:
tmp.append(1 + dp[lo + 2][hi])
for match in range(lo + 2, hi + 1):
if c == l[match]:
tmp.append(dp[lo + 1][match - 1] + dp[match + 1][hi])
row[hi] = min(tmp)
print(dp[0][n - 1])
if __name__ == '__main__':
main()
``` | output | 1 | 11,211 | 7 | 22,423 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
Submitted Solution:
```
n = int(input())
t = tuple(map(int, input().split()))
m = [[1] * n for i in range(n + 1)]
for d in range(2, n + 1):
for i in range(n - d + 1):
m[d][i] = min(m[x][i] + m[d - x][i + x] for x in range(1, d))
if t[i] == t[i + d - 1]: m[d][i] = min(m[d][i], m[d - 2][i + 1])
print(m[n][0])
``` | instruction | 0 | 11,214 | 7 | 22,428 |
Yes | output | 1 | 11,214 | 7 | 22,429 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
Submitted Solution:
```
from sys import stdin
n=int(input())
s=list(map(int,stdin.readline().strip().split()))
dp=[[-1 for i in range(501)] for j in range(500)]
def sol(i,j):
if i>j:
return 0
if i==j:
return 1
if dp[i][j]!=-1:
return dp[i][j]
x=502
if s[i]==s[i+1]:
x=min(x,sol(i+2,j)+1)
for k in range(i+2,j+1):
if s[i]==s[k]:
x=min(x,sol(1+i,k-1)+sol(k+1,j))
dp[i][j]=min(1+sol(i+1,j),x)
return dp[i][j]
print(sol(0,n-1))
``` | instruction | 0 | 11,215 | 7 | 22,430 |
Yes | output | 1 | 11,215 | 7 | 22,431 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
Submitted Solution:
```
n = int(input())
dp = [[None for j in range(n)] for i in range(n)]
cl = input().split(' ')
cl = [int(color) for color in cl]
for bias in range(0, n):
for l in range(n-bias):
r = l + bias
loc = float('+inf')
if bias == 0:
dp[l][r] = 1
elif bias == 1:
if cl[l] == cl[r]:
dp[l][r] = 1
else:
dp[l][r] = 2
else:
if cl[l] == cl[r]:
loc = dp[l+1][r-1]
for k in range(l, r):
loc = min(loc, dp[l][k]+dp[k+1][r])
dp[l][r] = loc
print(dp[0][n-1])
``` | instruction | 0 | 11,216 | 7 | 22,432 |
Yes | output | 1 | 11,216 | 7 | 22,433 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
Submitted Solution:
```
import sys
from math import *
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
n = mint()
c = list(mints())
dp = [[1e9]*n for i in range(n)]
for i in range(n):
dp[i][i] = 1
for i in range(n-1):
dp[i][i+1] = 1 if c[i] == c[i+1] else 2
for i in range(2,n):
for j in range(n-i):
z = dp[j+1][j+i]+1
if c[j] == c[j+1]:
z = min(z, dp[j+2][j+i] + 1)
for k in range(j+2,j+i):
if c[j] == c[k]:
z = min(z, dp[j][k] + dp[k+1][j+i])
if c[j] == c[j+i]:
z = min(z, dp[j+1][j+i-1])
dp[j][j+i] = z
#print(*dp, sep='\n')
print(dp[0][n-1])
``` | instruction | 0 | 11,217 | 7 | 22,434 |
Yes | output | 1 | 11,217 | 7 | 22,435 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
Submitted Solution:
```
from sys import stdin
n=int(input())
s=list(map(int,stdin.readline().strip().split()))
dp=[[-1 for i in range(501)] for j in range(500)]
dp1=[[False for i in range(501)] for j in range(500)]
suf=[1 for i in range(n)]
pref=[1 for i in range(n)]
for i in range(n-1,-1,-1):
for j in range(i+1,n):
if s[i]==s[j] and (j-i<=2 or dp1[i+1][j-1]==True):
dp1[i][j]=True
suf[i]=j-i+1
pref[j]=max(pref[j],suf[i])
def sol(i,j):
if i>j:
return 1
if i==j:
return 1
if dp[i][j]!=-1:
return dp[i][j]
if s[i]==s[j]:
dp[i][j]=sol(i+1,j-1)
return dp[i][j]
dp[i][j]=min(2+sol(i+suf[i],j-pref[j]),1+sol(i,j-pref[j]),1+sol(i+suf[i],j))
return dp[i][j]
print(sol(0,n-1))
``` | instruction | 0 | 11,218 | 7 | 22,436 |
No | output | 1 | 11,218 | 7 | 22,437 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
Submitted Solution:
```
from sys import stdin,stdout
