Problem:
 Score : 400 points    Problem Statement You are given an integer N . Find the number of strings of length N that satisfy the following conditions, modulo 10^9+7 :   The string does not contain characters other than A , C , G and T .  The string does not contain AGC as a substring.  The condition above cannot be violated by swapping two adjacent characters once.       Notes A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T .  For example, the substrings of ATCODER include TCO , AT , CODER , ATCODER and (the empty string), but not AC .      Constraints  3 \leq N \leq 100         Input Input is given from Standard Input in the following format:  N       Output Print the number of strings of length N that satisfy the following conditions, modulo 10^9+7 .        Sample Input 1 3      Sample Output 1 61  There are 4^3 = 64 strings of length 3 that do not contain characters other than A , C , G and T . Among them, only AGC , ACG and GAC violate the condition, so the answer is 64 - 3 = 61 .       Sample Input 2 4      Sample Output 2 230       Sample Input 3 100      Sample Output 3 388130742  Be sure to print the number of strings modulo 10^9+7 .

Solution (Python):
N, MOD = int(input()), 10 ** 9 + 7
memo = [{} for i in range(N+1)]

def ok(last4):
    for i in range(4):
        t = list(last4)
        if i >= 1:
            t[i-1], t[i] = t[i], t[i-1]
        if ''.join(t).count('AGC') >= 1:
            return False
    return True

def dfs(cur, last3):
    if last3 in memo[cur]:
        return memo[cur][last3]
    if cur == N:
        return 1
    ret = 0
    for c in 'ACGT':
        if ok(last3 + c):
            ret = (ret + dfs(cur + 1, last3[1:] + c)) % MOD
    memo[cur][last3] = ret
    return ret

print(dfs(0, 'TTT'))

Solution (Python):
N = int(input())
dp = [[0]*64 for i in range(N-2)]

mod = 10**9+7

d = dict()
d2 = dict()
d2[0] = 'A'
d2[1] = 'G'
d2[2] = 'C'
d2[3] = 'T'
for i in range(64):
    k = i
    ret = ''
    for j in range(3):
        ret += d2[k % 4]
        k //= 4
    d[i] = ret


for i in range(64):
    if d[i] == 'AGC' or d[i] == 'GAC' or d[i] == "ACG":
        continue

    else:
        dp[0][i] = 1


for i in range(N-3):
    for j in range(64):
        if dp[i][j] == 0:
            continue
        tmp = j // 4
        for k in range(4):
            idx = tmp + k * 16
            if d[idx] == "AGC" or d[idx] == 'ACG' or d[idx] == "GAC" or (d[j][0] == 'A' and d[j][1] == 'G' and k == 2) or (d[j][0] == 'A' and d[j][2] == 'G' and k == 2):
                
                continue
            dp[i+1][idx] += dp[i][j]


print(sum(dp[-1]) % mod)

Solution (Python):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N = int(input())
mod = 10**9+7

memo = [{} for _ in range(N+1)]

def ok(x, y, z, nx):
    if y=='A' and z=='G' and nx=='C':
        return False
    if x=='A' and z=='G' and nx=='C':
        return False
    if y=='G' and z=='A' and nx=='C':
        return False
    if y=='A' and z=='C' and nx=='G':
        return False
    if x=='A' and y=='G' and nx=='C':
        return False
    return True

def dfs(idx, lis):
    if idx==N:
        return 1
    x, y, z = lis
    if (x, y, z) in memo[idx]:
        return memo[idx][(x, y, z)]
    ret = 0
    for nx in ['A', 'G', 'C', 'T']:
        if ok(x, y, z, nx):
            ret += dfs(idx+1, (y, z, nx))
    memo[idx][(x, y, z)] = ret%mod
    return ret%mod

print(dfs(0, 'TTT'))

Solution (Python):
n = int(input())
dp = [[0] * 4 for i in range(n + 2)]  

for i in range(4):
    dp[2][i] = 1
mod = 10**9 + 7
for i in range(3, n + 2):
    for j in range(4):
        for k in range(4):
            dp[i][j] += dp[i - 1][k]
    dp[i][2] -= dp[i - 2][0]  
    dp[i][2] -= dp[i - 2][1]  
    dp[i][1] -= dp[i - 2][0] - dp[i - 3][1]  
    dp[i][2] -= 3 * dp[i - 3][0]  

    for j in range(4):
        dp[i][j]%mod
print(sum(dp[-1])%mod)

