求最大子序列

付翔 — Sun, 13 Jun 2010 15:19:00 GMT

#include <iostream>
#include <vector>
using namespace std;
int max3( int a, int b, int c )
{
return a > b ? a > c ? a : c : b > c ? b : c;
}

/** 分治法求最大子序列
* Recursive maximum contiguous subsequence sum algorithm.
* Finds maximum sum in subarray spanning a[left..right].
* Does not attempt to maintain actual best sequence.
*/
int maxSumRec( const vector<int> & a, int left, int right )
{
    if ( left == right ) // Base case
        if ( a[ left ] > 0 )
            return a[ left ];
        else
            return 0;

    int center = ( left + right ) / 2;
    int maxLeftSum  = maxSumRec( a, left, center );
    int maxRightSum = maxSumRec( a, center + 1, right );

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

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

    return max3( maxLeftSum, maxRightSum,
                 maxLeftBorderSum + maxRightBorderSum );
}

/**
* Driver for divide-and-conquer maximum contiguous
* subsequence sum algorithm.
*/
int maxSubSum3( const vector<int> & a )
{
    return maxSumRec( a, 0, a.size( ) - 1 );
}

/**
* Linear-time maximum contiguous subsequence sum algorithm.
*/
int maxSubSum4( const vector<int> & a )
{
    int maxSum = 0, thisSum = 0;

    for ( int j = 0; j < a.size( ); j++ )
    {
        thisSum += a[ j ];

        if ( thisSum > maxSum )
            maxSum = thisSum;
        else if ( thisSum < 0 )
            thisSum = 0;
    }

    return maxSum;
}
/*
最大正子序列所有的sub 都为正数
*/
int maxSubPositiveSum( const vector<int> & a)
{
    int maxSum = 0, thisSum = 0,i;
    bool isPositive[8];
    for (i = 0 ;i < 8 ; i ++)
        isPositive[i] = a[i]>0?true:false;
    for ( int j = 0; j < a.size( ); j++ )
    {

        if ( isPositive[j])
        {
            thisSum += a[ j ];
            if ( thisSum > maxSum )
                maxSum = thisSum;
            else if ( thisSum < 0 )
                thisSum = 0;
        }
        else if (!isPositive[j]  )
            thisSum = 0;

    }

    return maxSum;
}
int main( )
{
    vector<int> a( 8 );
    a[ 0 ] = 4;a[ 1 ] = -3;a[ 2 ] = 5;a[ 3 ] = -2;
    a[ 4 ] = -1;a[ 5 ] = 2;a[ 6 ] = 6;a[ 7 ] = -2;
    int maxSum,i;

    maxSum = maxSubSum3( a );
    cout << "Max sum is " <<  maxSum << endl;
    maxSum = maxSubPositiveSum( a );
    cout << "Max sum is " <<  maxSum << endl;

    return 0;
}

付翔 2010-06-13 23:19 发表评论

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求最大子序列