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Last Updated: 8 Jul, 2020
Product Of Array Except Self
Easy
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You have been given an integer array/list (ARR) of size N. You have to return an array/list PRODUCT such that PRODUCT[i] is equal to the product of all the elements of ARR except ARR[i]
Note :
Each product can cross the integer limits, so we should take modulo of the operation.
Take MOD = 10^9 + 7 to always stay in the limits.
Follow up :
Can you try solving the problem in O(1) space?
Input format :
The first line contains an integer 'T' which denotes the number of test cases or queries to be run. Then the test cases follow.
The first line of each test case or query contains an integer 'N' representing the size of the array/list.
The second line contains 'N' single space-separated integers representing the elements in the array/list.
Output Format :
For each test case, print the elements of the 'PRODUCT' array separated by a single space.
Output for every test case will be printed in a separate line.
Important Note :
You are required to return the product array and no need to print the result explicitly. It has already been taken care of.
Constraints :
1 <= T <= 100
0 <= N <= 10^5
0 <= ARR[i] <= 10^5
Time Limit: 1 sec
Approaches
Traverse through every index of the array/list and compute the product of all the other elements in the array/list. This would require a new array/list of the same size as that of the input array/list in which we will store the product of the elements corresponding to every index.
1. Create a new array/list to store the product at every index
2. Start traversing on the input array/list till its length
3. For every ith iteration, find the product of all the elements to the left of i [0 - (i - 1)] and the product of all the elements to the right of i [(i + 1) - (n -1)]
4. Take the product of left and right and assign the result to the i-th position in the new array keeping the result for every i
5. Repeat the above two steps till the end of the input array
6. Return the array in which you stored the products
The idea is to create prefixProduct array/list and suffixProduct array/list. Both the arrays/list will be of the same length as that of the input array/list.
1. Assign 1 initially to all the elements of the suffix and prefix product arrays/list.
2. Create a suffix and prefix arrays/list for the input array/list.
3. The prefixProduct array can be created by traversing the input array from the start till the end and filling prefixProduct[i] with the product of the elements from index 0 to index i.
4. The suffixProduct array can be created by traversing the input array from the end till the start and filling suffixProduct[i] with the product of the elements from index n - 1 to index i, where n is the size of the input array
5. Run over the input array/list and for each i in the input array/list, assign the product of suffixProduct[i] and prefixProduct[i]
6. Make a answerArray where answerArray[i] = suffixProduct[i] * prefixProduct[i]
7. Return the answerArray
- Create an output array
- Traverse the input array from the start till the end
- Update the i'th element of the output array with the product of elements of the input array from index 0 to index i - 1. This can be done by just maintaining a single product variable and updating it each iteration
- Now, traverse the input array from the end till the start
- Multiply the i'th element of the output array with the product of elements of the input array from index i + 1 to index n - 1, where n is the size of the input array. Just like before, this can also be done by maintaining a single product variable
- Return the output array
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