kuangbin专题十三：基础计算几何

POJ2318 TOYS

思路：二分。

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn = 5005;
int n, m, x1, y1, x2, y2;

int box[maxn];

struct Board{
    int x1, x2;
} board[maxn];

bool onLeft(int idx, int x, int y){
    Board &b = board[idx];
    return (b.x2 - b.x1) * (y - y1) - (y2 - y1) * (x - b.x1) < 0;
}

int findPosition(int x, int y){
    int l = 0, r = n + 1;
    while(l + 1 != r){
        int mid = (l + r) >> 1;
        if (onLeft(mid, x, y))
            r = mid;
        else
            l = mid;
    }
    return l;
}

int main(){

    while(scanf("%d", &n) && n){
        memset(box, 0, sizeof(box));
        scanf("%d%d%d%d%d", &m, &x1, &y1, &x2, &y2);

        board[0].x1 = board[0].x2 = x1;
        board[n+1].x1 = board[n+1].x2 = x2;
        for(int i = 1; i <= n; i++) scanf("%d%d", &board[i].x1, &board[i].x2);

        for(int i = 0; i < m; i++) {
            int x, y;
            scanf("%d%d", &x, &y);
            int position = findPosition(x, y);
            box[position]++;
        }

        for(int i = 0; i <= n; i++)
            printf("%d: %d\n", i, box[i]);
        printf("\n");

    }
    return 0;
}

 

POJ2398 Toy Storage

思路：同上，记得给挡板排序。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn = 5005;
int n, m, x1, y1, x2, y2;

int box[maxn];

struct Cnt{
    int cnt, idx;
} cnt[maxn];

struct Board{
    int x1, x2;
} board[maxn];

bool onLeft(int idx, int x, int y){
    Board &b = board[idx];
    return (b.x2 - b.x1) * (y - y1) - (y2 - y1) * (x - b.x1) < 0;
}

int findPosition(int x, int y){
    int l = 0, r = n + 1;
    while(l + 1 != r){
        int mid = (l + r) >> 1;
        if (onLeft(mid, x, y))
            r = mid;
        else
            l = mid;
    }
    return l;
}

bool cmpBoard(const Board& b1, const Board& b2){
    if(b1.x1 == b2.x1)
        return b1.x2 < b2.x2;
    return b1.x1 < b2.x1;
}

int main(){
    while(scanf("%d", &n) && n){
        memset(box, 0, sizeof(box));
        memset(cnt, 0, sizeof(cnt));
        scanf("%d%d%d%d%d", &m, &x1, &y1, &x2, &y2);

        board[0].x1 = board[0].x2 = x1;
        board[n+1].x1 = board[n+1].x2 = x2;
        for(int i = 1; i <= n; i++) scanf("%d%d", &board[i].x1, &board[i].x2);
        sort(board, board + n + 2, cmpBoard);

        for(int i = 0; i < m; i++) {
            int x, y;
            scanf("%d%d", &x, &y);
            int position = findPosition(x, y);
            box[position]++;
        }

        for(int i = 0; i <= n; i++){
            cnt[box[i]].cnt++;
        }

        printf("Box\n");
        for(int i = 1; i <= m; i++)
            if(cnt[i].cnt)
                printf("%d: %d\n", i, cnt[i].cnt);

    }
    return 0;
}

 

POJ1269 Intersection Lines

思路：处理各种情况，代码较丑。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
const int maxn = 105;

int main(){
    int t;
    cin >> t;
    cout << "INTERSECTING LINES OUTPUT" << endl;
    while(t--){
        double x[4], y[4];
        for(int i = 0; i < 4; i++) cin >> x[i] >> y[i];
        double dy1 = y[1] - y[0], dy2 = y[3] - y[2];
        double dx1 = x[1] - x[0], dx2 = x[3] - x[2];

        if (abs(dy1*dx2 - dy2*dx1) < 1e-6){
            double dy3 = y[2] - y[0], dx3 = x[2] - x[0];
            if(abs(dx1*dy3 - dx3*dy1) < 1e-6)
                cout << "LINE" << endl;
            else
                cout << "NONE" << endl;
        }
        else{
            if(abs(dx1) < 1e-6){
                double yy = (dy2 / dx2) * (x[1] - x[2]) + y[2];
                printf("POINT %.2f %.2f\n", x[1], yy);
            }
            else{
                double k1 = dy1 / dx1, k2 = dy2 / dx2;
                double xx = (y[2] - y[0] + k1*x[0] - k2*x[2]) / (k1-k2);
                double yy = k1*(xx - x[0]) + y[0];
                printf("POINT %.2f %.2f\n", xx, yy);
            }
        }
    }
    cout << "END OF OUTPUT" << endl;
    return 0;
}

 

POJ 2653 Pick-up sticks

思路：暴力。注意输入。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
const int maxn = 1e5+5;

struct Segment{
    float x1, y1, x2, y2;
} seg[maxn];

float cross(float x1, float y1, float x2, float y2){
    return x1 * y2 - x2 * y1;
}

bool aside(Segment& s1, Segment& s2){
    float dx = s1.x2 - s1.x1, dy = s1.y2 - s1.y1;
    float dx1 = s2.x1 - s1.x1, dy1 = s2.y1 - s1.y1;
    float dx2 = s2.x2 - s1.x1, dy2 = s2.y2 - s1.y1;
    return cross(dx, dy, dx1, dy1) * cross(dx, dy, dx2, dy2) <= 0;
}

bool intersect(Segment& s1, Segment& s2){
    return aside(s1, s2) && aside(s2, s1);
}

int main(){
    int n;
    while(~scanf("%d", &n) && n){
        for(int i = 0; i < n; i++)
            scanf("%f%f%f%f", &seg[i].x1, &seg[i].y1, &seg[i].x2, &seg[i].y2);

        printf("Top sticks: ");

        for(int i = 0; i < n; i++){
            bool flag = true;
            for(int j = i + 1; j < n; j++){
                if(intersect(seg[i], seg[j])){
                    flag = false;
                    break;
                }
            }
            if(flag){
                printf("%d", i + 1);
                if(i == n-1) printf(".\n");
                else printf(", ");
            }
        }
    }
    return 0;
}

 

POJ1066 Treasure Hunt