for _ in range(1):#(stdin.readline())):
n=int(stdin.readline())
# n,m=list(map(int,stdin.readline().split()))
a=list(map(int,stdin.readline().split()))
dp=[[0 for _ in range(n)] for _ in range(n)]
for sz in range(n):
for i in range(n-sz):
j=i+sz
# print(i,j)
if sz==0:dp[i][j]=1
elif sz==1:dp[i][j]=1+int(a[i]!=a[j])
elif a[i]==a[j]:dp[i][j]=dp[i+1][j-1]
else:
v=n
for k in range(i+1,j):
v=min(v,dp[i][k]+dp[k+1][j])
dp[i][j]=v
# print(*dp,sep='\n')
print(dp[0][n-1])
``` | instruction | 0 | 11,219 | 7 | 22,438 |
No | output | 1 | 11,219 | 7 | 22,439 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
Submitted Solution:
```
def gems(n, c):
c = "#{}#".format('#'.join(c))
n = 2*n + 1
T = [[None for i in range(n)] for j in range(n)]
def g(i, j): # c[i+1] is the first character, c[j-1] is the last
if j - i <= 2:
return 1
if T[i][j] is not None:
return T[i][j]
if c[i+1] == c[j-1]:
opt = g(i+2, j-2)
else:
opt = min((g(i, r) + g(r, j)) for r in range(i+2, j, 2))
T[i][j] = opt
return opt
return g(0, n-1)
n = int(input())
c = input().split()
print(gems(n, c))
``` | instruction | 0 | 11,220 | 7 | 22,440 |
No | output | 1 | 11,220 | 7 | 22,441 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.
In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?
Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.
The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.
Output
Print a single integer — the minimum number of seconds needed to destroy the entire line.
Examples
Input
3
1 2 1
Output
1
Input
3
1 2 3
Output
3
Input
7
1 4 4 2 3 2 1
Output
2
Note
In the first sample, Genos can destroy the entire line in one second.
In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.
In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.
Submitted Solution:
```
# -*- coding:utf-8 -*-
"""
created by shuangquan.huang at 1/9/20
"""
import collections
import time
import os
import sys
import bisect
import heapq
from typing import List
def solve(N, A):
dp = [[N for _ in range(N+1)] for _ in range(N)]
for i in range(N):
dp[i][0] = 0
dp[i][1] = 1
for l in range(2, N+1):
for i in range(N-l+1):
for j in range(1, l):
dp[i][l] = min(dp[i][l], dp[i][j] + dp[i+j][l-j])
# j = 0
# while j < l // 2 and A[i+j] == A[i+l-j-1]:
# j += 1
# if j >= l // 2:
# dp[i][l] = min(dp[i][l], 1)
# elif j > 0:
# dp[i][l] = min(dp[i][l], 1 + dp[i+j][l-2*j])
# for k in range(i+j, i+l-j):
# dp[i][l] = min(dp[i][l], 1 + dp[i+j][k-i-j] + dp[k][l - 2 * j-1])
if i + 1 < N and A[i] == A[i+l-1]:
dp[i][l] = max(1, dp[i+1][l-2])
else:
dp[i][l] = min(dp[i][l], 1 + dp[i][l-1])
if i + 1 < N:
dp[i][l] = min(dp[i][l], 1 + dp[i+1][l-1])
return dp[0][N]
N = int(input())
A = [int(x) for x in input().split()]
print(solve(N, A))
``` | instruction | 0 | 11,221 | 7 | 22,442 |
No | output | 1 | 11,221 | 7 | 22,443 |
Provide tags and a correct Python 3 solution for this coding contest problem.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa | instruction | 0 | 11,321 | 7 | 22,642 |
Tags: constructive algorithms, implementation
Correct Solution:
```
a=int(input())
if a%2==0:
print("aabb"*(a//4)+"aabb"[:a%4])
print("ccdd" * (a // 4) + "ccdd"[:a % 4])
a-=2
print('z'+"eeff"*(a//4)+"eeff"[:a%4]+'x')
print('z' + "iijj" * (a // 4) + "iijj"[:a % 4] + 'x')
else:
a-=1
print("z"+"aabb"*(a//4)+"aabb"[:a%4])
print("z"+"ccdd"*(a//4)+"ccdd"[:a%4])
print("eeff"*(a//4)+"eeff"[:a%4]+"x")
print("gghh"*(a//4)+"gghh"[:a%4]+"x")
``` | output | 1 | 11,321 | 7 | 22,643 |
