C. Heavy Intervals

合集 - codeforces(57)

1.C. Insert and Equalize2023-12-062.C. Removal of Unattractive Pairs2023-12-063.D. Jumping Through Segments2023-12-084.E. Good Triples2023-12-085.F. Shift and Reverse2023-12-086.D. Yet Another Monster Fight2023-12-117.A. Constructive Problems2023-12-188.C. Game with Multiset2023-12-199.A. Rating Increase2023-12-1910.B. Swap and Delete2023-12-1911.A. Problemsolving Log2023-12-2012.B. Preparing for the Contest2023-12-2013.C. Quests2023-12-2014.D. Three Activities2023-12-2015.E2. Game with Marbles (Hard Version)2023-12-2016.cf刷题有感2023-12-2017.A. Anonymous Informant2023-12-2118.A. Forked!2023-12-2319.B. Make Almost Equal With Mod2023-12-27

20.C. Heavy Intervals2023-12-27

21.D. Split Plus K2023-12-2822.A. 20232023-12-3123.B. Two Divisors2023-12-3124.C. Training Before the Olympiad2023-12-3125.D. Mathematical Problem2024-01-0226.F. Greetings2024-01-0227.C. Partitioning the Array2024-01-1528.G. Bicycles2024-01-1629.E. Eat the Chip2024-01-1730.G. Lights2024-01-1731.D. Array Repetition2024-01-1732.D. Berserk Monsters2024-01-2233.E. Increasing Subsequences2024-01-2334.D. Very Different Array2024-01-2435.G. Mischievous Shooter2024-01-2536.B. Plus-Minus Split2024-01-2737.B. A Balanced Problemset2024-01-2838.C. Did We Get Everything Covered2024-01-2839.D. Find the Different Ones!2024-02-0840.C. Grouping Increases2024-02-1041.D. Good Trip2024-02-1242.C. Physical Education Lesson2024-02-1243.E. Final Countdown2024-02-1844.D. Divisible Pairs2024-02-1945.G. Vlad and Trouble at MIT2024-02-2046.A. Brick Wall2024-02-2847.B. Minimize Inversions2024-02-2848.C. XOR-distance2024-02-2849.A. Moving Chips2024-02-2850.B. Monsters Attack!2024-02-2851.C. Find B2024-02-2852.D. Slimes2024-02-2853.C. Turtle Fingers: Count the Values of k2024-02-2854.D. Turtle Tenacity: Continual Mods2024-02-2855.D. Vlad and Division2024-02-2856.C. LR-remainders2024-02-2857.D. Lonely Mountain Dungeons2024-03-12

收起

原题链接

简化题目

有一些左端点，右端点和权重，总价值是区间的长度乘上权重（区间长度=右端点-左端点），求最小总价值

开始思考

事实1.所有区间长度加起来是个定值
开始思考：能不能贪心做？答案是能。
在贪心的情况下，交换任意两个区间的端点或权重都会使总价值上升。（可以简化到只有n=2的情况考虑）

细节

在求最短区间长度的时候注意，每个区间最短长度一定是右端点减去最近没有被用过的左端点，因此栈结构呼之欲出
但只是求了每个区间的最短值，并没有求出哪个是最短区间

代码

#include<bits/stdc++.h>
#define ll long long
using namespace std;
ll c[100005]={0},dis[100005]={0};
struct unit
{
    int pos;
    int id;
}edge[200005];
bool cmp(unit a,unit b)
{
    return a.pos<b.pos;
}
int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        ll n;
        cin>>n;
        int len=0;
        for(int i=1;i<=n;i++)
        {
            cin>>edge[i].pos;
            edge[i].id=1;
        }
        for(int i=1+n;i<=2*n;i++)
        {
            cin>>edge[i].pos;
            edge[i].id=2;
        }
        sort(edge+1,edge+1+2*n,cmp);

        for(int i=1;i<=n;i++)cin>>c[i];
        sort(c+1,c+n+1);

        stack<int> q;
        for(int i=1;i<=2*n;i++)
        {
            if(edge[i].id==2)
            {
                dis[++len]=edge[i].pos-q.top();
                q.pop();
            }
            else q.push(edge[i].pos);
        }

        sort(dis+1,dis+n+1);
        ll ans=0;
        for(int i=1;i<=n;i++)ans+=dis[i]*c[n-i+1];
        cout<<ans<<endl;
    }
    return 0;
}