1. Left product
Store the product of everything to the left of i.
result[i] = prefixTyporithm · medium
Product Except Self
product-except-selfprefix-sumsprefix-productsuffix-productno-division
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Full lesson · 8 learning steps Open any exercise for focused practice
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Step 1 of 8 · intro card
Learn Product Except Self
Prefix Sums
Two passes: fill result with left products, then multiply each by the running right product — no division needed.
Each output is the product of all elements except the one at that index.
A forward pass stores the product of everything to the left of each index.
A backward pass multiplies in the product of everything to the right, avoiding division entirely.
01
Left products in a forward pass.
02
Right products in a backward pass.
03
No division — handles zeros safely.
function productExceptSelf(nums) {
const n = nums.length;
const result = new Array(n).fill(1);
let prefix = 1;
for (let i = 0; i < n; i += 1) {
result[i] = prefix;
prefix *= nums[i];
}
let suffix = 1;
for (let i = n - 1; i >= 0; i -= 1) {
result[i] *= suffix;
suffix *= nums[i];
}
return result;
}Read the implementation
Connect each part of the code to the concept before you type.
2. Extend prefix
Fold nums[i] into the running left product.
prefix *= nums[i]3. Times right product
Multiply by the product of everything to the right.
result[i] *= suffix4. Extend suffix
Fold nums[i] into the running right product.
suffix *= nums[i]A complete learning loop
01
Understand
Read the concept map and follow the code breakdown.
02
Reconstruct
Type the implementation, repair mistakes and work through every recall exercise.
03
Verify
Use the final check without hints; revisit weak concepts in short practice sessions.