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.)
Solutions
Solution 1: Two Passes
We define two variables left and right to represent the product of all elements to the left and right of the current element, respectively. Initially, left = 1 and right = 1. We define an answer array ans of length n.
First, we traverse the array from left to right. For the i-th element, we update ans[i] with left, then multiply left by nums[i].
Next, we traverse the array from right to left. For the i-th element, we update ans[i] to ans[i] × right, then multiply right by nums[i].
After the traversal, we return the answer array ans.
The time complexity is O(n), where n is the length of the array nums. Ignoring the space consumption of the answer array, the space complexity is O(1).
PythonJavaC++GoTypeScriptRustJavaScriptC#PHP
class Solution:
def productExceptSelf(self, nums: List[int]) -> List[int]:
n = len(nums)
ans = [0] * n
left = right = 1
for i, x in enumerate(nums):
ans[i] = left
left *= x
for i in range(n - 1, -1, -1):
ans[i] *= right
right *= nums[i]
return ans(code-box)
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;
}
}(code-box)
class Solution {
public:
vector<int> productExceptSelf(vector<int>& nums) {
int n = nums.size();
vector<int> ans(n);
for (int i = 0, left = 1; i < n; ++i) {
ans[i] = left;
left *= nums[i];
}
for (int i = n - 1, right = 1; ~i; --i) {
ans[i] *= right;
right *= nums[i];
}
return ans;
}
};(code-box)
func productExceptSelf(nums []int) []int {
n := len(nums)
ans := make([]int, n)
left, right := 1, 1
for i, x := range nums {
ans[i] = left
left *= x
}
for i := n - 1; i >= 0; i-- {
ans[i] *= right
right *= nums[i]
}
return ans
}(code-box)
function productExceptSelf(nums: number[]): number[] {
const n = nums.length;
const ans: number[] = new Array(n);
for (let i = 0, left = 1; i < n; ++i) {
ans[i] = left;
left *= nums[i];
}
for (let i = n - 1, right = 1; i >= 0; --i) {
ans[i] *= right;
right *= nums[i];
}
return ans;
}(code-box)
impl Solution {
pub fn product_except_self(nums: Vec<i32>) -> Vec<i32> {
let n = nums.len();
let mut ans = vec![1; n];
for i in 1..n {
ans[i] = ans[i - 1] * nums[i - 1];
}
let mut r = 1;
for i in (0..n).rev() {
ans[i] *= r;
r *= nums[i];
}
ans
}
}(code-box)
/**
* @param {number[]} nums
* @return {number[]}
*/
var productExceptSelf = function (nums) {
const n = nums.length;
const ans = new Array(n);
for (let i = 0, left = 1; i < n; ++i) {
ans[i] = left;
left *= nums[i];
}
for (let i = n - 1, right = 1; i >= 0; --i) {
ans[i] *= right;
right *= nums[i];
}
return ans;
};(code-box)
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;
}
}(code-box)
class Solution {
/**
* @param Integer[] $nums
* @return Integer[]
*/
function productExceptSelf($nums) {
$n = count($nums);
$ans = [];
for ($i = 0, $left = 1; $i < $n; ++$i) {
$ans[$i] = $left;
$left *= $nums[$i];
}
for ($i = $n - 1, $right = 1; $i >= 0; --$i) {
$ans[$i] *= $right;
$right *= $nums[$i];
}
return $ans;
}
}(code-box)
