## Tuesday, September 22, 2015

### LeetCode OJ - Sort Colors

Problem:

Solution:

This is simply the famous Dutch flag problem - we maintain four pointers.

Left (L) points to the next number to read on the left hand side
Right(R) points to the next number to read on the right hand side
Red(r) points to the next position to write a red element (and we assert all elements before it is red)
Blue(b) points to the next position to write a blue element (and we assert all elements before it is blue)

We move the left pointers towards the right - while moving - make sure we keep the elements before L is sorted - it stops when it reach a blue or the end of the list

We move the right pointer towards the left - while moving - make sure we keep the elements after R is sorted - it stops when it reach a red or the beginning of the list

A typical execution look like this

0 1 2 0 2 1 1 0 2 1 2 0 2 0 1 2 1 0
L                             R
r                               b

The next obvious thing to do is to swap the content of L and R, so that the red goes left and the green goes blue. In the process, we also make sure the prefix and suffix are sorted, than we move on until the pointer crosses.

Code:

#include "stdafx.h"

// https://leetcode.com/problems/sort-colors/

#include "LEET_SORT_COLORS.h"
#include <map>
#include <iostream>
#include <sstream>
#include <vector>
#include <string>
#include <algorithm>

using namespace std;

namespace _LEET_SORT_COLORS
{
#define LOG
class Solution
{
public:
void sortColors(vector<int>& nums)
{
int size = nums.size();
int left = 0;
int right = size - 1;
int red = 0;
int blue = size - 1;
while (true)
{
while (left < size && nums[left] != 2)
{
if (nums[left] == 0)
{
swap(nums[red], nums[left]);
red++;
}
left++;
}
// After this loop, we are certain either left == size || nums[left] == 2
// nums[0, red) is red
// nums[red, left) is green

while (right >= 0 && nums[right] != 0)
{
if (nums[right] == 2)
{
swap(nums[blue], nums[right]);
blue--;
}
right--;
}
// Similarly, after this loop, we are certain that either right == -1 || nums[right] == 0
// nums(blue, size) is blue
// nums(right, blue] is green

#ifdef LOG
for (int i = 0; i < size; i++)
{
cout << nums[i] << " ";
}
cout << endl;

for (int i = 0; i < size; i++)
{
if (i == left) { cout << 'L'; }
else if (i == right) { cout << 'R'; }
else { cout << ' '; }
cout << ' ';
}
cout << endl;
for (int i = 0; i < size; i++)
{
if (i == red) { cout << 'r'; }
else if (i == blue) { cout << 'b'; }
else { cout << ' '; }
cout << ' ';
}
cout << endl;
cout << endl;
#endif

if (left == size || right == -1)
{
// The iteration above have arranged the order correctly
// this is the case when the array do not need a swap at all
break;
}
if (left > right)
{
// We have reach the point where the pointer crosses, no point doing any more swaps
break;
}

swap(nums[red], nums[left]);
swap(nums[blue], nums[right]);
swap(nums[red], nums[blue]);
left++;
right--;
red++;
blue--;
}
}
};
};

using namespace _LEET_SORT_COLORS;

int LEET_SORT_COLORS()
{
int case1_array[] = { 0, 1, 2, 0, 2, 1, 1, 0, 2, 1, 2, 0, 2, 0, 1, 2, 1, 0 };
int case2_array[] = { 1, 2, 0, 0 };
vector<int> case1_vector(case1_array, case1_array + _countof(case1_array));
vector<int> case2_vector(case2_array, case2_array + _countof(case2_array));
Solution s;
s.sortColors(case1_vector);
s.sortColors(case1_vector);
s.sortColors(case2_vector);
for (int i = 0; i < _countof(case1_array); i++)
{
cout << case1_vector[i] << " ";
}
cout << endl;
for (int i = 0; i < _countof(case2_array); i++)
{
cout << case2_vector[i] << " ";
}
cout << endl;
return 0;
}