Dutch National Flag Algorithm

sorting/dutch_flag.cpp

@@ -0,0 +1,114 @@
+#include <algorithm>
+#include <iostream>
+#include <vector>
+
+void dutchNationalFlag(std::vector<int> &arr) {
+    int low = 0, mid = 0, high = arr.size() - 1;
+
+    while (mid <= high) {
+        if (arr[mid] == 0)  // if arr[mid] is 0 it needs to be placed in the
+                            // beginning so swap it with low position
+            swap(arr[low++], arr[mid++]);
+        else if (arr[mid] ==
+                 1)  // if arr[mid] is 1 it needs to be placed in the middle ,so
+                     // just increase the value of mid
+            mid++;
+        else
+            swap(arr[mid],
+                 arr[high--]);  // if arr[mid] is 2 it needs to be placed in the
+                                // beginning so swap it with high position
+    }
+}
+
+int main() {
+    vector<int> arr = {2, 0, 1, 2, 1, 0, 1, 2};
+    dutchNationalFlag(arr);
+
+    for (int x : arr) cout << x << " ";
+    cout << "\n";
+}
+// a dry run to explain the code:
+// arr = {2, 0, 1, 2, 1, 0, 1, 2} We have three pointers :
+
+//     low → start of 0’s segment
+
+//         mid → current element
+
+//             high → end of 2’s segment
+
+//                 Initially :
+
+//     ini Copy code low = 0,
+//                   mid = 0,
+//                   high = 7 arr = [ 2, 0, 1, 2, 1, 0, 1, 2 ] Step 1
+//     : arr[mid] = 2
+
+//                  Swap arr[mid] and
+//                  arr[high] → swap 2 with 2(no change)
+
+//                      Decrement high = 6
+
+//       ini Copy code arr = [ 2, 0, 1, 2, 1, 0, 1, 2 ] low = 0,
+//                   mid = 0,
+//                   high = 6 Step 2 : arr[mid] = 2
+
+//                                                Swap arr[mid] and
+//                                                arr[high] → swap 2 with 1
+
+//                                                Decrement high = 5
+
+//                                     ini Copy code arr =
+//                                         [ 1, 0, 1, 2, 1, 0, 2, 2 ] low = 0,
+//                   mid = 0,
+//                   high = 5 Step 3 : arr[mid] = 1
+
+//                                     Do nothing,
+//                   just increment mid = 1
+
+//                   ini Copy code arr = [ 1, 0, 1, 2, 1, 0, 2, 2 ] low = 0,
+//                   mid = 1,
+//                   high = 5 Step 4 : arr[mid] = 0
+
+//                                                Swap arr[low] and
+//                                                arr[mid] → swap 1 and 0
+
+//                                                Increment low = 1,
+//                   mid = 2
+
+//                   ini Copy code arr = [ 0, 1, 1, 2, 1, 0, 2, 2 ] low = 1,
+//                   mid = 2,
+//                   high = 5 Step 5 : arr[mid] = 1
+
+//                                     Increment mid = 3
+
+//                                     ini Copy code arr =
+//                                         [ 0, 1, 1, 2, 1, 0, 2, 2 ] low = 1,
+//                   mid = 3,
+//                   high = 5 Step 6 : arr[mid] = 2
+
+//                                                Swap arr[mid] and
+//                                                arr[high] → swap 2 and 0
+
+//                                                Decrement high = 4
+
+//                                     ini Copy code arr =
+//                                         [ 0, 1, 1, 0, 1, 2, 2, 2 ] low = 1,
+//                   mid = 3,
+//                   high = 4 Step 7 : arr[mid] = 0
+
+//                                                Swap arr[low] and
+//                                                arr[mid] → swap 1 and 0
+
+//                                                Increment low = 2,
+//                   mid = 4
+
+//                   ini Copy code arr = [ 0, 0, 1, 1, 1, 2, 2, 2 ] low = 2,
+//                   mid = 4,
+//                   high = 4 Step 8 : arr[mid] = 1
+
+//                                     Increment mid = 5 → now mid > high,
+//                   done !
+
+//  Final sorted array :
+
+//     csharp Copy code[0, 0, 1, 1, 1, 2, 2, 2]