Increase Subarray Sums

合集 - 思维题(99)

1.大雪球2024-01-16 2.E. Final Countdown2024-02-18 3.D. Divisible Pairs2024-02-19 4.F. Chat Screenshots2024-02-19 5.G. One-Dimensional Puzzle2024-02-20 6.P8775 [蓝桥杯 2022 省 A] 青蛙过河2024-02-21 7.Watering an Array2024-02-23 8.Dora and Search2024-02-24 9.P1137 旅行计划2024-02-24 10.P3067 [USACO12OPEN] Balanced Cow Subsets G2024-02-26 11.P4799 [CEOI2015 Day2] 世界冰球锦标赛2024-02-26 12.A. Brick Wall2024-02-28 13.B. Minimize Inversions2024-02-28 14.C. XOR-distance2024-02-28 15.A. Moving Chips2024-02-28 16.B. Monsters Attack!2024-02-28 17.C. Find B2024-02-28 18.D. Slimes2024-02-28 19.C. Turtle Fingers: Count the Values of k2024-02-28 20.D. Turtle Tenacity: Continual Mods2024-02-28 21.D. Vlad and Division2024-02-28 22.C. LR-remainders2024-02-28 23.P5322 [BJOI2019] 排兵布阵2024-03-03 24.P2946 [USACO09MAR] Cow Frisbee Team S2024-03-03 25.P1156 垃圾陷阱2024-03-03 26.P1064 [NOIP2006 提高组] 金明的预算方案2024-03-04 27.P3047 [USACO12FEB] Nearby Cows G2024-03-04 28.P5020 [NOIP2018 提高组] 货币系统2024-03-04 29.P3957 [NOIP2017 普及组] 跳房子2024-03-06 30.P1550 [USACO08OCT] Watering Hole G2024-03-06 31.P1525 [NOIP2010 提高组] 关押罪犯2024-03-07 32.P1379 八数码难题2024-03-07 33.P6121 [USACO16OPEN] Closing the Farm G2024-03-08 34.P2341 [USACO03FALL / HAOI2006] 受欢迎的牛 G2024-03-08 35.P9632 [ICPC2020 Nanjing R] K Co-prime Permutation2024-03-08 36.P9825 [ICPC2020 Shanghai R] Fibonacci2024-03-08 37.P2034 选择数字2024-03-09 38.P7072 [CSP-J2020] 直播获奖2024-03-09 39.P1714 切蛋糕2024-03-09 40.P4147 玉蟾宫2024-03-10 41.P2866 [USACO06NOV] Bad Hair Day S2024-03-10 42.P2032 扫描2024-03-10 43.P1884 [USACO12FEB] Overplanting S2024-03-10 44.D. Lonely Mountain Dungeons2024-03-12 45.F. Microcycle2024-03-12 46.E. Increasing Subsequences__22024-03-13 47.D. Valiant's New Map2024-03-14 48.Array Repetition2024-03-14 49.F. Rudolf and Imbalance2024-03-14 50.D. Exam in MAC2024-03-15 51.G. Rudolf and Subway2024-03-15 52.C. Ehab and Path-etic MEXs2024-03-17 53.A. String Transformation 12024-03-17 54.D. Solve The Maze2024-03-18 55.B. Array Fix2024-03-18 56.B. Equal XOR2024-03-18 57.F. Maximum White Subtree2024-03-19 58.P1652 圆2024-03-20 59.P2181 对角线2024-03-20 60.P1325 雷达安装2024-03-20 61.P3194 [HNOI2008] 水平可见直线2024-03-20 62.B - Make Many Triangles2024-03-23 63.[ARC172A] Chocolate2024-03-25 64.C. Theofanis' Nightmare2024-03-27 65.D. Birthday Gift2024-03-27 66.C. Arrow Path2024-03-27 67.P1265 公路修建2024-03-28 68.P1284 三角形牧场2024-03-28 69.Kirill and Mushrooms2024-03-28 70.C. Sasha and the Casino2024-03-28 71.P1470 [USACO2.3] 最长前缀 Longest Prefix2024-04-01 72.P5536 【XR-3】核心城市2024-04-02 73.P5836 [USACO19DEC] Milk Visits S2024-04-02 74.P4391 [BOI2009] Radio Transmission 无线传输2024-04-04 75.P3435 [POI2006] OKR-Periods of Words2024-04-04 76.P5960 【模板】差分约束2024-04-04 77.P3052 [USACO12MAR] Cows in a Skyscraper G2024-04-05 78.E. Long Inversions2024-04-09 79.C. Deep Down Below2024-04-09 80.C. Rings2024-04-09 81.F. Unfair Game2024-04-10 82.G. GCD on a grid2024-04-10 83.C. Inversion Graph2024-04-10

84.Increase Subarray Sums2024-04-10

85.D. Cross Coloring2024-04-12 86.M. Triangle Construction2024-04-12 87.D2. Set To Max (Hard Version)2024-04-12 88.C. Array Game2024-04-12 89.F. Alex's whims2024-04-12 90.Queue Sort2024-04-12 91.P1908 逆序对2024-04-13 92.P5094 [USACO04OPEN] MooFest G 加强版2024-04-15 93.P5149 会议座位2024-04-15 94.P10337 [UESTCPC 2024] 操作序列2024-04-15 95.P10330 [UESTCPC 2024] 黑白珠串2024-04-15 96.P10252 线性变换2024-04-16 97.P3901 数列找不同2024-04-16 98.P10288 [GESP样题八级] 区间2024-04-16 99.P5677 [GZOI2017] 配对统计2024-04-17

原题链接

题解

观察数据范围，看到 $n <= 5000$ 便确定了 $O (n^{2})$ 左右的算法，这样一来我可以遍历所有的区间
虽然每个 $f (k)$ 对应的答案区间都不同，但一定能遍历到，所以我可以再遍历一遍k，算出以该区间为答案区间时的 $f (k)$
但是这样一来时间复杂度就超了，于是能不能优化？
假如存在某个k，使得答案区间长度等于 $l e n$ , 那么这个答案区间一定是所有长度为 $l e n$ 的区间里原始区间和最大的那个

code

#include<bits/stdc++.h>
using namespace std;
int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        int pre[5005]={0},ans[5005]={0};
        int n,x;
        cin>>n>>x;
        int a;
        for(int i=1;i<=n;i++)
        {
            cin>>a;
            pre[i]=pre[i-1]+a;
        }


        for(int len=1;len<=n;len++)
        {
            int sum=pre[len];
            for(int r=len+1;r<=n;r++)
            {
                sum=max(sum,pre[r]-pre[r-len]);
            }

            for(int k=0;k<=n;k++)
            {
                ans[k]=max(ans[k],sum+min(k,len)*x);//构造样例，当只有某一段区间为正值，其他区间为负无穷大时，就算加上k我也不选
            }
        }

        for(int i=0;i<=n;i++) cout<<ans[i]<<" ";
        puts("");
    }
    return 0;
}