*******************************快速排序 start**********************************/
//随即取 当前取第一个，首先找到第一个的位置，然后分成left和right两组子集 ，分别对left和right继续执行分割(同上操作)

-(void)QuickSort:(NSMutableArray *)list StartIndex:(NSInteger)startIndex EndIndex:(NSInteger)endIndex{
    
    if(startIndex >= endIndex)return;
    
    NSNumber * temp = [list objectAtIndex:startIndex];
    NSInteger tempIndex = startIndex; //临时索引 处理交换位置(即下一个交换的对象的位置)
    
    for(int i = startIndex + 1 ; i <= endIndex ; i++){
        
        NSNumber *t = [list objectAtIndex:i];
        
        if([temp intValue] > [t intValue]){
            
            tempIndex = tempIndex + 1;
            
            [list exchangeObjectAtIndex:tempIndex withObjectAtIndex:i];
            
        }
        
    }
    
    [list exchangeObjectAtIndex:tempIndex withObjectAtIndex:startIndex];
    [self QuickSort:list StartIndex:startIndex EndIndex:tempIndex-1];
    [self QuickSort:list StartIndex:tempIndex+1 EndIndex:endIndex];

}




//取第一个 与其邻接的对比，若大则交换
-(void)BubbleSort:(NSMutableArray *)list{
    
    for (int j = 1; j<= [list count]; j++) {
            
        for(int i = 0 ;i < j ; i++){
            
            if(i == [list count]-1)return;
            
            NSInteger a1 = [[list objectAtIndex:i] intValue];
            NSInteger a2 = [[list objectAtIndex:i+1] intValue];
            
            if(a1 > a2){
                [list exchangeObjectAtIndex:i withObjectAtIndex:i+1];
            }
            
        }
        
    }
    
}



//从无序表中取出第一个元素，插入到有序表的合适位置，使有序表仍然有序
-(void)InsertSort:(NSMutableArray *)list{
    
    for(int i = 1 ; i < [list count] ; i++){
        
        
        int j = i;
        NSInteger temp= [[list objectAtIndex:i] intValue];
        
        while (j > 0 && temp < [[list objectAtIndex:j - 1]intValue]) {
            
            [list replaceObjectAtIndex:j withObject:[list objectAtIndex:(j-1)]];
            //list[j] = list[j-1];
            j--;
        
        }
        [list replaceObjectAtIndex:j withObject:[NSNumber numberWithInt:temp]];
        //list[j] = temp;
        
    }
    
}



//从无序表中取出第一个元素，利用折半查找插入到有序表的合适位置，使有序表仍然有序
-(void)BinaryInsertSort:(NSMutableArray *)list{
    
    //索引从1开始 默认让出第一元素为默认有序表 从第二个元素开始比较
    for(int i = 1 ; i < [list count] ; i++){
        
        //binary search start
        NSInteger temp= [[list objectAtIndex:i] intValue];
        
        int left = 0; 
        int right = i - 1;
        
        while (left <= right) {
            
            int middle = (left + right)/2;
            
            if(temp < [[list objectAtIndex:middle] intValue]){
                
                right = middle - 1;
                
            }else{
                
                left = middle + 1;
            
            }
            
        }
        //binary search end
        
        //移动3,5,6,[4] 4是当前目标对象 利用binarysearch 找到4应该在有续集{3,5,6}的位置，然后向后移动即{3,5,6,[4]}-->{3,[4],5,6}
        for(int j = i ; j > left; j--){
            
            [list replaceObjectAtIndex:j withObject:[list objectAtIndex:j-1]];
            
        }
        [list replaceObjectAtIndex:left withObject:[NSNumber numberWithInt:temp]];
        
    }
    
    
}



//对直接插入排序优化，创造一个gap 来对表进行分割，对分割后的每个子集进行直接插入排序 知道gap＝＝1结束
-(void)shellSort:(NSMutableArray *)list{

    int gap = [list count] / 2;
    
    while (gap >= 1) {
        
        
        for(int i = gap ; i < [list count]; i++){
        
            NSInteger temp = [[list objectAtIndex:i] intValue];
            int j = i;
            
            while (j >= gap && temp < [[list objectAtIndex:(j - gap)] intValue]) {
                [list replaceObjectAtIndex:j withObject:[list objectAtIndex:j-gap]];
                j -= gap;
            }
            [list replaceObjectAtIndex:j withObject:[NSNumber numberWithInt:temp]];
            
            
        }
        
        gap = gap / 2;
    }

}

 

//创建最大堆heap 最大／最小优先级队列
-(void)CreateBiggestHeap:(NSMutableArray *)list Count:(NSInteger)count{
    
    //int count = [list count];
    int lastParentIndex = (count - 2)/2;
    for(int i = lastParentIndex; i >= 0 ; i--){
        
        NSInteger parentIndex = i;
        NSInteger parentNode = [[list objectAtIndex:parentIndex] intValue];
        
        
        //获取左子结点为当前子结点
        int currentChildIndex = 2*i + 1;
        // 
        
        while (currentChildIndex <= count - 1) {
            
            NSInteger leftChildNode = [[list objectAtIndex:(currentChildIndex)] intValue];
            
            if((currentChildIndex + 1) <= count-1){//表示存在右子结点
                
                //读取右子结点
                int rightChildIndex =currentChildIndex + 1;
                NSInteger rightChildNode = [[list objectAtIndex:(rightChildIndex)] intValue];
                
                //如果右子结点为最大
                if(rightChildNode > leftChildNode && rightChildNode > parentNode){
                    [list exchangeObjectAtIndex:parentIndex withObjectAtIndex:rightChildIndex];
                    currentChildIndex = rightChildIndex;//右子结点为当前子结点 继续循环
                //左子结点最大
                }else if(leftChildNode > rightChildNode && leftChildNode > parentNode){
                    [list exchangeObjectAtIndex:parentIndex withObjectAtIndex:currentChildIndex];
                }
                
            }else{
                
                if(leftChildNode > parentNode){
                    [list exchangeObjectAtIndex:parentIndex withObjectAtIndex:currentChildIndex];
                    
                }
                
            }
            
            //更新父结点和下一个子结点
            parentIndex = currentChildIndex;
            currentChildIndex = 2*currentChildIndex + 1;
                        
        }

    }
    
}

//每次执行最大堆(索引要前移动 即排除已经排好的最大堆头元算 交换到list尾部的这个元素)
-(void)HeapSort:(NSMutableArray *)list{
    
    for(int i = [list count] ; i > 0; i--){
        
        [self CreateBiggestHeap:list Count:i];
        
        //NSLog(@"%@",list);
        
        [list exchangeObjectAtIndex:(i-1) withObjectAtIndex:0];
        
    }
    
}

//在对象集中选出最小的 若不是第一个 则与第一个交换 在剩余的对象集中选出最小的 执行前面的步骤
-(void)SelectSort:(NSMutableArray *)list{
    
    for(int i = 0 ; i<[list count]; i++){
        
        int k = i;
        for(int j = i+1 ; j<[list count]; j++){
            
            NSInteger jvalue = [[list objectAtIndex:j] intValue];
            NSInteger kvalue = [[list objectAtIndex:k] intValue];
            
            if(jvalue < kvalue){
                k = j;
            }
            
        }
        if(k != i){
            [list exchangeObjectAtIndex:i withObjectAtIndex:k];
        }
        
    }
    
}

原文地址  http://www.cnblogs.com/Jere-Jobs/archive/2013/03/07/2948662.html