Solution (Python):
n = int(input())
dp = [[0] * 4 for i in range(n + 2)]  

for i in range(4):
    dp[2][i] = 1
mod = 10**9 + 7
for i in range(3, n + 2):
    for j in range(4):
        for k in range(4):
            dp[i][j] += dp[i - 1][k]
    dp[i][2] -= dp[i - 2][0] 
    dp[i][2] -= dp[i - 2][1] 
    dp[i][1] -= dp[i - 2][0] - dp[i - 3][1] 
    dp[i][2] -= 3 * dp[i - 3][0] 
print(sum(dp[-1]) % mod)

Solution (Python):
n = int(input())
dp = [[0] * 4 for i in range(n + 2)]
for i in range(4):
    dp[2][i] = 1
mod = 10**9 + 7
for i in range(3, n + 2):
    for j in range(4):
        for k in range(4):
            dp[i][j] += dp[i - 1][k]
    dp[i][2] -= dp[i - 2][0]
    dp[i][2] -= dp[i - 2][1]
    dp[i][1] -= dp[i - 2][0] - dp[i - 3][1]
    dp[i][2] -= 3 * dp[i - 3][0]
print(sum(dp[-1]) % mod)

Solution (Python):
MOD = pow(10,9)+7
N = int(input())
dp = [[[[0 for _ in range(4)] for _ in range(4)] for _ in range(4)] for _ in range(N+1)]
dp[0][3][3][3] = 1 



for i in range(N):
  for j in range(4):
    for k in range(4):
      for l in range(4):
        if dp[i][j][k][l] == 0: 
          continue
        for a in range(4): 
          if a == 2 and j == 1 and k == 0: 
            continue
          if a == 1 and j == 2 and k == 0: 
            continue
          if a == 2 and j == 0 and k == 1: 
            continue
          if a == 2 and j == 1 and l == 0: 
            continue
          if a == 2 and k == 1 and l == 0: 
            continue
          dp[i+1][a][j][k] += dp[i][j][k][l]%MOD
ans = 0            
for j in range(4):
  for k in range(4):
    for l in range(4):
      ans += dp[N][j][k][l]
ans = ans%MOD
print(ans)

Solution (Python):
p = 10**9+7
N = int(input())
dp = [[[[[0 for _ in range(4)] for _ in range(4)] for _ in range(4)] for _ in range(4)] for _ in range(N+1)]
for i in range(4):
    for j in range(4):
        for k in range(4):
            for l in range(4):
                if i==0:
                    dp[3][i][j][k][l] = 1
for i in range(4):
    dp[3][i][0][1][2] = 0
    dp[3][i][1][0][2] = 0
    dp[3][i][0][2][1] = 0
for n in range(4,N+1):
    for i in range(4):
        for j in range(4):
            for k in range(4):
                for l in range(4):
                    for x in range(4):
                        dp[n][i][j][k][l] = (dp[n][i][j][k][l]+dp[n-1][x][i][j][k]*(str(j)+str(k)+str(l)!="012")\
                            *(str(j)+str(k)+str(l)!="102")*(str(j)+str(k)+str(l)!="021")\
                            *(str(i)+str(k)+str(l)!="012")*(str(i)+str(j)+str(l)!="012"))%p
cnt = 0
for i in range(4):
    for j in range(4):
        for k in range(4):
            for l in range(4):
                cnt = (cnt+dp[N][i][j][k][l])%p
print(cnt)

Solution (Python):
import sys
readline = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9+7

INF = 10**18
eps = 10**-7

import itertools

def check(s):
    if "AGC" in s:
        return False
    for i in range(len(s)-1):
        a = s[:i] + s[i+1] + s[i] + s[i+2:]
        if "AGC" in a:
            return False
    return True

N = int(readline())
dp = [[0]*61 for i in range(N-2)]
for i in range(61):
    dp[0][i] = 1

rel = {}
cnt = 0
L = list("AGCT")
for v in itertools.product(L,repeat=3):
    s = ''.join(v)
    if check(s):
        rel[s] = cnt
        cnt += 1

for i in range(N-3):
    for k,v in rel.items():
        for s in L:
            if check(k+s):
                dp[i+1][rel[k[1:]+s]] = (dp[i+1][rel[k[1:]+s]] + dp[i][v])%mod
ans = 0
for i in range(61):
    ans = (ans + dp[N-3][i])%mod
print(ans)

