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Product Array Puzzle

Easy
0/40
Average time to solve is 15m
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Contributed by
94 upvotes
Asked in companies
BarclaysExpedia GroupAmazon

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 )
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
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