Following lists 5 common sort algorithms JavaScript implementation.

#### Bubble Sort

function bubble_sort(arr) {
if (arr.length <= 1) return arr;
var alen = arr.length;
for (var i = 0; i < alen; i++) {
for (var j = 0; j < alen - 1; j++) {
if (arr[j] > arr[j + 1]) {
var temp = arr[j];
arr[j] = arr[j + 1];
arr[j + 1] = temp;
}
}
}
return arr;
}

var arr = [3, 8, 9, 1, 2, 6, 4, 7, 5];
bubble_sort(arr);

#### Quick Sort

function quick_sort(arr) {
if (arr.length <= 1) return arr;
var pivot = Math.floor((arr.length - 1) / 2),
pivotValue = arr[pivot],
left = [],
right = [];
arr = arr.slice(0, pivot).concat(arr.slice(pivot + 1));
for (var i = 0; i < arr.length; i++) {
if (arr[i] < pivotValue) {
left.push(arr[i]);
} else {
right.push(arr[i]);
}
}
return [].concat(quick_sort(left), [pivotValue], quick_sort(right));
}

var arr = [3, 8, 9, 1, 2, 6, 4, 7, 5];
quick_sort(arr);

#### Merge Sort

function merge(left, right) {
var result = [];
while (left.length && right.length) {
if (left[0] < right[0]) {
result.push(left.shift());
} else {
result.push(right.shift());
}
}
return result.concat(left).concat(right);
}

function merge_sort(arr) {
if (arr.length <= 1) return arr;
var mid = Math.floor(arr.length / 2),
left = arr.slice(0, mid),
right = arr.slice(mid);
return merge(merge_sort(left), merge_sort(right));
}

var arr = [3, 8, 9, 1, 2, 6, 4, 7, 5];
merge_sort(arr);

#### Selection Sort

function selection_sort(arr) {
for (var i = 0; i < arr.length; i++) {
var min = i;
for (var j = i + 1; j < arr.length; j++) {
if (arr[j] < arr[min]) {
min = j;
}
}
if (min != i) {
var temp = arr[min];
arr[min] = arr[i];
arr[i] = temp;
}
}
return arr;
}

var arr = [3, 8, 9, 1, 2, 6, 4, 7, 5];
selection_sort(arr);

#### Insertion Sort

function insertion_sort(arr) {
for (var i = 0; i < arr.length; i++) {
var j = i - 1,
temp = arr[i];
while (j >= 0 && arr[j] > temp) {
arr[j + 1] = arr[j];
arr[j] = temp;
j--;
}
}
return arr;
}

var arr = [3, 8, 9, 1, 2, 6, 4, 7, 5];
insertion_sort(arr);