Provide tags and a correct Python 3 solution for this coding contest problem.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa | instruction | 0 | 11,322 | 7 | 22,644 |
Tags: constructive algorithms, implementation
Correct Solution:
```
n = int(input())
k = n // 4
if n % 2:
if (n - 1) % 4:
a = 'aabb' * k + 'aac'
b = 'bbaa' * k + 'bbc'
c = 'dee' + 'ffee' * k
d = 'dff' + 'eeff' * k
else:
a = 'aabb' * k + 'c'
b = 'bbaa' * k + 'c'
c = 'd' + 'ffee' * k
d = 'd' + 'eeff' * k
print('\n'.join((a, b, c, d)))
else:
if n % 4:
a = 'aabb' * k + 'aa'
b = 'c' + 'ddcc' * k + 'd'
c = 'c' + 'eeff' * k + 'd'
else:
a = 'aabb' * k
b = 'c' + 'ddcc' * (k - 1) + 'ddc'
c = 'c' + 'eeff' * (k - 1) + 'eec'
print('\n'.join((a, b, c, a)))
``` | output | 1 | 11,322 | 7 | 22,645 |
Provide tags and a correct Python 3 solution for this coding contest problem.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa | instruction | 0 | 11,323 | 7 | 22,646 |
Tags: constructive algorithms, implementation
Correct Solution:
```
from sys import stdin
a=int(stdin.readline())
if a%2==0:
for b in range(0,int(a/2)):
if b%2==0:
if b==int(a/2)-1:
print('aa')
else:
print('aa',end='')
else:
if b==int(a/2)-1:
print('bb')
else:
print('bb', end='')
print('c',end='')
for d in range(0,int(a/2)-1):
if d%2==0:
print('dd',end='')
else:
print('ee', end='')
print('f')
print('c',end='')
for d in range(0, int(a/2)-1):
if d % 2 == 0:
print('hh', end='')
else:
print('ii', end='')
print('f')
for b in range(0,int(a/2)):
if b%2==0:
if b==int(a/2)-1:
print('aa')
else:
print('aa',end='')
else:
if b==int(a/2)-1:
print('bb')
else:
print('bb', end='')
else:
for b in range(0,int((a-1)/2)):
if b%2==0:
print('aa',end='')
else:
print('bb', end='')
print('c')
for b in range(0,int((a-1)/2)):
if b%2==0:
print('ee',end='')
else:
print('ff', end='')
print('c')
if a==1:
print('d')
else:
print('d',end='')
for b in range(0,int((a-1)/2)):
if b%2==0:
if b==int((a-1)/2)-1:
print('bb')
else:
print('bb',end='')
else:
if b==int((a-1)/2)-1:
print('aa')
else:
print('aa', end='')
if a==1:
print('d')
else:
print('d',end='')
for b in range(0,int((a-1)/2)):
if b%2==0:
if b==int((a-1)/2)-1:
print('ee')
else:
print('ee',end='')
else:
if b==int((a-1)/2)-1:
print('ff')
else:
print('ff', end='')
``` | output | 1 | 11,323 | 7 | 22,647 |
Provide tags and a correct Python 3 solution for this coding contest problem.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa | instruction | 0 | 11,324 | 7 | 22,648 |
Tags: constructive algorithms, implementation
Correct Solution:
```
n = int(input())
field = [[None] * n for _ in range(4)]
for i in range(0, n - 1, 2):
if i > 0 and field[0][i - 1] == 'a':
field[0][i] = field[0][i + 1] = 'b'
field[1][i] = field[1][i + 1] = 'd'
else:
field[0][i] = field[0][i + 1] = 'a'
field[1][i] = field[1][i + 1] = 'c'
for i in range(1, n - 1, 2):
if i > 0 and field[2][i - 1] == 'e':
field[2][i] = field[2][i + 1] = 'f'
field[3][i] = field[3][i + 1] = 'h'
else:
field[2][i] = field[2][i + 1] = 'e'
field[3][i] = field[3][i + 1] = 'g'
field[2][0] = field[3][0] = 'j'
if n % 2 == 0:
field[2][n - 1] = field[3][n - 1] = 'i'
else:
field[0][n - 1] = field[1][n - 1] = 'i'
for line in field:
print(''.join(line))
``` | output | 1 | 11,324 | 7 | 22,649 |
Provide tags and a correct Python 3 solution for this coding contest problem.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa | instruction | 0 | 11,325 | 7 | 22,650 |
Tags: constructive algorithms, implementation
Correct Solution:
```
import string
n = int(input())
l = 0