Solution (Python):
MOD=10**9+7
n=int(input())
dp=[]
for i in range(n+1):
  dp.append([])
  for j in range(4):
    dp[-1].append([])
    for k in range(4):
      dp[-1][-1].append([])
      for l in range(4):
        dp[-1][-1][-1].append(0)
for i in range(4):
  for j in range(4):
    for k in range(4):
      dp[3][i][j][k]=1
dp[3][0][1][2]=0
dp[3][0][2][1]=0
dp[3][1][0][2]=0
for i in range(3,n):
  for j in range(4):
    for k in range(4):
      for l in range(4):
        dp[i+1][k][l][0]=(dp[i+1][k][l][0]+dp[i][j][k][l])%MOD
        dp[i+1][k][l][1]=(dp[i][j][k][l]+dp[i+1][k][l][1])%MOD
        dp[i+1][k][l][3]=(dp[i][j][k][l]+dp[i+1][k][l][3])%MOD
        if not((j==0 and k==1) or (j==0 and l==1)):
          dp[i+1][k][l][2]=(dp[i+1][k][l][2]+dp[i][j][k][l])%MOD
  dp[i+1][0][1][2]=0
  dp[i+1][0][2][1]=0
  dp[i+1][1][0][2]=0
ans=0
for i in range(4):
  for j in range(4):
    for k in range(4):
      ans=(ans+dp[n][i][j][k])%MOD
print(ans)

Solution (Python):







n = int(input())
if n == 3:
    print(61)
    exit()

memo = {}
MOD = 10**9 + 7


def rec(i, pre3, pre2, pre1):
    if pre3 == "A" and pre2 == "G" and pre1 == "C":
        return 0
    if pre3 == "G" and pre2 == "A" and pre1 == "C":
        return 0
    if pre3 == "A" and pre2 == "C" and pre1 == "G":
        return 0
    if (i, pre1, pre2, pre3) in memo:
        return memo[(i, pre1, pre2, pre3)]
    if i == n - 3:
        return 1
    else:
        ret = 0
        if (pre1 == "G" and pre2 == "A") or (pre1 == "A" and pre2 == "G"):
            ret = rec(i + 1, pre2, pre1, "A") % MOD + rec(
                i + 1, pre2, pre1, "G") % MOD + rec(i + 1, pre2, pre1,
                                                    "T") % MOD
        elif pre1 == "C" and pre2 == "A":
            ret = rec(i + 1, pre2, pre1, "C") % MOD + rec(
                i + 1, pre2, pre1, "A") % MOD + rec(i + 1, pre2, pre1,
                                                    "T") % MOD
        elif pre3 == "A" and pre1 == "G":
            ret = rec(i + 1, pre2, pre1, "A") % MOD + rec(
                i + 1, pre2, pre1, "G") % MOD + rec(i + 1, pre2, pre1,
                                                    "T") % MOD
        elif pre3 == "A" and pre2 == "G":
            ret = rec(i + 1, pre2, pre1, "A") % MOD + rec(
                i + 1, pre2, pre1, "G") % MOD + rec(i + 1, pre2, pre1,
                                                    "T") % MOD
        else:
            ret = rec(i + 1, pre2, pre1,
                      "A") + rec(i + 1, pre2, pre1, "G") % MOD + rec(
                          i + 1, pre2, pre1, "C") % MOD + rec(
                              i + 1, pre2, pre1, "T") % MOD
        ret %= MOD
        memo[(i, pre1, pre2, pre3)] = ret
        return ret



ans = 0
for i in ["A", "G", "C", "T"]:
    for j in ["A", "G", "C", "T"]:
        for k in ["A", "G", "C", "T"]:
            ans += rec(0, i, j, k)

print(ans % MOD)

Solution (Python):
n=int(input())
mod1,mod2=10**9+7,998244353
mod=mod1
import sys
sys.setrecursionlimit(10**9)
memo=[{}for i in range(n+1)]
def ok(s):
    if "AGC"in s:return False
    for i in range(3):
        if "AGC"in s[:i]+s[i+1]+s[i]+s[i+2:]:
            return False
    return True
def dfs(cnt,las):
    if las in memo[cnt]:return memo[cnt][las]
    if cnt==n:return 1
    ret=0
    for nec in "AGCT":
        if ok(las+nec):
            ret=(ret+dfs(cnt+1,las[1:]+nec))%mod
    memo[cnt][las]=ret
    return ret
print(dfs(0,"TTT"))

