算法导论第五章实例伪码转C++_最大子数组

1. 犯了一个错误，引发出对递归中变量定义的思考 P71

递归中要看变量的使用范围，以及如果作为全局，下面语句是否会修改其值

#include<iostream>

#include<climits>

using namespace std;

//find_maximum used

//int mid; 这里犯了一个错误，看下面 ，递归中用变量，要考虑其是局部全局

int mleft_sum,mleft_low,mleft_high;

int mright_sum,mright_low,mright_high;

int mcross_sum,mcross_low,mcross_high;

int result_low,result_high;

//find_max_crossmid used

int left_sum,right_sum,sum;

int A[16] = {13,-3,-25,20,-3,-16,-23,18,20,-7,12,-5,-22,15,-4,7};

int find_max_crossmid(int a[],int low,int mid, int high, int& max_left, int& max_right)

{

 left_sum = INT_MIN;

  sum = 0;

 for (int i = mid; i >= low; i--)

 {

  sum = sum + a[i];

  if (sum > left_sum)

   {

    left_sum = sum;

    max_left = i;

   }

 }

 

  right_sum = INT_MIN;

 sum = 0;

 for (int j = mid + 1; j <= high; j++)

 {

  sum = sum + a[j];

  if (sum > right_sum)

  {

   right_sum = sum;

   max_right = j;

  }

 }

 return (left_sum + right_sum);

}

int find_maximum(int a[],int low, int high)

{

 if (low == high)

 {

  result_low = low;

  result_high = high;

  return a[low];

 }

 else

 {

   int mid = (low + high)/2;

   //问题在这里，mid 是全局变量结果就不一样，这是必须是局部变量，否则下面

   //第一行就改变了mid的值，第二行用的mid就是下次递归的mid

//而作为局部变量，其适用范围确定，编译时会产生mid1,mid2。。。不用担心重复定义

  mleft_sum = find_maximum(a,low,mid);

 

  mright_sum = find_maximum(a,mid + 1,high);

 

  mcross_sum = find_max_crossmid(a,low,mid,high,mcross_low,mcross_high);

  if ((mleft_sum >= mright_sum) && (mleft_sum >= mcross_sum))

   {

    result_low = mleft_low; result_high = mleft_high;

    return mleft_sum;

  }

  else if ((mright_sum >= mleft_sum) && (mright_sum >= mcross_sum))

  {

   result_low = mright_low; result_high = mright_high;

   return mright_sum;

  }

  else{

   result_low = mcross_low; result_high = mcross_high;

   return mcross_sum;

  }

 }

}

int main()

{

    cout << find_maximum(A,0,15);

    return 0;

}