标签：value nta res == inter nod EAP equal const
The median maintenance problem is a common programming challenge presented in software engineering job interviews.
In this lesson we cover an example of how this problem might be presented and what your chain of thought should be to tackle this problem efficiently.
Lets first refresh what is a median
- The median is the middle element in the sorted list
- Given a list of numbers
` The median is the middle element in the sorted list. Given 13, 23, 11, 16, 15, 10, 26 Sort them 10, 11, 13, 15, 16, 23, 26 ↑ Median If we have an even number of elements we average E.g. 10, 11, 13, 15, 16, 23, 26, 32 \ / 15.5
They way we solve the problem is by using two heaps (Low & High) to divide the array into tow parts.
Low | High
Max Heap | Min Heap
Low part is a max heap, high part is a min heap.
`
(n/2 ± 1) smallest items in a low MaxHeap (n/2 ± 1) biggest items in a high MinHeap
peek => n/2th smallest peek => n/2th smallest
\ /
MEDIAN!
`
If low part size is equals to high part size, then we get avg value, otherwise, we get from larger size heap.
function MedianMaintaince() { let lowMaxHeap = new Heap((b, a) => a - b); let highMinHeap = new Heap((a, b) => a - b); return { add(value) { // For the first element, we add to lowMaxHeap by default if (lowMaxHeap.size() === 0 || value < lowMaxHeap.peek()) { lowMaxHeap.add(value); } else { highMinHeap.add(value); } /** * Reblance: * * If low.size = 2; high.size = 4, then we move the root of high to the low part * so that low.size = 3, high.size = 3 */ let smallerHeap = lowMaxHeap.size() > highMinHeap.size() ? highMinHeap : lowMaxHeap; let biggerHeap = smallerHeap === lowMaxHeap ? highMinHeap : lowMaxHeap; if (biggerHeap.size() - smallerHeap.size() > 1) { smallerHeap.add(biggerHeap.extractRoot()); } /** * If low.szie === high.size, extract root for both and calculate the average value */ if (lowMaxHeap.size() === highMinHeap.size()) { return (lowMaxHeap.peek() + highMinHeap.peek()) / 2; } else { // get peak value from the bigger size of heap return lowMaxHeap.size() > highMinHeap.size() ? lowMaxHeap.peek() : highMinHeap.peek(); } } }; } const mm = new MedianMaintaince(); console.log(mm.add(4)); // 4 console.log(mm.add(2)); // 3 console.log(mm.add(5)); // 4 console.log(mm.add(3)); // 3.5
We have heap data structure:
function printArray(ary) {
console.log(JSON.stringify(ary, null, 2));
}
function Heap(cmpFn = () => {}) {
let data = [];
return {
data,
// 2n+1
leftInx(index) {
return 2 * index + 1;
},
//2n + 2
rightInx(index) {
return 2 * index + 2;
},
// left: (n - 1) / 2, left index is always odd number
// right: (n - 2) / 2, right index is always even number
parentInx(index) {
return index % 2 === 0 ? (index - 2) / 2 : (index - 1) / 2;
},
add(val) {
this.data.push(val);
this.siftUp(this.data.length - 1);
},
extractRoot() {
if (this.data.length > 0) {
const root = this.data[0];
const last = this.data.pop();
if (this.data.length > 0) {
// move last element to the root
this.data[0] = last;
// move last elemment from top to bottom
this.siftDown(0);
}
return root;
}
},
siftUp(index) {
// find parent index
let parentInx = this.parentInx(index);
// compare
while (index > 0 && cmpFn(this.data[index], this.data[parentInx]) < 0) {
//swap parent and current node value
[this.data[index], this.data[parentInx]] = [
this.data[parentInx],
this.data[index]
];
//swap index
index = parentInx;
//move to next parent
parentInx = this.parentInx(index);
}
},
siftDown(index) {
const minIndex = (leftInx, rightInx) => {
if (cmpFn(this.data[leftInx], this.data[rightInx]) <= 0) {
return leftInx;
} else {
return rightInx;
}
};
let min = minIndex(this.leftInx(index), this.rightInx(index));
while (min >= 0 && cmpFn(this.data[index], this.data[min]) > 0) {
[this.data[index], this.data[min]] = [this.data[min], this.data[index]];
index = min;
min = minIndex(this.leftInx(index), this.rightInx(index));
}
},
peek() {
return this.data[0];
},
print() {
printArray(this.data);
},
size() {
return this.data.length;
}
};
}
[Algorithm] Median Maintenance algorithm implementation using TypeScript / JavaScript
标签：value nta res == inter nod EAP equal const
原文地址：https://www.cnblogs.com/Answer1215/p/10222226.html
