TOP K I

问题：求一维数组中最小的k个数。

时间复杂度为O(n)的OC算法实现：

//
//  TopKI.h
//  Algorithm
//
//  Created by han shuai on 2016/9/26.
//  Copyright © 2016年 han shuai. All rights reserved.
//

/**
 12
 */

#import <Foundation/Foundation.h>

@interface TopKI : NSObject

- (NSArray *)topk:(NSMutableArray *)dataArr k:(int)k;

@end

//
//  TopKI.m
//  Algorithm
//
//  Created by han shuai on 2016/9/26.
//  Copyright © 2016年 han shuai. All rights reserved.
//

#import "TopKI.h"

@implementation TopKI

- (NSArray *)topk:(NSMutableArray *)dataArr k:(int)k
{
    NSInteger start = 0;
    NSInteger end = dataArr.count-1;
    NSInteger index = [self partition:dataArr start:start end:end];
    while (index != k-1) {
        if (index > k-1) {
            end = index -1;
            index = [self partition:dataArr start:start end:end];
        }
        else{
            start = index+1;
            index = [self partition:dataArr start:start end:end];
        }
    }
    
    return [dataArr objectsAtIndexes:[NSIndexSet indexSetWithIndexesInRange:NSMakeRange(0, k)]];
}

- (NSInteger)partition:(NSMutableArray *)dataArr start:(NSInteger)start end:(NSInteger)end
{
    if (start > end) {
        return -1;
    }
    
    NSInteger index = start;//可随机选择pivot，不一定是第一个元素
    //第一次交换
    [self swap:dataArr i:index j:end];
    for (NSInteger i = start; i <end; i++) {
        if ([dataArr[i] intValue] < [dataArr[end] intValue]) {
            if (i!=index) {
                [self swap:dataArr i:index j:i];
            }
            index++;
        }
    }
    
    [self swap:dataArr i:index j:end];
    
    return index;
}

- (void)swap:(NSMutableArray *)dataArr i:(NSInteger)i j:(NSInteger)j
{
    NSNumber *temp = dataArr[i];
    dataArr[i] = dataArr[j];
    dataArr[j] = temp;
}

@end