Find Missing Number in Sequence

hardcodingAlgorithmsData StructuresJavaScript~30 min

Asked at Google, Amazon, Meta

Overview

Given an array containing n distinct numbers taken from the range 0 to n, find the one number that is missing from the array.

Implement findMissing(nums).

Constraints

Input is an array of n distinct integers in the range [0, n].
Exactly one number in the range is missing.
The array is not necessarily sorted.
Aim for $O(n)$ time and $O(1)$ extra space.

Examples

findMissing([3, 0, 1]);          // 2
findMissing([0, 1]);             // 2
findMissing([9, 6, 4, 2, 3, 5, 7, 0, 1]);  // 8
findMissing([0]);                // 1

Notes

The Gauss formula approach: the sum of 0..n is n*(n+1)/2. Subtract the actual sum of the array to find the missing value.
An XOR-based approach also works in $O(1)$ space: XOR all numbers 0..n with all array values — the result is the missing number.
Beware of overflow with very large arrays if using the sum approach (not a concern in JS with Number, but good to know).

Solution

Reveal solution

function findMissing(nums) {
  const n = nums.length;
  const expectedSum = (n * (n + 1)) / 2;
  const actualSum = nums.reduce((sum, v) => sum + v, 0);
  return expectedSum - actualSum;
}

Resources

find-missing-number.js

Find Missing Number in Sequence

hardcodingAlgorithmsData Structures

Overview

Given an array containing n distinct numbers taken from the range 0 to n, find the one number that is missing from the array.

Implement findMissing(nums).

Constraints

Input is an array of n distinct integers in the range [0, n].
Exactly one number in the range is missing.
The array is not necessarily sorted.
Aim for $O(n)$ time and $O(1)$ extra space.

Examples

findMissing([3, 0, 1]);          // 2
findMissing([0, 1]);             // 2
findMissing([9, 6, 4, 2, 3, 5, 7, 0, 1]);  // 8
findMissing([0]);                // 1

Notes

The Gauss formula approach: the sum of 0..n is n*(n+1)/2. Subtract the actual sum of the array to find the missing value.
An XOR-based approach also works in $O(1)$ space: XOR all numbers 0..n with all array values — the result is the missing number.
Beware of overflow with very large arrays if using the sum approach (not a concern in JS with Number, but good to know).

Solution

Reveal solution

function findMissing(nums) {
  const n = nums.length;
  const expectedSum = (n * (n + 1)) / 2;
  const actualSum = nums.reduce((sum, v) => sum + v, 0);
  return expectedSum - actualSum;
}

Resources

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