ZOJ3959-Problem Preparation

Problem Preparation

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Time Limit: 1 Second      Memory Limit: 65536 KB

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It's time to prepare the problems for the 14th Zhejiang Provincial Collegiate Programming Contest! Almost all members of Zhejiang University programming contest problem setter team brainstorm and code day and night to catch the deadline, and empty bottles of Marjar Cola litter the floor almost everywhere!

To make matters worse, one of the team member fell ill just before the deadline. So you, a brilliant student, are found by the team leader Dai to help the team check the problems' arrangement.

Now you are given the difficulty score of all problems. Dai introduces you the rules of the arrangement:

1. The number of problems should lie between 10 and 13 (both inclusive).
2. The difficulty scores of the easiest problems (that is to say, the problems with the smallest difficulty scores) should be equal to 1.
3. At least two problems should have their difficulty scores equal to 1.
4. After sorting the problems by their difficulty scores in ascending order, the absolute value of the difference of the difficulty scores between two neighboring problems should be no larger than 2. BUT, if one of the two neighboring problems is the hardest problem, there is no limitation about the difference of the difficulty scores between them. The hardest problem is the problem with the largest difficulty score. It's guaranteed that there is exactly one hardest problem.

The team members have given you lots of possible arrangements. Please check whether these arrangements obey the rules or not.

Input

There are multiple test cases. The first line of the input is an integer T (1 ≤ T ≤ 10⁴), indicating the number of test cases. Then T test cases follow.

The first line of each test case contains one integer n (1 ≤ n ≤ 100), indicating the number of problems.

The next line contains n integers s₁, s₂, ... , s_n (-1000 ≤ s_i ≤ 1000), indicating the difficulty score of each problem.

We kindly remind you that this problem contains large I/O file, so it's recommended to use a faster I/O method. For example, you can use scanf/printf instead of cin/cout in C++.

Output

For each test case, output "Yes" (without the quotes) if the arrangement follows the rules, otherwise output "No" (without the quotes).

Sample Input

891 2 3 4 5 6 7 8 9101 2 3 4 5 6 7 8 9 1011999 1 1 2 3 4 5 6 7 8 911999 1 3 5 7 9 11 13 17 19 211015 1 13 17 1 7 9 5 3 11131 1 1 1 1 1 1 1 1 1 1 1 2102 3 4 5 6 7 8 9 10 111015 1 13 3 6 5 4 7 1 14

Sample Output

NoNoYesNoYesYesNoNo

Hint

The first arrangement has 9 problems only, which violates the first rule.

Only one problem in the second and the fourth arrangement has a difficulty score of 1, which violates the third rule.

The easiest problem in the seventh arrangement is a problem with a difficulty score of 2, which violates the second rule.

After sorting the problems of the eighth arrangement by their difficulty scores in ascending order, we can get the sequence 1, 1, 3, 4, 5, 6, 7, 13, 14, 15. We can easily discover that |13 - 7| = 6 > 2. As the problem with a difficulty score of 13 is not the hardest problem (the hardest problem in this arrangement is the problem with a difficulty score of 15), it violates the fourth rule.

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Author: DAI, Longao
Source: The 14th Zhejiang Provincial Collegiate Programming Contest Sponsored by TuSimple

题意：给定 N 个数，每个数 ai 代表第 i 题的难度。问能否满足下列条件：题目数在 10 到 13 题之间，包括 10 题、13 题，最简单题目的难度值应为 1，至少有两个题的题目难度为 1，若将题目难度从小到大排序，相邻题目的难度差不能大于 2 （除了最后一题）。

解题思路：模拟

#include <iostream>#include <cstdio>#include <cstring>#include <string>#include <algorithm>#include <cmath>#include <map>#include <set>#include <stack>#include <queue>#include <vector>#include <bitset>using namespace std;#define LL long longconst int INF = 0x3f3f3f3f;int main(){int t,n,a[105];scanf("%d", &t);while (t--){scanf("%d", &n);for (int i = 1; i <= n; i++) scanf("%d", &a[i]);if (n < 10 || n>13) { printf("No\n"); continue; }sort(a + 1, a + 1 + n);int flag = 1;if (a[1] != 1 || a[2] != 1) flag = 0;for (int i = 1; i <= n - 2; i++)if (a[i + 1] - a[i] > 2) flag = 0;if (flag) printf("Yes\n");else printf("No\n");}return 0;}