hdu 3255 Farming(扫描线)

题目链接：hdu 3255 Farming

题目大意：给定N个矩形，M个植物，然后给定每一个植物的权值pi，pi表示种植物i的土地，单位面积能够收获pi，每一个矩形给定左下角和右上角点的坐标，以及s，s表示该矩形能够中植物s。问说总的最大收益。

解题思路：由于一块仅仅能种一种植物，所以对于一块重叠的土地，要选取收益最大的植物种植。除去这一点，剩下的就是线段树扫描线的应用了。那对于pi能够视为第三维坐标，而植物的种类仅仅有3种，所以直接离散化就可以，注意要依照植物收益的权值大小离散。

#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>

using namespace std;

vector<int> pos;

const int maxn = 120000;

#define lson(x) ((x)<<1)
#define rson(x) (((x)<<1)|1)
int lc[maxn << 2], rc[maxn << 2], v[maxn << 2], s[maxn << 2];

inline void pushup(int u) {
    if (v[u])
        s[u] = pos[rc[u]+1] - pos[lc[u]];
    else if (lc[u] == rc[u])
        s[u] = 0;
    else
        s[u] = s[lson(u)] + s[rson(u)];
}

inline void maintain (int u, int d) {
    v[u] += d;
    pushup(u);
}

void build (int u, int l, int r) {
    lc[u] = l;
    rc[u] = r;
    v[u] = s[u] = 0;

    if (l == r)
        return;

    int mid = (l + r) / 2;
    build(lson(u), l, mid);
    build(rson(u), mid + 1, r);
    pushup(u);
}

void modify (int u, int l, int r, int d) {

    if (l <= lc[u] && rc[u] <= r) {
        maintain(u, d);
        return;
    }

    int mid = (lc[u] + rc[u]) / 2;
    if (l <= mid)
        modify(lson(u), l, r, d);
    if (r > mid)
        modify(rson(u), l, r, d);
    pushup(u);
}

struct Seg {
    int x, l, r, d;
    Seg (int x = 0, int l = 0, int r = 0, int d = 0) {
        this->x = x;
        this->l = l;
        this->r = r;
        this->d = d;
    }
    friend bool operator < (const Seg& a, const Seg& b) {
        return a.x < b.x;
    }
};

typedef long long ll;
typedef pair<int,int> pii;

int N, M, P[10];
pii H[10];
vector<Seg> vec[10];

inline int find (int k) {
    return lower_bound(pos.begin(), pos.end(), k) - pos.begin();
}

void init () {
    scanf("%d%d", &N, &M);
    for (int i = 1; i <= M; i++) {
        vec[i].clear();
        scanf("%d", &H[i].first);
        H[i].second = i;
    }
    sort(H, H + M + 1);
    for (int i = 0; i <= M; i++)
        P[H[i].second] = i;

    int x1, x2, y1, y2, d;
    for (int i = 0; i < N; i++) {
        scanf("%d%d%d%d%d", &x1, &y1, &x2, &y2, &d);
        for (int j = 1; j <= P[d]; j++) {
            vec[j].push_back(Seg(x1, y1, y2, 1));
            vec[j].push_back(Seg(x2, y1, y2, -1));
        }
    }
}

ll solve (int idx) {
    pos.clear();
    sort(vec[idx].begin(), vec[idx].end());

    for (int i = 0; i < vec[idx].size(); i++) {
        pos.push_back(vec[idx][i].l);
        pos.push_back(vec[idx][i].r);
    }

    sort(pos.begin(), pos.end());
    build(1, 0, pos.size());

    ll ret = 0;
    for (int i = 0; i < vec[idx].size(); i++) {
        modify(1, find(vec[idx][i].l), find(vec[idx][i].r) - 1, vec[idx][i].d);
        if (i + 1 != vec[idx].size())
            ret += 1LL * s[1] * (vec[idx][i+1].x - vec[idx][i].x);
    }
    return ret;

}

int main () {
    int cas;
    scanf("%d", &cas);
    for (int kcas = 1; kcas <= cas; kcas++) {
        init();
        ll ans = 0;
        for (int i = 1; i <= M; i++)
            ans += 1LL * (H[i].first - H[i-1].first) * solve(i);
        printf("Case %d: %I64d\n", kcas, ans);
    }
    return 0;
}