Product of Array Except Self

MEDIUM

Description

Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].

The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

You must write an algorithm that runs in O(n) time and without using the division operation.

Example 1:

Input: nums = [1,2,3,4]
Output: [24,12,8,6]

Example 2:

Input: nums = [-1,1,0,-3,3]
Output: [0,0,9,0,0]

Constraints:

2 <= nums.length <= 10⁵
-30 <= nums[i] <= 30
The input is generated such that answer[i] is guaranteed to fit in a 32-bit integer.

Follow up: Can you solve the problem in O(1) extra space complexity? (The output array does not count as extra space for space complexity analysis.)

Approaches

Checkout 3 different approaches to solve Product of Array Except Self. Click on different approaches to view the approach and algorithm in detail.

Brute Force Approach

For each index i, iterate through the array and calculate the product of all elements except nums[i].

Algorithm

Initialize result array of same length as input array
For each index i in the array:
- Initialize product as 1
- Iterate through array again
- Multiply all elements except nums[i] to product
- Store product in result[i]
Return result array

The brute force approach involves using nested loops. For each element at index i, we iterate through the array again to calculate the product of all elements except the current element.

public int[] productExceptSelf(int[] nums) {
    int n = nums.length;
    int[] result = new int[n];
    
    for (int i = 0; i < n; i++) {
        int product = 1;
        for (int j = 0; j < n; j++) {
            if (i != j) {
                product *= nums[j];
            }
        }
        result[i] = product;
    }
    
    return result;
}

Complexity Analysis

Time Complexity: O(n²) where n is the length of the input array as we use nested loopsSpace Complexity: O(1) extra space (not counting the output array)

Pros and Cons

Pros:

Simple to understand and implement
No extra space required except output array

Cons:

Time complexity is quadratic
Not efficient for large arrays
Does not meet the required O(n) time complexity

Code Solutions

Checking out 5 solutions in different languages for Product of Array Except Self. Click on different languages to view the code.

public class Solution {
    public int[] ProductExceptSelf(int[] nums) {
        int n = nums.Length;
        int[] ans = new int[n];
        for (int i = 0, left = 1; i < n; ++i) {
            ans[i] = left;
            left *= nums[i];
        }
        for (int i = n - 1, right = 1; i >= 0; --i) {
            ans[i] *= right;
            right *= nums[i];
        }
        return ans;
    }
}

Video Solution

Watch the video walkthrough for Product of Array Except Self

Patterns:

Prefix Sum

Data Structures:

Array

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