def get_next_l(exclusions = []):
global l
a = string.ascii_lowercase[l]
while a in exclusions:
l = (l + 1) % 26
a = string.ascii_lowercase[l]
l = (l + 1) % 26
return a
rows = [[""] * n for _ in range(4)]
if n == 1:
rows[0][0] = rows[1][0] = get_next_l()
rows[2][0] = rows[3][0] = get_next_l()
elif n == 2:
for i in range(4):
rows[i] = get_next_l() * 2
elif n % 2 == 0:
for i in range(0, n, 2):
rows[0][i] = rows[0][i+1] = get_next_l()
front = get_next_l(rows[0][0])
rows[1][0] = front
for i in range(1, n-1, 2):
rows[1][i] = rows[1][i+1] = get_next_l([rows[2][i-1]] + rows[1][i:i+2])
end = get_next_l(rows[0][-1] + rows[1][-2])
rows[1][-1] = end
rows[2][0] = front
for i in range(1, n-1, 2):
rows[2][i] = rows[2][i+1] = get_next_l([rows[2][i-1]] + rows[1][i:i+2] + [end])
rows[2][-1] = end
for i in range(0, n, 2):
rows[3][i] = rows[3][i+1] = get_next_l([rows[3][i-1]] + rows[2][i:i+2])
else:
for i in range(0, n-1, 2):
rows[0][i] = rows[0][i+1] = get_next_l()
end = get_next_l()
rows[0][-1] = end
for i in range(0, n-1, 2):
rows[1][i] = rows[1][i+1] = get_next_l([rows[1][i-1]] + rows[1][i:i+2] + [end])
rows[1][-1] = end
front = get_next_l(rows[1][0])
rows[2][0] = front
for i in range(1, n, 2):
rows[2][i] = rows[2][i+1] = get_next_l([rows[2][i-1]] + rows[1][i:i+2])
rows[3][0] = front
for i in range(1, n, 2):
rows[3][i] = rows[3][i+1] = get_next_l([rows[3][i-1]] + rows[2][i:i+2])
print("\n".join("".join(r) for r in rows))
``` | output | 1 | 11,325 | 7 | 22,651 |
Provide tags and a correct Python 3 solution for this coding contest problem.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa | instruction | 0 | 11,326 | 7 | 22,652 |
Tags: constructive algorithms, implementation
Correct Solution:
```
def computeTiling(n):
if n == 1:
print("a\na\nf\nf")
return
for tiling in generateRowTilings(n):
print("".join(tiling))
def generateRowTilings(n):
for (rowNum, firstTile, pattern) in generateRowTilingPatterns(n):
yield makeRowTiling(rowNum, firstTile, pattern, n)
def generateRowTilingPatterns(n):
rows = (1, 2, 3, 4)
firstTiles = ('a', 'a', 'd', 'e')
patterns = ('bbcc', 'ccbb', 'deed', 'edde')
return zip(rows, firstTiles, patterns)
def makeRowTiling(row, prefix, pattern, n):
yield prefix
yield from (pattern[i%4] for i in range(n-2))
yield pattern[(n-2)%4] if (n%2 != (row-1)//2) else 'f'
if __name__ == '__main__':
n = int(input())
computeTiling(n)
``` | output | 1 | 11,326 | 7 | 22,653 |
Provide tags and a correct Python 3 solution for this coding contest problem.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa | instruction | 0 | 11,327 | 7 | 22,654 |
Tags: constructive algorithms, implementation
Correct Solution:
```
def computeTiling(n):
printEvenLengthTiling(n) if isEven(n) else printOddLengthTiling(n)
def isEven(n):
return n%2 == 0
def printEvenLengthTiling(n):
print(buildRowFromPattern( '', 'nnoo', '', n))
print(buildRowFromPattern('l', 'xxzz', 'f', n))
print(buildRowFromPattern('l', 'zzxx', 'f', n))
print(buildRowFromPattern( '', 'nnoo', '', n))
def printOddLengthTiling(n):
print(buildRowFromPattern('l', 'xxzz', '', n))
print(buildRowFromPattern('l', 'zzxx', '', n))
print(buildRowFromPattern( '', 'nnoo', 'f', n))
print(buildRowFromPattern( '', 'oonn', 'f', n))
def buildRowFromPattern(prefix, infix, suffix, n):
return "".join(applyPattern(prefix, infix, suffix, n))
def applyPattern(prefix, infix, suffix, n):
n = n - bool(prefix) - bool(suffix)
yield prefix
yield from extendInfix(infix, n)
yield suffix
def extendInfix(infix, n):
