Product Array Puzzle

Easy

0/40

Average time to solve is 15m

Contributed by

96 upvotes

Asked in companies

Problem statement

You are given an array of ‘N’ integers. You need to return another array ‘product’ such that ‘product[i]’ contains the product of all the arrays except the element at the ith position in the given array.

Note

As the product of elements can be very large you need to return the answer in mod (10^9+7).

Follow Up

Try to do this without using the division operator ‘/’, in constant space. The output array does not count as extra space for the purpose of space complexity analysis.

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

The first line of the input contains an integer ‘T’ denoting the number of test cases.

The first line of each test case contains a single positive integer ‘N’ denoting the number of the elements present in the array.

The second line of each test case contains ‘N’ space-separated integers denoting the elements of the array.

Output Format:

The only line of output of each test case should contain ‘N’ space-separated integers where ith integer denotes the product of all the elements in the array except itself.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 10^2
2 <= N<= 10^4
1 <= A[i] <= 10^9 

Where ‘T’ is the number of test cases, ‘N’ is the size of the array,  ‘A[i]’ is the size of the array elements.

Time Limit: 1 sec

Sample Input 1:

2
5 
1 3 3 10 2
6 
2 4 6 3 1 1

Sample Output 1:

180 60 60 18 90
72 36 24 48 144 144

Explanation For Sample Input 1:

Test case 1:
Product of elements except 1 = 3 * 3 * 10 * 2 = 180       
Product of elements except 3 = 1  * 3 * 10 * 2 = 60       
Product of elements except 3 = 1 * 3  * 10 * 2 = 60       
Product of elements except 10 = 1 * 3 * 3 * 2 = 18       
Product of elements except 2 = 1 * 3 * 3 * 10 = 90       

Test case 2:
Product of elements except 2 = 4 * 6 * 3 * 1 * 1 = 72   
Product of elements except 4 = 2 * 6 * 3 * 1 * 1 = 36   
Product of elements except 6 = 2 * 4 * 3 * 1 * 1 = 24   
Product of elements except 3 = 2 * 4 * 6 * 1 * 1 = 48  
Product of elements except 1 = 2 * 4 * 6 * 1 * 1 = 144   
Product of elements except 1 = 2 * 4 * 6 * 3 * 1 = 144

Sample Input 2:

2
5 
1 10 1 2 2
6
2 12 1 1 20 1

Sample Output 2:

40 4 40 20 20
240 40 480 480 24 480

Explanation For Sample Input 2:

Test case 1:
Product of elements except 1 = 10 * 1 * 2 * 2 = 40      
Product of elements except 10 = 1  * 1 * 2 * 2 = 4      
Product of elements except 2 = 1 * 10 * 1 * 2 = 20
Product of elements except 2 = 1 * 10 * 1 * 2 = 20       

Test case 2:
Product of elements except 2 = 12 * 1 * 1 * 20 * 1 = 240
Product of elements except 12 = 2 * 1 * 1 * 20 * 1 = 40 
Product of elements except 1 = 2 * 12 * 1 * 20 * 1 = 480   
Product of elements except 1 = 2 * 12 * 1 * 20 * 1 = 480
Product of elements except 20 = 2 * 12 * 1 * 1 * 1 = 24  
Product of elements except 1 = 2 * 12 * 1 * 1* 20 = 480

Console