Box (Codeforces 1262B)
Tags: Others, constructive algorithms

Permutation $$$p$$$ is a sequence of integers $$$p=[p_1, p_2, \dots, p_n]$$$, consisting of $$$n$$$ distinct (unique) positive integers between $$$1$$$ and $$$n$$$, inclusive. For example, the following sequences are permutations: $$$[3, 4, 1, 2]$$$, $$$[1]$$$, $$$[1, 2]$$$. The following sequences are not permutations: $$$[0]$$$, $$$[1, 2, 1]$$$, $$$[2, 3]$$$, $$$[0, 1, 2]$$$.The important key is in the locked box that you need to open. To open the box you need to enter secret code. Secret code is a permutation $$$p$$$ of length $$$n$$$. You don't know this permutation, you only know the array $$$q$$$ of prefix maximums of this permutation. Formally:  $$$q_1=p_1$$$,  $$$q_2=\max(p_1, p_2)$$$,  $$$q_3=\max(p_1, p_2,p_3)$$$,  ...  $$$q_n=\max(p_1, p_2,\dots,p_n)$$$. You want to construct any possible suitable permutation (i.e. any such permutation, that calculated $$$q$$$ for this permutation is equal to the given array).

Input: The first line contains integer number $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases in the input. Then $$$t$$$ test cases follow.The first line of a test case contains one integer $$$n$$$ $$$(1 \le n \le 10^{5})$$$ — the number of elements in the secret code permutation $$$p$$$.The second line of a test case contains $$$n$$$ integers $$$q_1, q_2, \dots, q_n$$$ $$$(1 \le q_i \le n)$$$ — elements of the array $$$q$$$ for secret permutation. It is guaranteed that $$$q_i \le q_{i+1}$$$ for all $$$i$$$ ($$$1 \le i < n$$$).The sum of all values $$$n$$$ over all the test cases in the input doesn't exceed $$$10^5$$$.

Output: For each test case, print:  If it's impossible to find such a permutation $$$p$$$, print "-1" (without quotes).  Otherwise, print $$$n$$$ distinct integers $$$p_1, p_2, \dots, p_n$$$ ($$$1 \le p_i \le n$$$). If there are multiple possible answers, you can print any of them. 

Note: In the first test case of the example answer $$$[1,3,4,5,2]$$$ is the only possible answer:  $$$q_{1} = p_{1} = 1$$$;  $$$q_{2} = \max(p_{1}, p_{2}) = 3$$$;  $$$q_{3} = \max(p_{1}, p_{2}, p_{3}) = 4$$$;  $$$q_{4} = \max(p_{1}, p_{2}, p_{3}, p_{4}) = 5$$$;  $$$q_{5} = \max(p_{1}, p_{2}, p_{3}, p_{4}, p_{5}) = 5$$$. It can be proved that there are no answers for the second test case of the example.

Sample Inputs:
4
5
1 3 4 5 5
4
1 1 3 4
2
2 2
1
1

Sample Outputs:
1 3 4 5 2 
-1
2 1 
1

Solution (Python):
for i in range(int(input())):
    a = int(input())
    p = [int(i) for i in input().split()]
    s = set([p[0]])
    c = 1
    n = [str(p[0])]
    for i in p[1:]:
        if i in s:
            while c in s:
                c += 1
            if c < i:
                n.append(str(c))
                s.add(c)
            else:
                print(-1)
                n = []
                break
        else:
            n.append(str(i))
            s.add(i)
    if n:
        print(' '.join(n))

Solution (Python):
def printPerm(n, Q):
    exis = True
    for i in range(n):
        if Q[i] < i + 1:
            print(-1)
            exis = False
            break
    if exis:
        num = 1
        ans = [str(Q[0])]
        used = [False] * n
        used[Q[0] - 1] = True
        for i in range(1, n):
            if Q[i] != Q[i - 1]:
                ans.append(str(Q[i]))
                used[Q[i] - 1] = True
            else:
                while used[num - 1]:
                    num += 1
                ans.append(str(num))
                num += 1
        print(' '.join(ans))
t = int(input())
for _t in range(t):
    n = int(input())
    Q = list(map(int, input().split()))
    printPerm(n, Q)

Solution (Python):
t = int(input())
for i in range(t):
    n = int(input())
    q = list(map(int, input().split(' ')))
    arr = [j + 1 for j in range(n)]
    f = False
    s = 0
    for j in range(n):
        if q[j] > s:
            s = q[j]
            temp = arr[j]
            arr[j] = arr[s - 1]
            arr[s - 1] = temp
        elif arr[j] > q[j]:
            f = True
            break
    if not f:
        print(' '.join((str(x) for x in arr)))
    else:
        print('-1')