repetitions, reminder = divmod(n, len(infix))
for rep in range(repetitions):
yield infix
yield infix[:reminder]
if __name__ == '__main__':
n = int(input())
computeTiling(n)
``` | output | 1 | 11,327 | 7 | 22,655 |
Provide tags and a correct Python 3 solution for this coding contest problem.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa | instruction | 0 | 11,328 | 7 | 22,656 |
Tags: constructive algorithms, implementation
Correct Solution:
```
n=int(input())
s1,s2="aabb",'ccdd'
if n % 2 == 0:
print((s1*n)[:n])
print('e'+(s2*n)[:n-2]+'f')
print('e'+(s1*n)[:n-2]+'f')
print((s2*n)[:n])
else:
print((s1*n)[:n-1]+'e')
print((s1*n)[2:n+1]+'e')
print('f'+(s2*n)[:n-1])
print('f'+(s2*n)[2:n+1])
``` | output | 1 | 11,328 | 7 | 22,657 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa
Submitted Solution:
```
n = int(input())
if n == 1:
print('-1')
elif n == 2:
print('aa\nbb\ncc\ndd')
else:
print('aabb' * (n // 4) + 'aay'[:n % 4])
print('ccdd' * (n // 4) + 'ccy'[:n % 4])
print('z' + 'eeff' * ((n - 1) // 4) + ('ee' if n % 4 in (0, 3) else '') + ('' if n % 2 else 'y'))
print('z' + 'gghh' * ((n - 1) // 4) + ('gg' if n % 4 in (0, 3) else '') + ('' if n % 2 else 'y'))
``` | instruction | 0 | 11,329 | 7 | 22,658 |
No | output | 1 | 11,329 | 7 | 22,659 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa
Submitted Solution:
```
from sys import stdin
a=int(stdin.readline())
if a%2==0:
for b in range(0,int(a/2)):
if b%2==0:
if b==int(a/2)-1:
print('aa')
else:
print('aa',end='')
else:
if b==int(a/2)-1:
print('bb')
else:
print('bb', end='')
print('c',end='')
for d in range(0,int(a/2)-1):
if d%2==0:
print('dd',end='')
else:
print('ee', end='')
print('f')
print('c',end='')
for d in range(0, int(a/2)-1):
if d % 2 == 0:
print('ee', end='')
else:
print('dd', end='')
print('f')
for b in range(0,int(a/2)):
if b%2==0:
if b==int(a/2)-1:
print('aa')
else:
print('aa',end='')
else:
if b==int(a/2)-1:
print('bb')
else:
print('bb', end='')
else:
for b in range(0,int((a-1)/2)):
if b%2==0:
if b==int((a-1)/2)-1:
print('aa')
else:
print('aa',end='')
else:
if b==int((a-1)/2)-1:
print('bb')
else:
print('bb', end='')
print('c')
for b in range(0,int((a-1)/2)):
if b%2==0:
if b==int((a-1)/2)-1:
print('bb')
else:
print('bb',end='')
else:
if b==int((a-1)/2)-1:
print('aa')
else:
print('aa', end='')
print('c')
if a==1:
print('d')
else:
print('d',end='')
for b in range(0,int((a-1)/2)):
if b%2==0:
if b==int((a-1)/2)-1:
print('bb')
else:
print('bb',end='')
else:
if b==int((a-1)/2)-1:
print('aa')
else:
print('aa', end='')
if a==1:
print('d')
else:
print('d',end='')
for b in range(0,int((a-1)/2)):
if b%2==0:
if b==int((a-1)/2)-1:
print('aa')
else:
print('aa',end='')
else:
if b==int((a-1)/2)-1:
print('bb')
else:
print('bb', end='')
``` | instruction | 0 | 11,330 | 7 | 22,660 |
No | output | 1 | 11,330 | 7 | 22,661 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa
Submitted Solution:
```
n=int(input())
L=["aabb","cdde","cffe"]
if n%3==2:
print("-1")
else:
for i in range(0,n,3):
for j in range(3):
print(L[j])
for j in L[:n%3]:
print(j)
``` | instruction | 0 | 11,331 | 7 | 22,662 |
No | output | 1 | 11,331 | 7 | 22,663 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We all know the problem about the number of ways one can tile a 2 × n field by 1 × 2 dominoes. You probably remember that it goes down to Fibonacci numbers. We will talk about some other problem below, there you also are going to deal with tiling a rectangular field with dominoes.
