解題區/解題區 - UVa

UVa 13046 - Bus Collisions

contents

  1. 1. Problem
  2. 2. Sample Input
  3. 3. Sample Output
  4. 4. Solution

Problem

給予兩個公車行駛路線，每台公車的速度都相同，分別從起始位置出發，請問第一個碰撞位置為何？

Sample Input

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21
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0  4
2  4
2  5
0  5
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1  7
1  2
3  2
3  7
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5  0
6  0
6  1
5  1
4
7  0
8  0
8  1
7  1

Sample Output

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2
Case 1: 1 5
Case 2: No Collision

Solution

抓路線長度的最小公倍數，一定能在這段時間內找到碰撞位置，否則不存在碰撞地點。

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#include <bits/stdc++.h>
using namespace std;
struct Pt {
    int x, y;
    Pt(int x = 0, int y = 0): x(x), y(y) {
    }
    int dist(Pt u) {
        return abs(x - u.x) + abs(y - u.y);
    }
    bool operator==(const Pt &u) const {
        return x == u.x && y == u.y;
    }
    Pt operator-(const Pt &u) const {
        return Pt(x - u.x, y - u.y);
    }
    Pt operator+(const Pt &u) const {
        return Pt(x + u.x, y + u.y);
    }
};
int main() {
    int testcase, cases = 0;
    int N[2], x, y;
    Pt R[2][64];
    scanf("%d", &testcase);
    while (testcase--) {
        int Len[2] = {};
        for (int i = 0; i < 2; i++) {
            scanf("%d", &N[i]);
            for (int j = 0; j < N[i]; j++) {
                scanf("%d %d", &x, &y);
                R[i][j] = Pt(x, y);
            }
            for (int j = 0; j < N[i]; j++)
                Len[i] += R[i][j].dist(R[i][(j+1)%N[i]]);
        }
        
        printf("Case %d: ", ++cases);
        
        int simT = Len[0]/__gcd(Len[0], Len[1])*Len[1];
        int posIdx[2], has = 0;
        Pt posXY[2];
        for (int i = 0; i < 2; i++)
            posIdx[i] = 0, posXY[i] = R[i][0];
            
        for (int it = 0; it < simT; it++) {
            for (int i = 0; i < 2; i++) {
                // move
                if (posXY[i] == R[i][posIdx[i]])
                    posIdx[i] = (posIdx[i]+1)%N[i];
                Pt dv = R[i][posIdx[i]] - posXY[i];
                int lenDv = abs(dv.x) + abs(dv.y);
                dv.x /= lenDv, dv.y /= lenDv;
                posXY[i] = posXY[i] + dv;
            }
            if (posXY[0] == posXY[1]) {
                printf("%d %d\n", posXY[0].x, posXY[0].y);
                has = 1;
                break;
            }
        }
        if (!has)
            puts("No Collision");
    }
    return 0;
}