Solution (Python):
N = int(input())
dp = [[[[0] * 4 for _ in range(4)] for _ in range(4)] for _ in range(N+1)]
for i in range(4):
    for j in range(4):
        for k in range(4):
            if k == 1 and j == 0 and i == 2:
                pass
            elif k == 0 and j == 2 and i == 1:
                pass
            elif k == 0 and j == 1 and i == 2:
                pass
            else:
                dp[3][i][j][k] = 1
mod = 10**9 + 7

for i in range(4, N + 1):
    for j in range(4):
        for k in range(4):
            for l in range(4):
                for p in range(4):
                    if l == 1 and k == 0 and j == 2:
                        pass
                    elif l == 0 and k == 2 and j == 1:
                        pass
                    elif l == 0 and k == 1 and j == 2:
                        pass
                    elif p == 0 and k == 1 and j == 2:
                        pass
                    elif p == 0 and l == 1 and j == 2:
                        pass
                    else:
                        dp[i][j][k][l] += (dp[i - 1][k][l][p]) % mod

ans = 0
for i in range(4):
    for j in range(4):
        for k in range(4):
            ans += dp[N][i][j][k]

print(ans%mod)

Solution (Python):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
import heapq
import math
from fractions import gcd
import random
import string
import copy
from itertools import combinations, permutations, product
from operator import mul
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7






N = getN()
memo = [{} for i in range(N + 1)]
def ok(last4):
    for i in range(4):
        t = list(last4)
        if i >= 1:
            t[i - 1],t[i] = t[i], t[i - 1]
        if ''.join(t).count('AGC') >= 1:
            return False
    return True
def dfs(cur, last3):
    if last3 in memo[cur]:
        return memo[cur][last3]
    if cur == N: return 1
    res = 0
    for c in 'ACGT':
        if ok(last3 + c):
            res  = (res + dfs(cur + 1, last3[1:] + c)) % mod
    memo[cur][last3] = res
    return res
print(dfs(0,'TTT'))

Solution (Python):
N, MOD = int(input()), 10 ** 9 + 7
memo = [{} for i in range(N+1)]
def ok(last4):
    for i in range(4):
        t = list(last4)
        if i >= 1:
            t[i-1], t[i] = t[i], t[i-1]
        if ''.join(t).count('AGC') >= 1:
            return False
    return True
def dfs(cur, last3):
    if last3 in memo[cur]:
        return memo[cur][last3]
    if cur == N:
        return 1
    ret = 0
    for c in 'ACGT':
        if ok(last3 + c):
            ret = (ret + dfs(cur + 1, last3[1:] + c)) % MOD
    memo[cur][last3] = ret
    return ret
print(dfs(0, 'TTT'))

Solution (Python):
n,mod=int(input()),10**9+7
dp=[{} for i in range(n+1)]
def ok(last4):
    for i in range(4):
        t=list(last4)
        if i>=1:
            t[i-1],t[i]=t[i],t[i-1]
        if ''.join(t).count('AGC')>=1:
            return 0
    return 1
def dfs(cur,last3):
    if last3 in dp[cur]:
        return dp[cur][last3]
    if cur==n:
        return 1
    ret=0
    for c in 'AGCT':
        if ok(last3+c):
            ret+=dfs(cur+1,last3[1:]+c)
            ret%=mod
    dp[cur][last3]=ret
    return ret




print(dfs(0,'TTT'))

Solution (Python):






import sys
input = sys.stdin.readline

import math

import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache





MOD = 10**9+7
INF = float('inf')
AZ = "abcdefghijklmnopqrstuvwxyz"






def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]


def P(arg): print(arg); return
def Y(): print("Yes"); return
def N(): print("No"); return
def E(): exit()
def PE(arg): print(arg); exit()
def YE(): print("Yes"); exit()
def NE(): print("No"); exit()


def DD(arg): return defaultdict(arg)


def inv(n): return pow(n, MOD-2, MOD)


kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n): return kaijo_memo[n]
  if(len(kaijo_memo) == 0): kaijo_memo.append(1)
  while(len(kaijo_memo) <= n): kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n): return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0): gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n): gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if n == r: return 1
  if n < r or r < 0: return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret


def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0: 
        cnt+=1 
        temp //= i
      arr.append([i, cnt])
  if temp!=1: arr.append([temp, 1])
  if arr==[]: arr.append([n, 1])
  return arr


