2020杭电多校第八场题解

Clockwise or Counterclockwise

题目传送门

Clockwise or Counterclockwise

题目大意

给你三个点ABC,判断A->B->C的方向(逆时针或者顺时针)

思路

叉积

/*
A(x1,y1) B(x2,y2) C(x3,y3)
向量AB=(x2-x1,y2-y1)
向量AC=(x3-x1,y3-y1)
若 AB x AC < 0 则 ABC 顺时针
若 AB x AC > 0 则 ABC 逆时针
若 AB x AC = 0 则 AB、AC 共线 同向或者反向
*/
struct node{
    double x,y;
}a[N];
double cross(node a,node b,node c){//>0,ab在ac顺时针;<0,ab在ac逆时针
    return (b.x-a.x)*(c.y-a.y) - (c.x-a.x)*(b.y-a.y);
}

AC Code

#include
#include
#include
#include
using namespace std;
#define endl '\n'
#define INF 0x3f3f3f3f
#define int long long
// #define TDS_ACM_LOCAL
const int N=4;
struct node{
    double x,y;
}a[N];
double cross(node a,node b,node c){//>0,ab在ac顺时针;<0,ab在ac逆时针
    return (b.x-a.x)*(c.y-a.y) - (c.x-a.x)*(b.y-a.y);
}
void solve(){
    cin>>a[1].x>>a[1].y>>a[2].x>>a[2].y>>a[3].x>>a[3].y;
    double d=cross(a[1], a[2], a[3]);
    if(d<0) cout<<"Clockwise"<<endl;
    else    cout<<"Counterclockwise"<<endl;
    return ;
}

signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);
#ifdef TDS_ACM_LOCAL
    freopen("D:\\VS code\\.vscode\\testall\\in.txt", "r", stdin);
    freopen("D:\\VS code\\.vscode\\testall\\out.txt", "w", stdout);
#endif
    int T;
    cin>>T;
    while(T--)  solve();
    return 0;
}

Fluctuation Limit

题目传送门

Fluctuation Limit

题目大意

给你n个区间l和r,以及波动k
求是否有一个序列满足在l~r(可以波动k)

思路

官方题解:
如果 i 是在 [l,r] 范围内, 那么 i + 1 必须要在 [l−k,r + k] 范围内.这是因为如果 i + 1 选了 范围外的值, i 就无解了. 这样可以从左往右, 把左边的约束带到右边.再从右往左做一遍.最后剩下的区间应该就是可 行域.因为题目只要求一种方案, 全部选最低的即可.复杂度 O(n).

AC Code

#include
#include
#include
using namespace std;
#define endl '\n'
#define INF 0x3f3f3f3f
#define int long long
// #define TDS_ACM_LOCAL
const int N=1e5 +9;
int n, k;
int l[N], r[N], L, R;
void solve(){
    cin>>n>>k;
    l[0]=0, r[0]=INF;
    for(int i=1; i<=n; i++){
        cin>>L>>R;
        l[i]=max(l[i-1]-k, L);
        r[i]=min(r[i-1]+k, R);
    }
    int flag=1;
    for(int i=n-1; i>=1; i--){
        l[i]=max(l[i+1]-k, l[i]);
        r[i]=min(r[i+1]+k, r[i]);
        if(l[i]>r[i])   flag=0;
    }
    if(flag){
        cout<<"YES"<<endl;
        for(int i=1; i<=n; i++) cout<<l[i]<<" ";
        cout<<endl;
    }
    else    cout<<"NO"<<endl;
    return ;
}

signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);
#ifdef TDS_ACM_LOCAL
    freopen("D:\\VS code\\.vscode\\testall\\in.txt", "r", stdin);
    freopen("D:\\VS code\\.vscode\\testall\\out.txt", "w", stdout);
#endif
    int T;
    cin>>T;
    while(T--)  solve();
    return 0;
}

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