GCD operations codechef lunchtime Problem solution with explaination

 GCD operations  CodeChef lunchtime Problem solution with explanation-

Problem Statement-

Consider a sequence A1,A2,…,AN$A_1,A_2,\dots ,A_N$, where initially, Ai=i$A_i=i$ for each valid i$i$. You may perform any number of operations on this sequence (including zero). In one operation, you should choose two valid indices i$i$ and j$j$, compute the greatest common divisor of Ai$A_i$ and Aj$A_j$ (let's denote it by g$g$), and change both Ai$A_i$ and Aj$A_j$ to g$g$.

You are given a sequence B1,B2,…,BN$B_1,B_2,\dots ,B_N$. Is it possible to obtain this sequence, i.e. change A$A$ to B$B$, using the given operations?

Input

• The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
• The first line of each test case contains a single integer N$N$.
• The second line contains N$N$ space-separated integers B1,B2,…,BN$B_1,B_2,\dots ,B_N$.

Output

For each test case, print a single line containing the string < class="mathjax-support" style="background: 0px 0px; border: none; box-sizing: border-box; color: #333333; font-family: Consolas, "Liberation Mono", Courier, monospace; line-height: 1.3; padding: 0px;">"YES"

 if it is possible to obtain A=B$A=B$ or "NO" if it is impossible.

Constraints

• 1≤N≤104$1\le N\le {10}^4$
• 1≤Bi≤i$1\le B_i\le i$ for each valid i$i$
• the sum of N$N$ over all test cases does not exceed 105${10}^5$

Subtasks

Subtask #1 (10 points): N≤4$N\le 4$

Subtask #2 (20 points): there is at most one valid index p$p$ such that Bp≠p$B_p\ne p$

Subtask #3 (70 points): original constraints

Example Input

2
3
1 2 2
4
1 2 3 2

Example Output

NO
YES

Explanation

Example case 1: We cannot make the third element of the sequence (1,2,3)$(1,2,3)$ become 2$2$.

Example case 2: We can perform one operation with (i,j)=(2,4)$(i,j)=(2,4)$, which changes the sequence (1,2,3,4)$(1,2,3,4)$ to (1,2,3,2)$(1,2,3,2)$.

problem link-https://www.codechef.com/LTIME88B/problems/GCDOPS

GCD operations  codechef lunchtime Problem solution-

This is not a thought question actually. You need to know a few things only-

• GCD of two numbers (a,b) cannot grater then these two numbers.

let say GCD of number (x,y) is g. then it is necessary that x,y are multiple of g.

As mentioned in the question we have to check whether array A can be converted into array B or not.

We can perform any number of operations (gcd).

array A has initially 1-N value.

SO my approach says that I will iterate over the array A and compare value to array B.

if it is matching that will be fine otherwise I will check whether A[i ] is multiple of B[i] or not because we can change A[i] to B[i] only if A[i] is multiple of B[i] as I mentioned above in the first point.

SO this is how we can solve this problem.

code is mention below-