def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  return divisors


def make_primes(N):
  max = int(math.sqrt(N))
  seachList = [i for i in range(2,N+1)]
  primeNum = []
  while seachList[0] <= max:
    primeNum.append(seachList[0])
    tmp = seachList[0]
    seachList = [i for i in seachList if i % tmp != 0]
  primeNum.extend(seachList)
  return primeNum


def gcd(a, b):
    while b: a, b = b, a % b
    return a


def lcm(a, b):
    return a * b // gcd (a, b)


def count_bit(n):
  count = 0
  while n:
    n &= n-1
    count += 1
  return count


def base_10_to_n(X, n):
  if X//n: return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))

def base_10_to_n_without_0(X, n):
  X -= 1
  if X//n: return base_10_to_n_without_0(X//n, n)+[X%n]
  return [X%n]


def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count





N = I()
from itertools import product
dic = list(product(["A","C","G","T"],repeat=3))
NG = [("A","C","G"),("A","G","C"),("G","A","C")]
dp = {k:[0 for i in range(N)] for k in dic}
for k in dic:
  if k not in NG:
    dp[k][2] += 1
    

for i in range(3,N):
  for k in dic:
    if k in NG: continue
    for kk in dic:
      if k[0]!=kk[1] or k[1]!=kk[2]: continue
      if kk[0]=="A" and kk[1]=="G" and k[2]=="C":continue
      if kk[0]=="A" and k[1]=="G" and k[2]=="C":continue
      dp[k][i] += dp[kk][i-1]
  
ans = 0
for k in dic:
  ans += dp[k][-1]
  ans %= MOD
print(ans)

Solution (Python):
import sys
stdin = sys.stdin
sys.setrecursionlimit(10**6)
ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
nn = lambda: list(stdin.readline().split())
ns = lambda: stdin.readline().rstrip()

from functools import lru_cache

n = ni()
mod = 10**9+7

@lru_cache(maxsize=10000)
def dfs(n, l):
    rt = 0
    if n == 0:
        return 1
    if l[1:3] == 'AG' or l[1:3] == 'GA' or (l[0] == 'A' and l[2] == 'G') or l[:2] == 'AG':
        pass
    else:
        rt += dfs(n-1, l[1:]+'C')
    if l[1:] != 'AC':
        rt += dfs(n-1,l[1:]+'G')
    rt += dfs(n-1,l[1:]+'T')
    rt += dfs(n-1,l[1:]+'A')
    return rt%mod

print(dfs(n,'TTT')%mod)

Solution (Python):
import sys
stdin = sys.stdin
sys.setrecursionlimit(10**6)
ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
nn = lambda: list(stdin.readline().split())
ns = lambda: stdin.readline().rstrip()

n = ni()
mod = 10**9+7
from functools import lru_cache

@lru_cache(maxsize=1000)
def dfs(n, l):
    rt = 0
    if n == 0:
        return 1
    if l[1:3] == 'AG' or l[1:3] == 'GA' or (l[0] == 'A' and l[2] == 'G') or l[:2] == 'AG':
        pass
    else:
        rt += dfs(n-1, l[1:]+'C')
    if l[1:] != 'AC':
        rt += dfs(n-1,l[1:]+'G')
    rt += dfs(n-1,l[1:]+'T')
    rt += dfs(n-1,l[1:]+'A')
    return rt%mod



print(dfs(n,'TTT')%mod)

Solution (Python):
import sys
sys.setrecursionlimit(10**9)

def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))

def main():
    N = ii()
    a,g,c,t=0,1,2,3
    MOD = 10**9+7

    dp = [[[[0]*4 for _ in range(4)] for _ in range(4)] for _ in range(110)]

    def ok(j,k,l):
        f = True
        for x,y,z in [(j,k,l),(j,l,k),(k,j,l)]:
            f = f and not (x == a and y == g and z == c)
        return f


    for j in range(4):
        for k in range(4):
            for l in range(4):
                if not ok(j,k,l): continue
                dp[3][j][k][l] = 1
    
    ans = 0
    for i in range(3,N):
        for j in range(4):
            for k in range(4):
                for l in range(4):
                    for c_char in range(4):
                        if not ok(k,l,c_char): continue
                        elif j == a and c_char == c and (k == g or l == g): continue
                        dp[i+1][k][l][c_char] += dp[i][j][k][l] % MOD

    
    for j in range(4):
            for k in range(4):
                for l in range(4): 
                    ans += dp[N][j][k][l]  % MOD


    print(ans % MOD)



if __name__ == "__main__":
    main()

