Codeforces Round 949 (Div. 2) C. Turtle and an Incomplete Sequence 题解构造

Turtle and an Incomplete Sequence

题目描述

Turtle was playing with a sequence a 1 , a 2 , ... , a n a_1, a_2, \ldots, a_n a1,a2,...,an consisting of positive integers. Unfortunately, some of the integers went missing while playing.

Now the sequence becomes incomplete. There may exist an arbitrary number of indices i i i such that a i a_i ai becomes − 1 -1 −1. Let the new sequence be a ′ a' a′.

Turtle is sad. But Turtle remembers that for every integer i i i from 1 1 1 to n − 1 n - 1 n−1, either a i = ⌊ a i + 1 2 ⌋ a_i = \left\lfloor\frac{a_{i + 1}}{2}\right\rfloor ai=⌊2ai+1⌋ or a i + 1 = ⌊ a i 2 ⌋ a_{i + 1} = \left\lfloor\frac{a_i}{2}\right\rfloor ai+1=⌊2ai⌋ holds for the original sequence a a a.

Turtle wants you to help him complete the sequence. But sometimes Turtle makes mistakes, so you need to tell him if you can't complete the sequence.

Formally, you need to find another sequence b 1 , b 2 , ... , b n b_1, b_2, \ldots, b_n b1,b2,...,bn consisting of positive integers such that:

For every integer i i i from 1 1 1 to n n n, if a i ′ ≠ − 1 a'_i \ne -1 ai′=−1, then b i = a i ′ b_i = a'_i bi=ai′.
For every integer i i i from 1 1 1 to n − 1 n - 1 n−1, either b i = ⌊ b i + 1 2 ⌋ b_i = \left\lfloor\frac{b_{i + 1}}{2}\right\rfloor bi=⌊2bi+1⌋ or b i + 1 = ⌊ b i 2 ⌋ b_{i + 1} = \left\lfloor\frac{b_i}{2}\right\rfloor bi+1=⌊2bi⌋ holds.
For every integer i i i from 1 1 1 to n n n, 1 ≤ b i ≤ 1 0 9 1 \le b_i \le 10^9 1≤bi≤109.

If there is no sequence b 1 , b 2 , ... , b n b_1, b_2, \ldots, b_n b1,b2,...,bn that satisfies all of the conditions above, you need to report − 1 -1 −1.

输入描述

Each test contains multiple test cases. The first line contains the number of test cases t t t ( 1 ≤ t ≤ 1 0 5 1 \le t \le 10^5 1≤t≤105). The description of the test cases follows.

The first line of each test case contains a single integer n n n ( 2 ≤ n ≤ 2 ⋅ 1 0 5 2 \le n \le 2 \cdot 10^5 2≤n≤2⋅105) --- the length of the sequence.

The second line of each test case contains n n n integers a 1 ′ , a 2 ′ , ... , a n ′ a'_1, a'_2, \ldots, a'_n a1′,a2′,...,an′ ( a i ′ = − 1 a'_i = -1 ai′=−1 or 1 ≤ a i ′ ≤ 1 0 8 1 \le a'_i \le 10^8 1≤ai′≤108) --- the elements of the sequence a ′ a' a′.

It is guaranteed that the sum of n n n over all test cases does not exceed 2 ⋅ 1 0 5 2 \cdot 10^5 2⋅105.

输出描述

For each test case, if there is no sequence b 1 , b 2 , ... , b n b_1, b_2, \ldots, b_n b1,b2,...,bn that satisfies all of the conditions, output a single integer − 1 -1 −1.

Otherwise, output n n n integers b 1 , b 2 , ... , b n b_1, b_2, \ldots, b_n b1,b2,...,bn --- the elements of the sequence b 1 , b 2 , ... , b n b_1, b_2, \ldots, b_n b1,b2,...,bn you find. The sequence should satisfy that 1 ≤ b i ≤ 1 0 9 1 \le b_i \le 10^9 1≤bi≤109 for every integer i i i from 1 1 1 to n n n. If there are multiple answers, print any of them.

样例 #1

样例输入 #1

复制代码

9
8
-1 -1 -1 2 -1 -1 1 -1
4
-1 -1 -1 -1
6
3 -1 -1 -1 9 -1
4
-1 5 -1 6
4
2 -1 -1 3
4
1 2 3 4
2
4 2
5
-1 3 -1 3 6
13
-1 -1 3 -1 -1 -1 -1 7 -1 -1 3 -1 -1

样例输出 #1