selection algorithm to select nth small elements based on partition

http://en.wikipedia.org/wiki/Selection_algorithm

1. partition algorithm

 1  function partition(list, left, right, pivotIndex)
 2      pivotValue := list[pivotIndex]
 3      swap list[pivotIndex] and list[right]  // Move pivot to end
 4      storeIndex := left
 5      for i from left to right-1
 6          if list[i] < pivotValue
 7              swap list[storeIndex] and list[i]
 8              storeIndex := storeIndex + 1
 9      swap list[right] and list[storeIndex]  // Move pivot to its final place
10      return storeIndex

2. selection algorithm

 1 function select(list, left, right, k)
 2      loop
 3          select pivotIndex between left and right
 4          pivotNewIndex := partition(list, left, right, pivotIndex)
 5          if k = pivotNewIndex - left + 1
 6              return list[pivotNewIndex]
 7          else if k < pivotNewIndex - left + 1
 8              right := pivotNewIndex-1
 9          else
10              left := pivotNewIndex+1
11              k := k - pivotNewIndex    

 

>> In above last statement, one bug. Should be 
   k := k-pivotNewIndex-left+1
   left := pivotNewIndex+1

3. code Example

 1 int partition(std::vector<int>& a, int l, int r)
 2 {
 3     int i = l, j = l;
 4     int p = a[r];
 5     while (j<r) {
 6         if (a[j] < p) {
 7             std::swap(a[i], a[j]);
 8             i++;
 9         }
10         j++;
11     }
12     std::swap(a[r], a[i]);
13     return i;
14 }
15 
16 void select_kth_smallest(std::vector<int>& a, int l, int r, int k)
17 {
18     while (1) {
19         int cut = partition(a, l, r);
20 #if 0
21         std::copy(a.begin()+l, a.begin()+cut, std::ostream_iterator<int>(std::cout, " "));
22         std::cout << " <=" << a[cut] << "=> ";
23         std::copy(a.begin()+cut+1, a.begin()+r+1, std::ostream_iterator<int>(std::cout, " "));
24         std::cout << "cut("<<cut<<"),k("<<k<<"),l("<<l<<"),r("<<r<<")\n";
25 #endif
26         if (cut-l+1==k)
27             break;
28         else if (k < cut-l+1)
29             r = cut-1;
30         else {
31             k = k-cut-1+l;
32             l = cut+1;
33         }
34     }
35 }
36