算法笔记-快速排序之无序数组中查找中位数

问题描述：

给一个无序数组array和数组长度n，找出其中的中位数（这里考虑n为奇数）

Sample:

 ***** Input:
 ***** @[@(500),@(120),@(7),@(220),@(3),@(8),@(4),@(200),@(100)
 ***** Output:
 ***** 100

解法一：将数组进行排序，然后输出array(n-1)/2，排序算法中我们选取快速排序：

- (void)quickSortingWitharray:(NSMutableArray *)array andleftIndex:(NSInteger)left withRightIndex:(NSInteger)right{

    if (left >= right) {
        return;
    }

    NSInteger leftIndex = left;
    NSInteger rightIndex = right;
    NSInteger key = [array[left] integerValue];

    while (leftIndex < rightIndex) {

        while ([array[rightIndex] integerValue] >= key && leftIndex < rightIndex) {
            rightIndex --;
        }
        array[leftIndex] = array[rightIndex];


        while ([array[leftIndex] integerValue] <= key && leftIndex < rightIndex) {
            leftIndex ++;
        }
        array[rightIndex] = array[leftIndex];
    }

    array[leftIndex] = @(key);

    [self quickSortingWitharray:array andleftIndex:left withRightIndex:leftIndex - 1];
    [self quickSortingWitharray:array andleftIndex:leftIndex + 1 withRightIndex:right];


}

解法二：还是用快速排序，但是我们可以减少一部分排序，因为每次快排都是将数组分成左右两个小数组再进行排序，我们知道右边的数组中的值都是大于左边数组中的值，而且我们可以获取到每次分组时的位置index，index和(n-1)/2,做比较，当相等时,array[index]就找到了我们要的值

- (NSInteger)yquickSortingWitharray:(NSMutableArray *)array andleftIndex:(NSInteger)left withRightIndex:(NSInteger)right{

    NSInteger leftIndex = left;
    NSInteger rightIndex = right;
    NSInteger key = [array[left] integerValue];

    while (leftIndex < rightIndex) {

        while ([array[rightIndex] integerValue] >= key && leftIndex < rightIndex) {
            rightIndex --;
        }
        array[leftIndex] = array[rightIndex];


        while ([array[leftIndex] integerValue] <= key && leftIndex < rightIndex) {
            leftIndex ++;
        }
        array[rightIndex] = array[leftIndex];
    }

    array[leftIndex] = @(key);

    return leftIndex;


}

- (NSInteger)finmidArray:(NSMutableArray *)array {
    NSInteger mid = (array.count-1)/2;
    NSInteger start = 0;
    NSInteger end = array.count - 1;

    NSInteger index = [self yquickSortingWitharray:array andleftIndex:start withRightIndex:end];
    while (index != mid) {
        if (mid < index) {
            index = [self yquickSortingWitharray:array andleftIndex:start withRightIndex:index - 1];
        } else {
            index = [self yquickSortingWitharray:array andleftIndex:index + 1 withRightIndex:end];
        }
    }

    return [array[index] integerValue];
}

• 通过下图我们可以看到通过解法二，可以省略很多次排序也可以拿到中位数100.