Cod sursa(job #863699)

Utilizator PlayLikeNeverB4George Marcus PlayLikeNeverB4 Data 23 ianuarie 2013 23:12:24
Problema Gradina Scor 10
Compilator cpp Status done
Runda Arhiva de probleme Marime 4.3 kb
#include <cstdio>
#include <iostream>
#include <fstream>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <cstdlib>
#include <ctype.h>
#include <cstring>
#include <ctime>
#include <cassert>
#include <utility>

using namespace std;

#define INF 1e15
#define MAXN 255

struct Point {
    int x, y;
};

int N;
Point P[MAXN];
int idx[MAXN];
int FIRST;
int st[MAXN];
int head;
bool v[MAXN];
char distr1[MAXN], distr2[MAXN];
string minDistr;

long long crossProduct(const Point &A, const Point &B, const Point &C) {
    return (long long)(B.x - A.x) * (C.y - A.y) - (long long)(B.y - A.y) * (C.x - A.x);
}

bool cmp(const int &A, const int &B) {
    return P[A].y < P[B].y || (P[A].y == P[B].y && P[A].x < P[B].x);
}

void convexHull(vector<int> &pts, vector<int> &R) {
    if(pts.size() < 3)
        return;
    memset(v, false, sizeof(v));
    st[0] = pts[0];
    st[1] = pts[1];
    v[pts[1]] = true;
    head = 1;
    for(size_t i = 2; i < pts.size(); i++) {
        if(v[i]) continue;
        while(head >= 1 && crossProduct(P[st[head - 1]], P[st[head]], P[pts[i]]) < 0) {
            v[st[head]] = false;
            head--;
        }
        v[pts[i]] = true;
        st[++head] = pts[i];
    }
    for(int i = (int)pts.size() - 1; i >= 0; i--) {
        if(v[pts[i]]) {
            v[pts[i]] = false;
            continue;
        }
        while(head >= 1 && crossProduct(P[st[head - 1]], P[st[head]], P[pts[i]]) < 0) {
            v[st[head]] = false;
            head--;
        }
        st[++head] = pts[i];
    }

    for(int i = 0; i < head; i++)
        R.push_back(st[i]);
}

long long ariePoligon(vector<int> &pts) {
    long long ret = 0;
    for(size_t i = 1; i + 1 < pts.size(); i++) {
        long long cp = crossProduct(P[pts[0]], P[pts[i]], P[pts[i + 1]]);
        ret += cp;
    }
    return abs(ret);
}

string getDistr(vector<int> P[2]) {
    for(int i = 0; i < 2; i++)
        for(size_t j = 0; j < P[i].size(); j++) {
            if(i == 0) {
                distr1[P[i][j]] = 'I';
                distr2[P[i][j]] = 'V';
            }
            else {
                distr1[P[i][j]] = 'V';
                distr2[P[i][j]] = 'I';
            }
        }
    string v1(distr1);
    string v2(distr2);
    return min(v1, v2);
}

int main() {
	freopen("gradina.in", "r", stdin);
	freopen("gradina.out","w", stdout);

    scanf("%d", &N);
    for(int i = 0; i < N; i++)
        scanf("%d %d", &P[i].x, &P[i].y);

    for(int i = 0; i < N; i++)
        idx[i] = i;

    sort(idx, idx + N, cmp);

    long long minDiff = INF;
    for(int x = 0; x < N; x++)
        for(int y = 0; y < N; y++)
            if(x != y) {
                vector<int> sp[2];

                for(int i = 0; i < N; i++) {
                    if(i == x)
                        sp[0].push_back(idx[x]);
                    else if(i == y)
                        sp[1].push_back(idx[y]);
                    else {
                        long long cp = crossProduct(P[idx[x]], P[idx[y]], P[idx[i]]);
                        int side = (cp > 0);
                        sp[side].push_back(idx[i]);
                    }
                }

                vector<int> inf[2];
                convexHull(sp[0], inf[0]);
                if(sp[0].size() != inf[0].size())
                    continue;

                convexHull(sp[1], inf[1]);
                if(sp[1].size() != inf[1].size())
                    continue;

                long long arie[2];
                arie[0] = ariePoligon(inf[0]);
                arie[1] = ariePoligon(inf[1]);

                long long diff = arie[0] - arie[1];
                if(diff < 0)
                    diff = -diff;
                if(diff < minDiff) {
                    minDiff = diff;
                    minDistr = getDistr(inf);
                }
                else if(diff == minDiff) {
                    string s = getDistr(inf);
                    if(s < minDistr)
                        minDistr = s;
                }
            }

    printf("%.1lf\n", (double)minDiff / 2.0);
    printf("%s\n", minDistr.c_str());

	return 0;
}