You are given a 4 × n rectangular field, that is the field that contains four lines and n columns. You have to find for it any tiling by 1 × 2 dominoes such that each of the n - 1 potential vertical cuts along the grid lines intersects at least one domino, splitting it in two. No two dominoes in the sought tiling should overlap, each square of the field should be covered by exactly one domino. It is allowed to rotate the dominoes, that is, you can use 2 × 1 as well as 1 × 2 dominoes.
Write a program that finds an arbitrary sought tiling.
Input
The input contains one positive integer n (1 ≤ n ≤ 100) — the number of the field's columns.
Output
If there's no solution, print "-1" (without the quotes). Otherwise, print four lines containing n characters each — that's the description of tiling, where each vertical cut intersects at least one domino. You should print the tiling, having painted the field in no more than 26 colors. Each domino should be painted a color. Different dominoes can be painted the same color, but dominoes of the same color should not be side-neighbouring. To indicate colors you should use lowercase Latin letters. Print any of the acceptable ways of tiling.
Examples
Input
4
Output
yyzz
bccd
bxxd
yyaa
Submitted Solution:
```
import string
n = int(input())
l = 0
def get_next_l():
global l
a = string.ascii_lowercase[l]
l = (l + 9) % 26
return a
rows = [""] * 4
if n == 1:
rows[0] = rows[1] = get_next_l()
rows[2] = rows[3] = get_next_l()
elif n == 2:
for i in range(4):
rows[i] = get_next_l() * 2
elif n % 2 == 0:
rows[0] = "".join([get_next_l() * 2 for _ in range(n//2)])
front = get_next_l()
rows[1] = front + "".join([get_next_l() * 2 for _ in range(n//2 - 1)])
# delay until we get there
end = get_next_l()
rows[1] += end
rows[2] = front + "".join([get_next_l() * 2 for _ in range(n//2 - 1)]) + end
rows[3] = "".join([get_next_l() * 2 for _ in range(n//2)])
else:
rows[0] = "".join([get_next_l() * 2 for _ in range(n//2)])
end = get_next_l()
rows[0] += end
rows[1] = "".join([get_next_l() * 2 for _ in range(n//2)]) + end
front = get_next_l()
rows[2] = front + "".join([get_next_l() * 2 for _ in range(n//2)])
rows[3] = front + "".join([get_next_l() * 2 for _ in range(n//2)])
print("\n".join(rows))
``` | instruction | 0 | 11,332 | 7 | 22,664 |
No | output | 1 | 11,332 | 7 | 22,665 |
Provide a correct Python 3 solution for this coding contest problem.
problem
There are the following games.
N characters are lined up in a vertical row. The color of these characters is red, blue, or yellow, and in the initial state, four or more characters of the same color are not lined up in a row. The player can select a character at a certain position and change it to another color. By this operation, if four or more characters of the same color are lined up in a row, those characters will disappear. When four or more characters of the same color are lined up in a row due to the disappearance of the characters, those characters also disappear, and this chain continues until there are no more places where four or more characters of the same color are lined up in a row. .. The purpose of this game is to reduce the number of characters remaining without disappearing.
For example, if the color of the sixth character from the top is changed from yellow to blue in the state at the left end of the figure below, five blue characters will disappear in a row, and finally three characters will remain without disappearing.
<image>
Given the color sequence of N characters in the initial state, create a program that finds the minimum value M of the number of characters that remain without disappearing when the color of the character is changed in only one place.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The first line consists of only the number of characters N (1 ≤ N ≤ 10000). The following N lines contain one of 1, 2, and 3 integers, and the i + 1st line (1 ≤ i ≤ N) represents the color of the i-th character from the top in the initial state (1). Is red, 2 is blue, and 3 is yellow).
When N is 0, it indicates the end of input. The number of datasets does not exceed 5.
output
For each dataset, output the minimum value M of the number of characters remaining without disappearing on one line.