Solution (Python):


import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi,factorial
from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [[LI()]for i in range(n)]
def SI(): return input().rstrip()
def printns(x): print('\n'.join(x))
def printni(x): print('\n'.join(list(map(str,x))))
inf = 10**17
mod = 10**9 + 7

n=I()
out=[(0,0,2,1),(1,0,2,1),(2,0,2,1),(3,0,2,1),(0,0,2,1),(0,1,2,1),(0,2,2,1),(0,3,2,1),(0,0,1,2),(1,0,1,2),(2,0,1,2),(3,0,1,2),(0,2,0,1),(1,2,0,1),(2,2,0,1),(3,2,0,1),(0,2,0,1),(0,2,1,1),(0,2,2,1),(0,2,3,1)]
dp=[[[[0]*4 for i in range(4)]for j in range(4)] for k in range(n-2)]
dp[0]=[[[1]*4 for i in range(4)] for j in range(4)]
dp[0][0][2][1]=0
dp[0][0][1][2]=0
dp[0][2][0][1]=0
for i in range(n-3):
    for j in range(4):
        for k in range(4):
            for l in range(4):
                for m in range(4):
                    if (j,k,l,m) in out:
                        continue
                    else:
                        dp[i+1][k][l][m]+=dp[i][j][k][l]%mod

ans=0
for i in range(4):
    for j in range(4):
        ans+=sum(dp[-1][i][j])%mod
print(ans%mod)

Solution (Python):
n=int(input())
mod=10**9+7
memo=[{} for i in range(n+1)]

def ok(last4):
  for i in range(4):
    t=list(last4)
    if i>=1:
      t[i-1],t[i]=t[i],t[i-1]
    if "".join(t).count("AGC")>=1:
      return False
  return True

def dfs(cur,last3):
  if last3 in memo[cur]:
    return memo[cur][last3]
  if cur==n:
    return 1
  res=0
  for c in "ACGT":
    if ok(last3+c):
      res=(res+dfs(cur+1,last3[1:]+c))%mod
  memo[cur][last3]=res
  return res

print(dfs(0,"TTT"))

Solution (Python):
import re
n = int(input())
MOD = 10**9 + 7

string = "ACGT"







table = [{} for i in range(n + 1)]
def dfs(s="", depth=n):
    if table[depth].get(s) is not None:
        return table[depth][s]
    if re.search(r"(AGC|A.GC|GAC|ACG|AG.C)", s):
        table[depth][s] = 0
        return 0
    if depth == 0:
        table[depth][s] = 1
        return 1

    cnt = 0
    for i in string:
        cnt += dfs(s[-3:] + i, depth - 1)
        if cnt >= MOD:
            cnt %= MOD
    table[depth][s] = cnt
    return cnt

print(dfs())

Solution (Python):
N = int(input())
mod = int(1e9) + 7
line = 'TAGC'
ng = {"AGC", "ACG", "GAC", "ATGC", "AGGC", "ACGC", "AGTC", "AGCC"}
D = {line[(i//16)%4]+line[(i//4)%4]+line[i%4]: i for i in range(64)}
invD = {i: line[(i//16)%4]+line[(i//4)%4]+line[i%4] for i in range(64)}
dp = [[0 for _ in range(N+1)] for __ in range(64)]
dp[0][0] = 1
for i in range(4):
  dp[i][1] = 1
for i in range(16):
  dp[i][2] = 1
for i in range(3, N+1):
  for j in range(64):
    for k in range(4):
      last = invD[j]
      if last not in ng:
        if (last[1:] + line[k]) not in ng and last + line[k] not in ng:
          dp[D[last[1:]+line[k]]][i] += dp[D[last]][i-1]
          dp[D[last[1:]+line[k]]][i] %= mod
S = 0
for i in range(64):
  S += dp[i][N]
  S %= mod
print(S)

