sort colors

Problem

Given an array with n objects colored red, white or blue, sort them so that objects of the same color are adjacent, with the colors in the order red, white and blue.

Here, we will use the integers 0, 1, and 2 to represent the color red, white, and blue respectively.

Note:
You are not suppose to use the library's sort function for this problem.

click to show follow up.

Follow up:
A rather straight forward solution is a two-pass algorithm using counting sort.
First, iterate the array counting number of 0's, 1's, and 2's, then overwrite array with total number of 0's, then 1's and followed by 2's.

Could you come up with an one-pass algorithm using only constant space?

Soluttion

其实这是一个比较有名的 Dutch national flag problem  , refer https://en.wikipedia.org/wiki/Dutch_national_flag_problem#Pseudocode

先考虑下简易版，如果只排两个颜色 0 和 1，要求从前往后一次扫过就拍好要怎么排？

用两个index i， j 从零开始向后扫。  i 表示前方都为0，它所指的是第一个为1的数； j 表示从 i 到 j 都是1 。

void func( vector<int>& nums){
    const int N = nums.size();
    for( int i = 0, j = 0; j < N; j++) {
        if(nums[j] == 0) {
            swap(nums[i++], nums[j]);
        }
    }
    
}

这样如果是排列三个数的话 ： 

void func( vector<int>& nums){
    const int N = nums.size();
    for( int i = 0, j = 0, k = N-1; j <= k; j++) {
        if(nums[j] == 0) {
            swap(nums[i++], nums[j]);
        }
        if(nums[j] == 2) {
            swap(nums[k--], nums[j--]);
        }
    }
}