Examples
Input
12
3
2
1
1
2
3
2
2
2
1
1
3
12
3
2
1
1
2
3
2
1
3
2
1
3
0
Output
3
12
Input
None
Output
None | instruction | 0 | 12,418 | 7 | 24,836 |
"Correct Solution:
```
def myinput(n):
C=[int(input())]
L=[1]
for i in range(1,n):
c = int(input())
if C[-1] == c:
L[-1]+=1
else:
C.append(c)
L.append(1)
return [C,L]
def check(C,L,low, hih):
m = len(C)
ret = 0
if 0<=low and L[low]>=4 and (hih>=m or C[low] != C[hih]):
ret += L[low]
low -= 1
if hih<m and L[hih]>=4 and (low<0 or C[low] != C[hih]):
ret += L[hih]
hih += 1
while 0 <= low and hih < m and C[low] == C[hih] and L[low] + L[hih] >= 4:
ret += L[low] + L[hih]
low -= 1
hih += 1
return ret
def solve(C,L):
m = len(C)
ret = 0
for i in range(m):
L[i]-=1
if i+1 < m:
L[i+1]+=1
if L[i]>0:
ret = max(ret, check(C, L, i , i+1))
else:
ret = max(ret, check(C, L, i-1, i+1))
L[i+1]-=1
if i-1 >= 0:
L[i-1]+=1
if L[i]>0:
ret = max(ret, check(C, L, i-1, i))
else:
ret = max(ret, check(C, L, i-1, i+1))
L[i-1]-=1
L[i]+=1
return ret
while True:
n = int(input())
if n == 0:
break
C,L = myinput(n)
print(n - solve(C,L))
``` | output | 1 | 12,418 | 7 | 24,837 |
Provide a correct Python 3 solution for this coding contest problem.
problem
There are the following games.
N characters are lined up in a vertical row. The color of these characters is red, blue, or yellow, and in the initial state, four or more characters of the same color are not lined up in a row. The player can select a character at a certain position and change it to another color. By this operation, if four or more characters of the same color are lined up in a row, those characters will disappear. When four or more characters of the same color are lined up in a row due to the disappearance of the characters, those characters also disappear, and this chain continues until there are no more places where four or more characters of the same color are lined up in a row. .. The purpose of this game is to reduce the number of characters remaining without disappearing.
For example, if the color of the sixth character from the top is changed from yellow to blue in the state at the left end of the figure below, five blue characters will disappear in a row, and finally three characters will remain without disappearing.
<image>
Given the color sequence of N characters in the initial state, create a program that finds the minimum value M of the number of characters that remain without disappearing when the color of the character is changed in only one place.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The first line consists of only the number of characters N (1 ≤ N ≤ 10000). The following N lines contain one of 1, 2, and 3 integers, and the i + 1st line (1 ≤ i ≤ N) represents the color of the i-th character from the top in the initial state (1). Is red, 2 is blue, and 3 is yellow).
When N is 0, it indicates the end of input. The number of datasets does not exceed 5.
output
For each dataset, output the minimum value M of the number of characters remaining without disappearing on one line.
Examples
Input
12
3
2
1
1
2
3
2
2
2
1
1
3
12
3
2
1
1
2
3
2
1
3
2
1
3
0
Output
3
12
Input
None
Output
None | instruction | 0 | 12,419 | 7 | 24,838 |
"Correct Solution:
```
# p周辺の4つは消えることが前提
def erase(array, i, N):
if array[i - 1] == array[i]:
up = i - 1
down = i
elif array[i] == array[i + 1]:
up = i
down = i + 1
else:
return N - 2
while True:
if array[up] == -1 or array[down] == -1 or not array[up] == array[down]:
return up + N - down - 1
save_up = up
save_down = down
c = array[up]
while array[up] == c:
up -= 1
while array[down] == c:
down += 1
if save_up - up + down - save_down < 4:
return save_up + N - save_down - 1
def main():
while True:
N = int(input())
if N == 0:
return
a = [-1]
for i in range(N):
a.append(int(input()))
a.append(-1)
min_erased = N
for i in range(1, N + 1):
save = a[i]
a[i] = save % 3 + 1
min_erased = min(min_erased, erase(a, i, N + 2))
a[i] = (save + 1) % 3 + 1
min_erased = min(min_erased, erase(a, i, N + 2))
a[i] = save
print(min_erased)
if __name__ == '__main__':
main()
``` | output | 1 | 12,419 | 7 | 24,839 |
Provide a correct Python 3 solution for this coding contest problem.
problem
There are the following games.
N characters are lined up in a vertical row. The color of these characters is red, blue, or yellow, and in the initial state, four or more characters of the same color are not lined up in a row. The player can select a character at a certain position and change it to another color. By this operation, if four or more characters of the same color are lined up in a row, those characters will disappear. When four or more characters of the same color are lined up in a row due to the disappearance of the characters, those characters also disappear, and this chain continues until there are no more places where four or more characters of the same color are lined up in a row. .. The purpose of this game is to reduce the number of characters remaining without disappearing.
For example, if the color of the sixth character from the top is changed from yellow to blue in the state at the left end of the figure below, five blue characters will disappear in a row, and finally three characters will remain without disappearing.
