Problem:


Score : 400 points

Problem Statement

We have a permutation of the integers from 1 through N, p_1, p_2, .., p_N.
We also have M pairs of two integers between 1 and N (inclusive), represented as (x_1,y_1), (x_2,y_2), .., (x_M,y_M).
AtCoDeer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 ≤ i ≤ N) such that p_i = i is maximized:

Choose j such that 1 ≤ j ≤ M, and swap p_{x_j} and p_{y_j}.

Find the maximum possible number of i such that p_i = i after operations.

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

p is a permutation of integers from 1 through N.

1 ≤ x_j,y_j ≤ N

x_j ≠ y_j

If i ≠ j, \{x_i,y_i\} ≠ \{x_j,y_j\}.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
p_1 p_2 .. p_N
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the maximum possible number of i such that p_i = i after operations.

Sample Input 1

5 2
5 3 1 4 2
1 3
5 4

Sample Output 1

2

If we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.

Sample Input 2

3 2
3 2 1
1 2
2 3

Sample Output 2

3

If we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.
Note that we may choose the same j any number of times.

Sample Input 3

10 8
5 3 6 8 7 10 9 1 2 4
3 1
4 1
5 9
2 5
6 5
3 5
8 9
7 9

Sample Output 3

8

Sample Input 4

5 1
1 2 3 4 5
1 5

Sample Output 4

5

We do not have to perform the operation. 



Sample input:
5 2
5 3 1 4 2
1 3
5 4


Sample output:
2

Submission status: Runtime Error

Solution code:
import copy

N,M = map(int,input().split())
p = [i for i in map(int,input().split())]
x,y = [0 for i in range(M)], [0 for i in range(M)]
for i in range(M):
  x[i],y[i] = map(int,input().split())

def findall(n,lst):
  ids = []  
  while n in lst:
    i = lst.index(n)
    ids.append(i+len(ids))
    lst.remove(n)    
  return(ids)

def isreach(n):
  s = p.index(n)
  reach = [0 for i in range(N)]
  reach[s] = 1
  diff = [1 for i in range(N)]
  while sum(diff) != 0:
    reach2 = copy.deepcopy(reach)
    for i in findall(s+1,x):
      reach2[y[i]-1] = 1
    for i in findall(s+1,y):
      reach2[x[i]-1] = 1
    diff = [reach2[i]-reach[i] for i in range(len(reach))]
    reach = copy.deepcopy(reach2)
  return reach[n-1] == 1
#print(findall(1,y))
#print(isreach(1))
#for i in range(1,6):
#  print(isreach(i))
  
res = [isreach(n) for n in range(1,N+1)]
print(len(res))

Submission status: Runtime Error

Solution code:
col = input().split()
n = int(col[0])
m = int(col[1])

p = input().split()

xy = []
for i in range(0, m):
    xy.append(input().split())

xy2 = []
for i in xy:
    i[0] = int(i[0])
    i[1] = int(i[1])
    if i[0] > i[1]:
        i[0], i[1] = i[1], i[0]
    xy2.append((i[0], i[1]))

for i in range(0, len(xy2)):
    for j in range(i+1, len(xy2)):
        if xy2[i][1] == xy2[j][0]:
            xy2.append((xy2[i][0], xy2[j][1]))

xy3 = list(set(xy2))

for i in range(0, len(xy3)):
    if i[0] == p[i[1]-1] and i[1] == p[i[0]-1]:
        p[i[0]-1], p[i[1]-1] == p[i[1]-1], p[i[0]-1]
    elif i[0] == p[i[1]-1] and i[1] != p[i[0]-1]:
        p[i[0]-1], p[i[1]-1] == p[i[1]-1], p[i[0]-1]
    elif i[0] != p[i[1]-1] and i[1] == p[i[0]-1]:
        p[i[0]-1], p[i[1]-1] == p[i[1]-1], p[i[0]-1]

count = 0
for i in p:
    if i+1 == p[i]:
        count += 1

print(count)

