# Seeking continuous element array and matrix sub-matrix of the largest and the largest and

2010-04-16  来源：本站原创  分类：CPP  人气：201

1
Given a length n of the one-dimensional array a, please find a sub-array in this array, so this sub-array and the sum = a [i] + a [i +1] + ... ... + a [j] the largest , where i> = 0, i <n,j> = i, j <n,
For example, 31 -41 5926-535897-93 -23 84
59 +26-53 +58 +97 submatrix = 187 was asked for the maximum sub array.
Example code:

```#include <iostream>
using namespace std ;

// Direct brute, find out all the possible combinations and    O(N^3)
int getSum1(int a[],int N)
{
int max=-10000000;
for(int i=0;i<N;i++)
{
for(int j=i;j<N;j++)
{
int tmp=0;
for(int k=i;k<=j;k++)
tmp+=a[k];
if(tmp>max)
max=tmp;
}
}
return max;
}

// With memory of recursive method   O(N^2)
int getSum2(int a[],int N)
{
int* cumarr=new int[N];
cumarr[0]=a[0];
// Pretreatment, makes the combinatorial and easier
for(int i=0;i<N;i++)// Some parts and to build first
{
cumarr[i]=cumarr[i-1]+a[i];
}
int max=-10000000;

for(int i=0;i<N;i++)
{
for(int j=i;j<N;j++)
{
// Optimization of place
int tmp=cumarr[j]=cumarr[i];
if(tmp>max)
max=tmp;
}
}
delete[] cumarr;
return max;
}

// The third kind  ,
int maxSubArray(int a[],int N)
{
int b=0,max=-10000000;
for(int i=0;i<N;i++)
{
if(b>0) b+=a[i]; // Greater than 0, the previous accumulated
else b=a[i];
if(b>max) max=b;
}
return max;
}

int main ()
{
int a[]={31,-41,59,26,-53,58,97,-93,-23, 84};
int N=sizeof(a)/sizeof(a[0]);
cout<<getSum1(a,N)<<endl;
cout<<getSum1(a,N)<<endl;
cout<<maxSubArray(a,N)<<endl;
return 0 ;
}
```

2

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