Product Array Puzzle - Get elements by multiplying all other elements

We need to construct an array where ith element will be the product of all the elements in the given array except element at ith position

Example

Input array

Output array element 1: 3 x 5 x 6 x 2
Output array element 2: 10 x 5 x 6 x 2
Output array element 3:  10 x 3 x 6 x 2
Output array element 4: 10 x 3 x 5 x 2
Output array element 5: 10 x 3 x 5 x 6

Output array will be

 

Algorithm

Time Complexity: O(n)
Space Complexity: O(n)

Step 1 : Take a vector product to store the products.
a)    Initialize it by vector product

Step 2 : Construct two arrays left[] and right[], left stores product of elements upto left of ith index in the array. right stores product of elements right of ith index.
a)    Initialize the first element of left as 1 and last element of right as 1.
b)    from left, update the ith elements of left array with product of the i-1 th element of given array with previous element of left array. (left[i] = left [i-1] * array[i-1]). by doing this, It stores the product till the previous index in the left array from the given array.
c)    from right, update the ith elements of right array with product of the i+1 th element of given array with next element of right array. (right[i] = right[i+1] *array[i+1]). by doing this, It stores the product till the previous index in the left array from the given array.

Step 3 :  Product except the present element will be same as product of left and right arrays elements.
a)    product array will be, product[i] = left[i]*right[i].

Algorithm working Example

C++ Program

#include <bits/stdc++.h>
using namespace std;
#define ll long long

int main(){
	
	ll arr[] = { 10, 3, 5, 6, 2}; //array
	int N = sizeof(arr) / sizeof(arr[0]); // size of array
	
	int left[N],right[N]; //arrays to store product upto left of ith index and right of ith index stored in left and right array respectively
	
	vector<int> product;
	left[0] = 1; //initialize the first element as 1
	for(int i=1; i<N; i++)
		left[i] = left[i-1]*arr[i-1]; // store the product till just previous index

	right[N-1] = 1;//initialzie the first element as 1
	for(int i = N-2; i>= 0 ;i--)
		right[i] = right[i+1]*arr[i+1]; //store the product till just next index
	 	
	 for(int i = 0; i < N; i++)
	 product.push_back(left[i]*right[i]); // product of the whole array except the current element is same as product of left and right array's ith index
	 
	 for(int i=0;i<N;i++)//display the product array
	 cout<<product[i]<<"  "; 
	 
	return 0;
}
Try It

 


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