<image>
Given the color sequence of N characters in the initial state, create a program that finds the minimum value M of the number of characters that remain without disappearing when the color of the character is changed in only one place.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The first line consists of only the number of characters N (1 ≤ N ≤ 10000). The following N lines contain one of 1, 2, and 3 integers, and the i + 1st line (1 ≤ i ≤ N) represents the color of the i-th character from the top in the initial state (1). Is red, 2 is blue, and 3 is yellow).
When N is 0, it indicates the end of input. The number of datasets does not exceed 5.
output
For each dataset, output the minimum value M of the number of characters remaining without disappearing on one line.
Examples
Input
12
3
2
1
1
2
3
2
2
2
1
1
3
12
3
2
1
1
2
3
2
1
3
2
1
3
0
Output
3
12
Input
None
Output
None | instruction | 0 | 12,420 | 7 | 24,840 |
"Correct Solution:
```
def doChain(ar, si, ei):
p, c = 0, [] #p:ar[i]のcolor, c:4連続以上のarのindex
for i in range(si, ei):
if ar[i]==p:
c.append(i)
if i==len(ar)-1 and len(c)>=4:
del ar[min(c):max(c)+1]
return True, max(0, si-3),min(ei+5, len(ar))
else:
if len(c)>=4:
del ar[min(c):max(c)+1]
return True, max(0, si-3),min(ei+5, len(ar))
p = ar[i]
c = [i]
return False, 0, len(ar)
while True:
N = int(input())
if N==0: break
A = [int(input()) for _ in range(N)]
minvalue = N
for j in range(len(A)-1):
B = A[:]
if B[j+1]!=B[j]:
B[j+1] = B[j]
result = True
si, ei = max(0, j-3), min(j+5, len(A))
while result==True:
result, si, ei = doChain(B, si, ei)
if len(B)<minvalue:
minvalue = len(B)
print(minvalue)
``` | output | 1 | 12,420 | 7 | 24,841 |
Provide a correct Python 3 solution for this coding contest problem.
problem
There are the following games.
N characters are lined up in a vertical row. The color of these characters is red, blue, or yellow, and in the initial state, four or more characters of the same color are not lined up in a row. The player can select a character at a certain position and change it to another color. By this operation, if four or more characters of the same color are lined up in a row, those characters will disappear. When four or more characters of the same color are lined up in a row due to the disappearance of the characters, those characters also disappear, and this chain continues until there are no more places where four or more characters of the same color are lined up in a row. .. The purpose of this game is to reduce the number of characters remaining without disappearing.
For example, if the color of the sixth character from the top is changed from yellow to blue in the state at the left end of the figure below, five blue characters will disappear in a row, and finally three characters will remain without disappearing.
<image>
Given the color sequence of N characters in the initial state, create a program that finds the minimum value M of the number of characters that remain without disappearing when the color of the character is changed in only one place.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The first line consists of only the number of characters N (1 ≤ N ≤ 10000). The following N lines contain one of 1, 2, and 3 integers, and the i + 1st line (1 ≤ i ≤ N) represents the color of the i-th character from the top in the initial state (1). Is red, 2 is blue, and 3 is yellow).
When N is 0, it indicates the end of input. The number of datasets does not exceed 5.
output
For each dataset, output the minimum value M of the number of characters remaining without disappearing on one line.
Examples
Input
12
3
2
1
1
2
3
2
2
2
1
1
3
12
3
2
1
1
2
3
2
1
3
2
1
3
0
Output
3
12
Input
None
Output
None | instruction | 0 | 12,421 | 7 | 24,842 |
"Correct Solution:
```
while True:
n = int(input())
if not n:
break
puyos = []
pre = int(input())
cnt = 1
for _ in range(n - 1):
p = int(input())
if pre != p:
puyos.append((pre, cnt))
pre = p
cnt = 0
cnt += 1
puyos.append((pre, cnt))
lp = len(puyos)
min_puyo = n
for i, puyo in enumerate(puyos):
color, num = puyo
if num == 2:
continue
tn, j = n, 1
while True:
if i - j < 0 or i + j >= lp:
break
tp_c, tp_n = puyos[i - j]
up_c, up_n = puyos[i + j]
if tp_c != up_c:
break
first_adjust = 0
if j == 1:
if num == 1:
first_adjust = 1
else:
first_adjust = -1
tn -= 4
dp = tp_n + up_n + first_adjust
if dp < 4:
break
tn -= dp
j += 1
if min_puyo > tn:
min_puyo = tn
print(min_puyo)
``` | output | 1 | 12,421 | 7 | 24,843 |
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