B. Tell Your World
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http://codeforces.com/contest/849/problem/B
题目是给出n个点,要求把这n个点分成两组,每组都是一条直线。而且这两组不能为空,还要是平行的。
思路:
对于前3个点来说,他们不可能各自一组,因为只能分成2组。
他们有可能同时一组,或者两个点在一组。
这一共就4种情况,然后O(n)判断即可
#include <bits/stdc++.h>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;
const int maxn = 1e3 + 20;
struct coor {
LL x, y;
} a[maxn], b[maxn];
int vis[maxn], DFN = 1;
int n;
bool same(int i, int j, int k) {
return (a[j].y - a[i].y) * (a[k].x - a[i].x) == (a[k].y - a[i].y) * (a[j].x - a[i].x);
}
bool init(int one, int two) {
++DFN;
vis[one] = vis[two] = DFN;
for (int i = 1; i <= n; ++i) {
if (vis[i] == DFN) continue;
if (same(one, two, i)) {
vis[i] = DFN;
}
}
int lenb = 0;
for (int i = 1; i <= n; ++i) {
if (vis[i] == DFN) continue;
if (lenb == 0) b[++lenb] = a[i];
else {
b[++lenb] = a[i];
if ((a[two].y - a[one].y) * (b[lenb].x - b[1].x) != (b[lenb].y - b[1].y) * (a[two].x - a[one].x)) {
return false;
}
}
}
return lenb != 0;
}
void work() {
scanf("%d", &n);
for (int i = 1; i <= n; ++i) {
scanf("%I64d", &a[i].y);
a[i].x = i;
}
for (int i = 1; i <= 3; ++i) {
for (int j = i + 1; j <= 3; ++j) {
if (init(i, j)) {
printf("Yes\n");
return;
}
}
}
printf("No\n");
}
int main() {
#ifdef local
freopen("data.txt", "r", stdin);
// freopen("data.txt", "w", stdout);
#endif
work();
return 0;
}