P2034 选择数字

合集 - 思维题(99)

1.大雪球2024-01-162.E. Final Countdown2024-02-183.D. Divisible Pairs2024-02-194.F. Chat Screenshots2024-02-195.G. One-Dimensional Puzzle2024-02-206.P8775 [蓝桥杯 2022 省 A] 青蛙过河2024-02-217.Watering an Array2024-02-238.Dora and Search2024-02-249.P1137 旅行计划2024-02-2410.P3067 [USACO12OPEN] Balanced Cow Subsets G2024-02-2611.P4799 [CEOI2015 Day2] 世界冰球锦标赛2024-02-2612.A. Brick Wall2024-02-2813.B. Minimize Inversions2024-02-2814.C. XOR-distance2024-02-2815.A. Moving Chips2024-02-2816.B. Monsters Attack!2024-02-2817.C. Find B2024-02-2818.D. Slimes2024-02-2819.C. Turtle Fingers: Count the Values of k2024-02-2820.D. Turtle Tenacity: Continual Mods2024-02-2821.D. Vlad and Division2024-02-2822.C. LR-remainders2024-02-2823.P5322 [BJOI2019] 排兵布阵2024-03-0324.P2946 [USACO09MAR] Cow Frisbee Team S2024-03-0325.P1156 垃圾陷阱2024-03-0326.P1064 [NOIP2006 提高组] 金明的预算方案2024-03-0427.P3047 [USACO12FEB] Nearby Cows G2024-03-0428.P5020 [NOIP2018 提高组] 货币系统2024-03-0429.P3957 [NOIP2017 普及组] 跳房子2024-03-0630.P1550 [USACO08OCT] Watering Hole G2024-03-0631.P1525 [NOIP2010 提高组] 关押罪犯2024-03-0732.P1379 八数码难题2024-03-0733.P6121 [USACO16OPEN] Closing the Farm G2024-03-0834.P2341 [USACO03FALL / HAOI2006] 受欢迎的牛 G2024-03-0835.P9632 [ICPC2020 Nanjing R] K Co-prime Permutation2024-03-0836.P9825 [ICPC2020 Shanghai R] Fibonacci2024-03-08

37.P2034 选择数字2024-03-09

38.P7072 [CSP-J2020] 直播获奖2024-03-0939.P1714 切蛋糕2024-03-0940.P4147 玉蟾宫2024-03-1041.P2866 [USACO06NOV] Bad Hair Day S2024-03-1042.P2032 扫描2024-03-1043.P1884 [USACO12FEB] Overplanting S2024-03-1044.D. Lonely Mountain Dungeons2024-03-1245.F. Microcycle2024-03-1246.E. Increasing Subsequences__22024-03-1347.D. Valiant's New Map2024-03-1448.Array Repetition2024-03-1449.F. Rudolf and Imbalance2024-03-1450.D. Exam in MAC2024-03-1551.G. Rudolf and Subway2024-03-1552.C. Ehab and Path-etic MEXs2024-03-1753.A. String Transformation 12024-03-1754.D. Solve The Maze2024-03-1855.B. Array Fix2024-03-1856.B. Equal XOR2024-03-1857.F. Maximum White Subtree2024-03-1958.P1652 圆2024-03-2059.P2181 对角线2024-03-2060.P1325 雷达安装2024-03-2061.P3194 [HNOI2008] 水平可见直线2024-03-2062.B - Make Many Triangles2024-03-2363.[ARC172A] Chocolate2024-03-2564.C. Theofanis' Nightmare2024-03-2765.D. Birthday Gift2024-03-2766.C. Arrow Path2024-03-2767.P1265 公路修建2024-03-2868.P1284 三角形牧场2024-03-2869.Kirill and Mushrooms2024-03-2870.C. Sasha and the Casino2024-03-2871.P1470 [USACO2.3] 最长前缀 Longest Prefix2024-04-0172.P5536 【XR-3】核心城市2024-04-0273.P5836 [USACO19DEC] Milk Visits S2024-04-0274.P4391 [BOI2009] Radio Transmission 无线传输2024-04-0475.P3435 [POI2006] OKR-Periods of Words2024-04-0476.P5960 【模板】差分约束2024-04-0477.P3052 [USACO12MAR] Cows in a Skyscraper G2024-04-0578.E. Long Inversions2024-04-0979.C. Deep Down Below2024-04-0980.C. Rings2024-04-0981.F. Unfair Game2024-04-1082.G. GCD on a grid2024-04-1083.C. Inversion Graph2024-04-1084.Increase Subarray Sums2024-04-1085.D. Cross Coloring2024-04-1286.M. Triangle Construction2024-04-1287.D2. Set To Max (Hard Version)2024-04-1288.C. Array Game2024-04-1289.F. Alex's whims2024-04-1290.Queue Sort2024-04-1291.P1908 逆序对2024-04-1392.P5094 [USACO04OPEN] MooFest G 加强版2024-04-1593.P5149 会议座位2024-04-1594.P10337 [UESTCPC 2024] 操作序列2024-04-1595.P10330 [UESTCPC 2024] 黑白珠串2024-04-1596.P10252 线性变换2024-04-1697.P3901 数列找不同2024-04-1698.P10288 [GESP样题 八级] 区间2024-04-1699.P5677 [GZOI2017] 配对统计2024-04-17

收起

原题链接

题解

不能连续选k个元素 $\to$ 任意每k个元素就有一个不选 $\to$ 每k个点就有一个断点
$\to$ 每个点都有可能是断点 $\to$ dp求解

$sol.1$
令 $f[i]$ 为第i个点为断点且为结尾的最大值
则 $f[i]=max(f[j]+sum[j+1,i-1])$

$sol.2$
至少每隔k个点就取一个点，取点和的最小值

$code1$,优先队列，$O(n·logn)$

#include<bits/stdc++.h>
using namespace std;
#define ll long long
struct node
{
    ll v,x;
    bool operator <(const node &b)const {return b.v<v;}
};
ll dp[1000005]={0};
ll a[1000005];
int main()
{
    ll n,k,sum=0;
    cin>>n>>k;
    for(ll i=1;i<=n;i++)
    {
        cin>>a[i];
        sum+=a[i];
    }

    priority_queue<node> q;
    ll ans=2e18;
    for(ll i=1;i<=n;i++)
    {
        q.push({dp[i-1],i-1});
        while(q.size()&&i-q.top().x>k+1) q.pop();
        dp[i]=a[i];
        if(q.size()) dp[i]+=q.top().v;
        if(i+k>=n)ans=min(ans,dp[i]);
        //cout<<dp[i]<<endl;
    }

    cout<<sum-ans;
    return 0;
}

$code2$,单调队列，$O(n)$

#include<bits/stdc++.h>
using namespace std;
#define ll long long
ll sum[1000005]={0},f[100005]={0};
ll a[1000005];
int main()
{
    ll n,k;
    cin>>n>>k;
    for(ll i=1;i<=n;i++)
    {
        cin>>a[i];
        sum[i]=sum[i-1]+a[i];
    }

    deque<ll> q;
    q.push_back(0);
    for(int i=1;i<=n;i++)
    {
        if(q.size()&&i-q.front()>k+1)q.pop_front();

        if(q.size())  f[i]=f[q.front()]+sum[i-1]-sum[q.front()];
        while(q.size()&&f[q.back()]-sum[q.back()]<=f[i]-sum[i]) q.pop_back();
        q.push_back(i);
        //cout<<f[i]<<endl;
    }

    if(q.size()&&n-q.front()>k) q.pop_front();
    cout<<f[q.front()]+sum[n]-sum[q.front()];
    return 0;
}