Solution (Python):
N = int(input())
mod = 10**9+7
memo = [{} for _ in range(N+1)]
def ok(last4):
    for i in range(4):
        t = list(last4)
        if i >=1:
            t[i-1],t[i] = t[i],t[i-1]
        if ''.join(t).count('AGC') >=1:
            return False
    return True
def dfs(cur,last3):
    if last3 in memo[cur]:
        return memo[cur][last3]
    if cur ==N: return 1
    res = 0
    for c in 'ACGT':
        if ok(last3+c):
            res  = (res + dfs(cur+1,last3[1:]+c))%mod
    memo[cur][last3] = res
    return res
print(dfs(0,'TTT'))

Solution (Python):
n = int(input())
mod = 10**9+7
a = []
l = ["A","C","G","T"]
ban = ["AAGC","CAGC","GAGC","TAGC","AGCA","AGCC","AGCG","AGCT","AGAC","CGAC","GGAC","TGAC","GACA","GACC","GACG","GACT","AACG","CACG","GACG","TACG","ACGA","ACGC","ACGG","ACGT","ATGC","ACGC","AGGC","AGTC","AGGC","AGAC"]
for i in l:
    for j in l:
        for k in l:
            a.append(i+j+k)
dp = [[0]*64 for _ in range(n+1)]
for i in range(64):
    if (a[i]=="AGC" or a[i]=="ACG" or a[i]=="GAC"):
        continue
    dp[3][i] = 1
for i in range(4,n+1):
    for j in range(64):
        for k in l:
            b = a[j]+k
            if b in ban:
                continue
            else:
                dp[i][a.index(b[1:])] += dp[i-1][j]
                dp[i][a.index(b[1:])] %= mod
print(sum(dp[-1])%mod)

Solution (Python):
N=int(input())
mod=10**9+7
dp=[{}for i in range(N)]
list=['AGC','ACG','GAC']
def dfs(x,y):
  if x in list:
    return 0
  if y==N:
    return 1
  if x in dp[y]:
    return dp[y][x]
  ans=0
  for i in 'ACGT':
    if x[0]=='A' and i=='C' and (x[1]=='G' or x[2]=='G'):
      continue
    ans+=dfs(x[1:]+i,y+1)
  dp[y][x]=ans%mod
  return ans%mod
print(dfs('TTT',0))

Solution (Python):





MOD = 10**9 + 7
n = int(input())
dp = [[[[0 for _ in range(4)] for _ in range(4)] for _ in range(4)] for _ in range(n + 1)]
for s in range(4):
    for t in range(4):
        for u in range(4):
            dp[3][s][t][u] = 1
dp[3][0][2][1] = 0
dp[3][0][1][2] = 0
dp[3][2][0][1] = 0
for i in range(3, n):
    for s in range(4):
        for t in range(4):
            for u in range(4):
                for v in range(4):
                    dp[i+1][t][u][v] = (dp[i+1][t][u][v] + dp[i][s][t][u]) % MOD
    dp[i+1][2][2][1] -= dp[i][0][2][2]
    dp[i+1][2][0][1] -= dp[i][3][2][0]
    dp[i+1][0][2][1] -= dp[i][2][0][2]
    dp[i+1][0][2][1] -= dp[i][0][0][2]
    dp[i+1][2][3][1] -= dp[i][0][2][3]
    dp[i+1][2][0][1] -= dp[i][2][2][0]
    dp[i+1][2][0][1] -= dp[i][0][2][0]
    dp[i+1][0][2][1] -= dp[i][1][0][2]
    dp[i+1][0][1][2] -= dp[i][2][0][1]
    dp[i+1][2][1][1] -= dp[i][0][2][1]
    dp[i+1][0][1][2] -= dp[i][1][0][1]
    dp[i+1][2][0][1] -= dp[i][1][2][0]
    dp[i+1][0][1][2] -= dp[i][0][0][1]
    dp[i+1][1][2][1] -= dp[i][0][1][2]
    dp[i+1][0][2][1] -= dp[i][3][0][2]
    dp[i+1][3][2][1] -= dp[i][0][3][2]
    dp[i+1][0][1][2] -= dp[i][3][0][1]
print(sum(dp[n][s][t][u] for s in range(4) for t in range(4) for u in range(4)) % MOD)

Solution (Python):
import sys
import numpy as np

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline

input_n = lambda: int(readline())
input_nn = lambda: map(int, readline().split())
input_s = lambda: readline().rstrip().decode('utf-8')
input_ss = lambda: readline().rstrip().decode('utf-8').split()

mod = 10 ** 9 + 7


def judge(a, b, c, k):

    ret = False
    ret |= (b == 0 and c == 2 and k == 1)
    ret |= (b == 0 and c == 1 and k == 2)
    ret |= (b == 2 and c == 0 and k == 1)
    ret |= (a == 0 and b == 2 and k == 1)
    ret |= (a == 0 and c == 2 and k == 1)

    return not ret


def main():

