了解荷兰国旗计划

Question

I was reading the Dutch national flag problem , but couldn't understand what the low and high arguments are in the threeWayPartition function in the C++ implementation.

If I assume them as min and max elements of the array to be sorted, then the if and else if statements doesn't makes any sense since (data[i] < low) and (data[i] > high) always returns zero.

Where am I wrong?

Answer 1

low and high are the values you have defined to do the three-way partition ie to do a three-way partition you only need two values:

[bottom] <= low  < [middle] < high <= [top]

In the C++ program what you are moving are the positions where the partitions occurred. A step-by-step example:

data = [ 3, 1, 4, 9, 8, 2, 6, 9, 0 ]
low  = 4
high = 8

   [ 3 , 1 , 4 , 9 , 8 , 2 , 6 , 9 , 0 ]
p^  i^                                  q^

   [ 3 , 1 , 4 , 9 , 8 , 2 , 6 , 9 , 0 ]
    p^  i^                              q^

   [ 3 , 1 , 4 , 9 , 8 , 2 , 6 , 9 , 0 ]
        p^  i^                          q^

   [ 3 , 1 , 4 , 9 , 8 , 2 , 6 , 9 , 0 ]
        p^      i^                      q^

   [ 3 , 1 , 4 , 0 , 8 , 2 , 6 , 9 , 9 ]
        p^      i^                  q^

   [ 3 , 1 , 0 , 4 , 8 , 2 , 6 , 9 , 9 ]
            p^      i^              q^

   [ 3 , 1 , 0 , 4 , 9 , 2 , 6 , 8 , 9 ]
            p^      i^          q^

   [ 3 , 1 , 0 , 4 , 6 , 2 , 9 , 8 , 9 ]
            p^      i^      q^

   [ 3 , 1 , 0 , 4 , 6 , 2 , 9 , 8 , 9 ]
            p^          i^  q^

   [ 3 , 1 , 0 , 2 , 6 , 4 , 9 , 8 , 9 ]
                p^         iq^

As the algorithm says you:

• Swap the element above the bottom (ie p + 1 ) because everything below the bottom has been already checked, or
• Swap the element below the top (ie q - 1 ) because everything above the top has been already checked, or
• Leave the element where it is because it belongs to middle.

You get [3, 1, 0, 2] , [6, 4] and [9, 8, 9] as bottom, middle and top partitions respectively.

Answer 2

} else if (data[i] >= high) {表明您看到的内容可能不是文章中所写的内容。

Answer 3

Think of low and high as the half-open range [low,high) for values in the middle partition. All values less than low end up in the left partition. The middle partition will contain the values from low up to, but not including, high . Finally, all values greater than or equal to high end up in the right partition.