最大和子数组

编程之美2.14, 2.15节。这个问题在编程珠玑中的算法章有很深入的分析。

可以试解下题：

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=113&page=show_problem&problem=448

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=113&page=show_problem&problem=44

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=113&page=show_problem&problem=1768

下面为求maximum sum on torus的代码：

template<class It>
typename iterator_traits<It>::value_type
maxsum(It first, It last) {
    typedef typename iterator_traits<It>::value_type value_type;
    value_type maxsofar, maxatend;
    maxsofar = maxatend = *first++;
    for (It it = first; it != last; ++it) {
        maxatend = max(maxatend + *it, *it);
        maxsofar = max(maxsofar, maxatend);
    }
    return maxsofar;
}

template<class It>
typename iterator_traits<It>::value_type
minsum(It first, It last) {
    typedef typename iterator_traits<It>::value_type value_type;
    value_type minsofar, minatend;
    minsofar = minatend = *first++;
    for (It it = first; it != last; ++it) {
        minatend = min(minatend + *it, *it);
        minsofar = min(minsofar, minatend);
    }
    return minsofar;
}

template<class It>
typename iterator_traits<It>::value_type
sum(It first, It last) {
    typename iterator_traits<It>::value_type s = 0;
    for (It it = first; it != last; ++it)
        s += *it;
    return s;
}

template<class It>
typename iterator_traits<It>::value_type
rotatedmaxsum(It first, It last) {
    return max(maxsum(first, last), sum(first, last) - minsum(first, last));
}

template<class It>
typename iterator_traits<It>::value_type
torusmaxsum(It first, It last, size_t row) {
    typedef typename iterator_traits<It>::value_type value_type;
    size_t col = distance(first, last)/row;

    vector<value_type> sums(col, 0);
    for (size_t i = 0; i < row; ++i) {
        for (size_t j = 0, p = i*col; j < col; ++j) {
            It it = first;
            advance(it, p + j);
            sums[j] += *it;
        }
    }

    value_type r = *first;
    for (size_t i = 0; i < row; ++i) {
        vector<value_type> vec(col, 0);

        for (size_t j = i; j < row; ++j) {
            for (size_t k = 0, p = j*col; k < col; ++k) {
                It it = first;
                advance(it, p + k);
                vec[k] += *it;
            }
            r = max(r, rotatedmaxsum(vec.begin(), vec.end()));

            vector<value_type> rvec(col, 0);
            for (size_t i = 0; i < col; ++i)
                rvec[i] = sums[i] - vec[i];
            r = max(r, rotatedmaxsum(rvec.begin(), rvec.end()));
        }
    }
    return r;
}