    N = input_n()
    dp = np.full((4, 4, 4), 1, np.int32)
    dp[0, 2, 1] = 0
    dp[0, 1, 2] = 0
    dp[2, 0, 1] = 0

    for n in range(N - 3):
        next_dp = np.zeros((4, 4, 4), np.int32)
        for a in range(4):
            for b in range(4):
                for c in range(4):
                    for k in range(4):
                        if judge(a, b, c, k):
                            next_dp[b, c, k] += dp[a, b, c]
                            next_dp[b, c, k] %= mod
        dp = next_dp

    print(dp.sum() % mod)


if __name__ == '__main__':
    main()

Solution (Python):
N = int(input())
MOD = 10 ** 9 + 7

memo = [{} for i in range(N+1)]

def f(x):
  for i in range(4):
    temp = list(x)
    if i >= 1:
      temp[i-1], temp[i] = temp[i], temp[i-1]
    if ''.join(temp).count('AGC') >= 1:
      return False
  return True

def dfs(temp, x):
  if x in memo[temp]:
    return memo[temp][x]
  if temp == N:
    return 1
  ans = 0
  for c in 'ACGT':
    if f(x + c):
      ans = (ans + dfs(temp + 1, x[1:] + c)) % MOD
  memo[temp][x] = ans
  return ans

print(dfs(0, 'XXX'))

Solution (Python):
n = int(input())
mod = 1000000007
dp = [[[0]*4 for _ in range(4)] for _ in range(n+1)]
for j in range(4):
    for k in range(4): dp[2][j][k] = 1

for i in range(2,n):
    for j in range(4):
        for k in range(4):
            for l in range(4):
                if (j,k,l) in ((2,1,0),(1,2,0),(1,0,2)): continue
                dp[i+1][j][k] += dp[i][k][l]
                dp[i+1][j][k] %= mod
    dp[i+1][1][2] -= dp[i-1][2][0]
    dp[i+1][1][2] %= mod
    dp[i+1][1][3] -= dp[i-1][2][0]
    dp[i+1][1][3] %= mod
    dp[i+1][1][2] -= dp[i-1][3][0]
    dp[i+1][1][2] %= mod

ans = 0
for j in range(4):
    for k in range(4):
        ans += dp[n][j][k]
        ans %= mod
print(ans)

Solution (Python):
n = int(input())
MOD = 10**9+7
d = {"A":0, "C":1, "G":2, "T":3}
dic = {}
dic_r = {}
for i0 in "ACGT":
    for i1 in "ACGT":
        for i2 in "ACGT":
            v = 4**2*d[i2] + 4*d[i1] + d[i0]
            k = i2+i1+i0
            dic[k] = v
            dic_r[v] = k

dp = [[0] * 64 for i in range(n)]
for i in range(64):
    dp[0][i] = 1
dp[0][dic["AGC"]] = 0
dp[0][dic["ACG"]] = 0
dp[0][dic["GAC"]] = 0
for i in range(n-3):
    for j in range(64):
        v = dic_r[j]
        for s in "ACGT":
            
            if v[0] == "A" and v[1] == "G":
                if s != "C":
                    new = v[1]+v[2]+s
                    dp[i+1][dic[new]] += dp[i][dic[v]]
            
            elif v[0] == "A" and v[2] == "G":
                if s != "C":
                    new = v[1]+v[2]+s
                    dp[i+1][dic[new]] += dp[i][dic[v]]
            
            elif v[1] == "G" and v[2] == "A":
                if s != "C":
                    new = v[1]+v[2]+s
                    dp[i+1][dic[new]] += dp[i][dic[v]]
            
            elif v[1] == "A" and v[2] == "C":
                if s != "G":
                    new = v[1]+v[2]+s
                    dp[i+1][dic[new]] += dp[i][dic[v]]
            
            elif v[1] == "A" and v[2] == "G":
                if s != "C":
                    new = v[1]+v[2]+s
                    dp[i+1][dic[new]] += dp[i][dic[v]]
            else:
                new = v[1] + v[2] + s
                dp[i+1][dic[new]] += dp[i][dic[v]]
    continue
print(sum(dp[n-3])%MOD)