#### Find the Median of a Stream of Integers

Given a stream of integers, this problem seeks to find the median of the stream at any given point. For example, given the input of [2, 1, 5, 7, 2 , 0, 5], the corresponding output would be [2, 1.5, 2, 3.5, 2, 2, 2].

#### Problem

```Given a stream of integers, find the median of the stream at any given point.
Example input: [2, 1, 5, 7, 2, 0, 5]
Example output: [2, 1.5, 2, 3.5, 2, 2, 2]```

#### Solution

This solution is in JavaScript. Our A.I. can create solutions in multiple languages.
```// Solution:
// The median of a set of numbers is the middle number when the numbers are sorted.
// To find the median of a stream of numbers, we can keep track of the numbers in a sorted array.
// When a new number is added, we can insert it into the array in the correct position.
// This will take O(n) time, but we can use a binary search to find the correct position,
// which will take O(log n) time.
// The median is the middle number in the array, so we can find it in O(1) time.
// The total time complexity is O(log n).

function medianStream(stream) {
const sorted = [];
const medians = [];

for (let i = 0; i < stream.length; i++) {
const num = stream[i];
const index = binarySearch(sorted, num);
sorted.splice(index, 0, num);
medians.push(getMedian(sorted));
}

return medians;
}

function binarySearch(arr, num) {
let start = 0;
let end = arr.length - 1;

while (start <= end) {
const mid = Math.floor((start + end) / 2);

if (arr[mid] === num) {
return mid;
} else if (arr[mid] < num) {
start = mid + 1;
} else {
end = mid - 1;
}
}

return start;
}

function getMedian(arr) {
const mid = Math.floor(arr.length / 2);

if (arr.length % 2 === 0) {
return (arr[mid - 1] + arr[mid]) / 2;
} else {
return arr[mid];
}
}

console.log(medianStream([2, 1, 5, 7, 2, 0, 5])); // [2, 1.5, 2, 3.5, 2, 2, 2]```

A.I. Evaluation of the Solution

The candidate's solution is correct and demonstrates a level of completeness. The candidate has correctly identified the problem and has provided a solution that solves the problem. The candidate's approach is sound and their use of a binary search is clever. The only improvement that could be made is to provide more comments explaining the code.

Evaluated at: 2022-11-26 04:16:53