【1】 最大子序列和问题



#include <iostream>
using  std::cout;
using  std::cin;
using  std::endl;

#include <vector>
using  std::vector;

// function declarations
int maxSubSum1(const vector<int> &a);
int maxSubSum2(const vector<int> &a);
int maxSubSum3(const vector<int> &a);
int maxSubSum4(const vector<int> &a);

int main()
{
 vector<int>  iv{ 4, -3, 5, -2, -1, 2, 6, -2 };

 cout << "max sub sum1: " << maxSubSum1(iv) << endl;
 cout << "max sub sum2: " << maxSubSum2(iv) << endl;
 cout << "max sub sum3: " << maxSubSum3(iv) << endl;
 cout << "max sub sum4: " << maxSubSum4(iv) << endl;

 cout << endl;

 system("pause");
 return 0;
}

int maxSubSum1(const vector<int> &a)
{
 int res = 0, sz = a.size();
 int i, j, k;
 for (i = 0; i < sz; ++i)
  for (j = i; j < sz; ++j)
  {
   int  thisSum = 0;
   for (k = i; k <= j; ++k)
    thisSum += a[k];

   if (thisSum > res)
    res = thisSum;
  }
 return  res;
}

int  maxSubSum2(const vector<int> &a)
{
 int  maxSum = 0, thisSum = 0;
 int  sz = a.size();
 int i, j;
 for (i = 0; i < sz; ++i)
 {
  for (j = i; j < sz; ++j)
  {
   thisSum += a[j];
   if (thisSum > maxSum)
    maxSum = thisSum;
  }
  thisSum = 0;
 }
 return  maxSum;
}

int max3(int a, int b, int c)
{
 int res = a;
 if (b > res)  res = b;
 if (c > res)   res = c;
 return  res;
}

int maxSumRec(const vector<int> &a, int left, int right)
{
 if (left == right)
  if (a[left] > 0)
   return  a[left];
  else
   return  0;

 int  center = (left + right) / 2;
 int  maxLS = maxSumRec(a, left, center);
 int  maxRS = maxSumRec(a, center + 1, right);

 int  maxLBS = 0, LBS = 0;
 for (int i = center; i >= left; --i)
 {
  LBS += a[i];
  if (LBS > maxLBS)
   maxLBS = LBS;
 }

 int  maxRBS = 0, RBS = 0;
 for (int j = center+1; j <= right; ++j)
 {
  RBS += a[j];
  if (RBS > maxRBS)
   maxRBS = RBS;
 }

 return  max3(maxLS, maxRS, maxLBS + maxRBS);
}

int  maxSubSum3(const vector<int> &a)
{
 return  maxSumRec(a, 0, a.size() - 1);
}

int  maxSubSum4(const vector<int> &a)
{
 int  maxSum = 0, thisSum = 0;
 for (int i = 0; i < a.size(); ++i)
 {
  thisSum += a[i];
  if (thisSum > maxSum)
   maxSum = thisSum;
  else if (thisSum < 0)
   thisSum = 0;
 }

 return  maxSum;
}