[CareerCup][Google Interview] 找最大序列

A circus is designing a tower routine consisting of people standing atop one another’s
shoulders. For practical and aesthetic reasons, each person must be both shorter and lighter than the person below him or her. Given the heights and weights of each person in the circus, write a method to compute the largest possible number of people
in such a tower.
EXAMPLE:
Input (ht, wt): (65, 100) (70, 150) (56, 90) (75, 190) (60, 95) (68, 110)
Output: The longest tower is length 6 and includes from top to bottom: (56, 90) (60,95) (65,100) (68,110) (70,150) (75,190)

http://www.careercup.com/question?id=9339758

先把数组按height或者weight排个序，然后就变为找最长上升子序列问题了。

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

struct Node
{
    int height;
    int weight;

    Node(){}
    Node(int h, int w):height(h), weight(w){}
};

bool comp(const Node &lhs, const Node &rhs)
{
    return lhs.height < rhs.height;
}

int solve(vector<Node> &a)
{
    sort(a.begin(), a.end(), comp);

    vector<int> f(a.size());

    f[0] = 1;

    for(int i = 1; i < a.size(); i++)
    {
        f[i] = 1;
        for(int j = 0; j < i; j++)
            if (a[i].height > a[j].height && a[i].weight > a[j].weight)
                f[i] = max(f[i], f[j] + 1);
    }

    int maxF = 0;
    for(int i = 0; i < f.size(); i++)
        maxF = max(maxF, f[i]);

    return maxF;
}

int main()
{
    vector<Node> a;
    a.push_back(Node(65, 100));
    a.push_back(Node(70, 150));
    a.push_back(Node(56, 90));
    a.push_back(Node(75, 190));
    a.push_back(Node(60, 95));
    a.push_back(Node(68, 110));

    cout << solve(a) << endl;

    vector<Node> b;
    b.push_back(Node(1, 2));
    b.push_back(Node(1, 3));

    cout << solve(b) << endl;
}