算法笔记整理

10块钱买5瓶酒，2个瓶盖换一瓶，4个酒瓶换一瓶。问10块钱能买多少瓶酒？递归算法解决

#import "ViewController.h"
@interface ViewController ()
 
@property (nonatomic ,assign) int i;
@property (nonatomic ,assign) int number;
 
@end
 
@implementation ViewController
 
- (void)viewDidLoad {
    [super viewDidLoad];
    // Do any additional setup after loading the view, typically from a nib.
    self.i = 1;
    self.number = 5;
    [self calculateBeerWithBeer:5 bottleCaps:0 bottle:0];
}
 
/**
 *  @author djr
 *  
 *  计算酒瓶数
 *  @param beer 啤酒数
 *  @param bottleCaps 瓶盖数
 *  @param bottle 瓶子数
 */
- (void)calculateBeerWithBeer:(int)beer bottleCaps:(int)bottleCaps bottle:(int)bottle{
    NSLog(@"第%d次的啤酒数:%d,瓶盖数:%d,瓶子数:%d",self.i,beer,bottleCaps,bottle);
    /** 不管什么，反正瓶盖和瓶子等于啤酒（可能有换不完的） */
    bottle += beer;
    bottleCaps += beer;
    /** 换完瓶盖和瓶子之后的啤酒数，瓶盖数，瓶子数 */
    beer = bottleCaps / 2 + bottle / 4;
    bottleCaps = bottleCaps % 2;
    bottle = bottle % 4;
    NSLog(@"最后一共喝了:%d瓶啤酒",self.number += beer);
    if (beer == 0) return ;
    self.i ++;
    [self calculateBeerWithBeer:beer bottleCaps:bottleCaps bottle:bottle];
    
}
@end

为了排序A[1..n]，我们递归的排序A[1..n-1]，然后把A[n]插入到已排序的数组A[1..n-1]。为插入排序的这个递归版本的最坏运行情况运行时间写一个递归式：

归并排序算法

归并排序算法详情

NSMutableArray * array = [NSMutableArray arrayWithObjects:@8,@7,@6,@5,@4,@3,@2,@1, nil];
//调用排序
[self mergeSortArray:array];

- (void)mergeSortArray:(NSMutableArray *)array {
  //创建一个副本数组
  NSMutableArray * auxiliaryArray = [[NSMutableArray alloc]initWithCapacity:array.count];

  //对数组进行第一次二分，初始范围为0到array.count-1
  [self mergeSort:array auxiliary:auxiliaryArray low:0 high:array.count-1];
}
- (void)mergeSort:(NSMutableArray *)array auxiliary:(NSMutableArray *)auxiliaryArray low:(int)low high:(int)high {
  //递归跳出判断
  if (low>=high) {
    return;
  }
  //对分组进行二分
  int middle = (high - low)/2 + low;

  //对左侧的分组进行递归二分 low为第一个元素索引，middle为最后一个元素索引
  [self mergeSort:array auxiliary:auxiliaryArray low:low high:middle];

  //对右侧的分组进行递归二分 middle+1为第一个元素的索引，high为最后一个元素的索引
  [self mergeSort:array auxiliary:auxiliaryArray low:middle + 1 high:high];

  //对每个有序数组进行回归合并
  [self merge:array auxiliary:auxiliaryArray low:low middel:middle high:high];
}
- (void)merge:(NSMutableArray *)array auxiliary:(NSMutableArray *)auxiliaryArray low:(int)low middel:(int)middle high:(int)high {
  //将数组元素复制到副本
  for (int i=low; i<=high; i++) {
    auxiliaryArray[i] = array[i];
  }
  //左侧数组标记
  int leftIndex = low;
  //右侧数组标记
  int rightIndex = middle + 1;

  //比较完成后比较小的元素要放的位置标记
  int currentIndex = low;

  while (leftIndex <= middle && rightIndex <= high) {
    //此处是使用NSNumber进行的比较，你也可以转成NSInteger再比较
    if ([auxiliaryArray[leftIndex] compare:auxiliaryArray[rightIndex]]!=NSOrderedDescending) {
        //左侧标记的元素小于等于右侧标记的元素
        array[currentIndex] = auxiliaryArray[leftIndex];
        currentIndex++;
        leftIndex++;
    }else{
        //右侧标记的元素小于左侧标记的元素
        array[currentIndex] = auxiliaryArray[rightIndex];
        currentIndex++;
        rightIndex++;
    }
  }
  //如果完成后左侧数组有剩余
  if (leftIndex <= middle) {
     for (int i = 0; i<=middle - leftIndex; i++) {
        array[currentIndex +i] = auxiliaryArray[leftIndex +i ];
    }
  }
 }

此处只写思路，代码细节不细扣