Submission status: Runtime Error

Solution code:
from sys import stdin
stdin = open('sample.txt')


def check(pi):
    result = 0
    for i, x in enumerate(pi):
        if i + 1 == x:
            result = x
    return result


def spam(xyi):
    for i in range(len(xyi) - 1):
        a = xyi[i]
        b = xyi[i + 1]
        if set(a) & set(b):
            xyi.remove(a)
            xyi.remove(b)
            xyi.append(list(set(a) | set(b)))
            return True
    return False


def check_max(pi, item):
    result = 0
    a = [pi[i - 1] for i in item]
    a = set(a) | set(item)
    if not a:
        return 0

    return max(list(a))


def main():
    N, M = [int(x) for x in stdin.readline().rstrip().split()]
    pi = [int(x) for x in stdin.readline().rstrip().split()]
    xyi = [[int(x) for x in stdin.readline().rstrip().split()]
           for _ in range(M)]
    while True:
        result = spam(xyi)
        if not result:
            break
    result = 0
    for item in xyi:
        result = max(result, check_max(pi, item))
    print(result)


if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
def is_sorted(l):
    for i in range(len(l)):
        if l[i] != i + 1:
            return False
    return True


def can_go(start, goal, sw, d):
    if d > M: return False
    if start == goal: return True

    for s in sw:
        if s[0] == start:
            if can_go(s[1], goal, sw, d + 1):
                return True
        elif s[1] == start:
            if can_go(s[0], goal, sw, d + 1):
                return True
    return False


def try_s(l, sw):
    count = 0
    for idx, c in enumerate(l):
        if idx == c:
            count += 1
            continue
        if can_go(idx, c, sw, 0):
            # print(str(c) + ' can go home')
            count += 1
    print(count)


N, M = map(int, input().split())
p = list(map(int, input().split()))

swaps = []
for i in range(M):
    x, y = map(int, input().split())
    swaps.append((x-1, y-1))


p = list(map(lambda x: x - 1, p))
# print(p)
# print(swaps)


if is_sorted(p):
    print(len(p))
else:
    try_s(p, swaps)

Submission status: Runtime Error

Solution code:
def is_sorted(l):
    for i in range(len(l)):
        if l[i] != i + 1:
            return False
    return True


def can_go(start, goal, sw, d):
    if d > M: return False
    if start == goal: return True

    for s in sw:
        if s[0] == start:
            if can_go(s[1], goal, sw, d + 1):
                return True
        elif s[1] == start:
            if can_go(s[0], goal, sw, d + 1):
                return True
    return False


def try_s(l, sw):
    count = 0
    for idx, c in enumerate(l):
        if idx == c:
            continue
        if can_go(idx, c, sw, 0):
            # print(str(c) + ' can go home')
            count += 1
    print(count)


N, M = map(int, input().split())
p = list(map(int, input().split()))

swaps = []
for i in range(M):
    x, y = map(int, input().split())
    swaps.append((x-1, y-1))


p = list(map(lambda x: x - 1, p))
# print(p)
# print(swaps)


if is_sorted(p):
    print(len(p))
else:
    try_s(p, swaps)

Submission status: Runtime Error

Solution code:
def is_sorted(l):
    for i in range(len(l)):
        if l[i] != i + 1:
            return False
    return True


def can_go(start, goal, sw, d):
    if d > M: return False
    if start == goal: return True

    for s in sw:
        if s[0] == start:
            if can_go(s[1], goal, sw, d + 1):
                return True
        elif s[1] == start:
            if can_go(s[0], goal, sw, d + 1):
                return True
    return False


def try_s(l, sw):
    count = 0
    for idx, c in enumerate(l):
        if can_go(idx, c, sw, 0):
            # print(str(c) + ' can go home')
            count += 1
    print(count)


N, M = map(int, input().split())
p = list(map(int, input().split()))

swaps = []
for i in range(M):
    x, y = map(int, input().split())
    swaps.append((x-1, y-1))


p = list(map(lambda x: x - 1, p))
# print(p)
# print(swaps)


if is_sorted(p):
    print(len(p))
else:
    try_s(p, swaps)

Submission status: Runtime Error

Solution code:
x = int(input())

sosu = [2,3,5,7,11,13,17,19,23,29,31]

ans = 1
for i in range(len(sosu)):
  now = sosu[i]
  while now < x:
    now = now*sosu[i]
    if(now <= x and ans <= now):
      ans = now
print(ans)

Submission status: Runtime Error

Solution code:
import sys

N, M = map(int, sys.stdin.readline().strip().split())
ps = map(int, sys.stdin.readline().strip().split())

reps = []
for i in range(M):
    reps.append(map(int, sys.stdin.readline().strip().split()))

# print(N, M)
# print(ps)
# print(reps)

def search(path, goal, ops):
    # print(path, goal)
    cur = path[-1]
    if cur == goal:
        return True

    r = False
    for op in ops:
        if op[0] == cur and op[1] not in path:
            r = search(path + [op[1]], goal, ops)
            if r: return r
        if op[1] == cur and op[0] not in path:
            r = search(path + [op[0]], goal, ops)
            if r: return r
    return r

cnt = 0
for i in range(N):
    x = ps[i]
    if search([i+1], x, reps):
        cnt += 1
print(cnt)