Geometric Mean Inequality solution codechef – You are given an array AA of length NN containing the elements −1−1 and 11 only. Determine if it is possible to rearrange the array AA in such a way that AiAi is not the geometric mean of Ai−1Ai−1 and Ai+1Ai+1, for all ii such that 2≤i≤N−12≤i≤N−1.
[Solution] Geometric Mean Inequality solution codechef
YY is said to be the geometric mean of XX and ZZ if Y2=X⋅ZY2=X⋅Z.
Input Format
- The first line contains a single integer TT – the number of test cases. Then the test cases follow.
- The first line of each test case contains an integer NN – the size of the array AA.
- The second line of each test case contains NN space-separated integers A1,A2,…,ANA1,A2,…,AN denoting the array AA.
Output Format
For each test case, output Yes if it is possible to rearrange AA in such a way that AiAi is not the geometric mean of Ai−1Ai−1 and Ai+1Ai+1, where 2≤i≤N−12≤i≤N−1. Otherwise output No.
You may print each character of Yes and No in uppercase or lowercase (for example, yes, yEs, YES will be considered identical).
Constraints
- 1≤T≤2001≤T≤200
- 3≤N≤10003≤N≤1000
- Ai∈{−1,1}Ai∈{−1,1}
[Solution] Geometric Mean Inequality solution codechef
3
5
1 1 1 -1 -1
3
1 1 1
6
1 -1 -1 -1 -1 1
Sample Output 1
Yes
No
Yes
Geometric Mean Inequality solution Explanation
Test case 1: We can rearrange the array AA to [1,1,−1,−1,1][1,1,−1,−1,1]. One can see that Ai2≠Ai−1⋅Ai+1Ai2≠Ai−1⋅Ai+1, for any 2≤i≤N−12≤i≤N−1.
Test case 2: None of the rearrangements of AA satisy the given condition.