# Dijkstra's 3-way quick sort

Posted by chunyang on September 24, 2019

Quick-sort is one of the greatest inventions. Most of the time, its time complexity is O(nlogn). However, when the input array contains lots of duplicates, the performance will drop. For example,

vector<int> a{1, 1, 1, 1}


The elements of the array a are all the same. A naive quick-sort algorithm will have a O(n^2) time complexity.

I have implemented the Dijkstra 3-way quick-sort manually.

typedef pair<int, int> IntPair;
IntPair partition(vector<int>& arr, int start, int end) {
if (start >= end) return make_pair(end, end);
// select the first element as the pivot

int i = start;
int j = start;
int k = end;
int pivot = arr[i];
while (j < k) {
if (arr[j] == pivot) {
++j;
} else if (arr[j] < pivot) {
swap(arr[i], arr[j]);
++i;
++j;
} else {
swap(arr[j], arr[k-1]);
--k;
}
}
return make_pair(i, j);

}


Actually STL has already supported this kind of operation. You can refer to partition for more details.

void quick_sort(vector<int>& arr, int start, int end) {
if (start >= end) return make_pair(end, end);
auto beg = arr.begin(); advance(beg, start);
auto end = arr.begin(); advance(end, end);
int pivot = *beg;
auto middle1 = std::partition(beg, end, [](int x) {return x < pivot;});
auto middle2 = std::partition(middle1, end, [](int x){return x <= pivot;});
// middle1 and middle2 are the start and end of the array with same element;

quick_sort(arr, start, distance(middle1, arr.begin()));
quick_sort(arr, distance(middle2, arr.begin()), end);
}