P5094 [USACO04OPEN] MooFest G 加强版

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] Fibonacci2024-03-0837.P2034 选择数字2024-03-0938.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2024-04-13

92.P5094 [USACO04OPEN] MooFest G 加强版2024-04-15

93.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

$O(n^2)$ 不可能，所以考虑线性，将奶牛按下标排序，顺序遍历，对于 $i$ 而言，它的贡献等于 $\sum _{j<i,v[j]⩽v[i]}dis(i,j)·v[i]$ ，等于 $v[i]·((\sum _{j<i,v[j]⩽v[i]}1)·x[i]-\sum _{j<i,v[j]⩽v[i]}x[j])$
逆序遍历贡献为 $v[i]·((\sum _{j>i,v[j]<v[i]}1)·x[i]-\sum _{j>i,v[j]<v[i]}x[j])$

把 $v$ 看作x轴 , 等价于求 小于v的个数 和 小于v的dis和 ，用两个树状数组解决

code

#include<bits/stdc++.h>
#define ll long long
#define lowbit(x) ((x)&(-x))
using namespace std;
#define ll long long
inline void read(ll &x) {
    x = 0;
    ll flag = 1;
    char c = getchar();
    while(c < '0' || c > '9'){
        if(c == '-')flag = -1;
        c = getchar();
    }
    while(c >= '0' && c <= '9') {
        x = (x << 3) + (x << 1) + (c ^ 48);
        c = getchar();
    }
    x *= flag;
}

inline void write(ll x)
{
    if(x < 0){
        putchar('-');
        x = -x;
    }
    if(x > 9)
        write(x / 10);
    putchar(x % 10 + '0');
}
ll n;
struct node
{
    ll v,x,haxi;
} cow[50005];
ll cnt[50005]={0}, sum[50005]={0};

ll query_cnt(ll x)
{
    ll cal=0;
    while(x)
    {
        cal+=cnt[x];
        x-=lowbit(x);
    }
    return cal;
}

ll query_sum(ll x)
{
    ll cal=0;
    while(x)
    {
        cal+=sum[x];
        x-=lowbit(x);
    }
    return cal;
}

void update_cnt(ll x)
{
    while(x<=50005)//Because x is small, discretization is not necessary.
    {
        cnt[x]++;
        x+=lowbit(x);
    }
}

void update_sum(ll x, ll val)
{
    while(x<=50005)
    {
        sum[x]+=val;
        x+=lowbit(x);
    }
}

bool cmp(node a, node b)
{
    return a.x<b.x;
}

int main()
{
    ll n;
    read(n);
    for(ll i=1; i<=n; i++)
    {
        read(cow[i].v);
        read(cow[i].x);
    }

    ll ans=0;

    sort(cow+1, cow+1+n, cmp);
    for(ll i=1; i<=n; i++)
    {
        ll index=cow[i].v;
        ans+=cow[i].v*(query_cnt(index)*cow[i].x-query_sum(index));
        update_cnt(index);
        update_sum(index, cow[i].x);
    }

    memset(cnt, 0, sizeof cnt);
    memset(sum, 0, sizeof sum);

    for(ll i=n; i>=1; i--)
    {
        ll index=cow[i].v;
        ans+=cow[i].v*(query_sum(index-1)-query_cnt(index-1)*cow[i].x);
        update_cnt(index);
        update_sum(index, cow[i].x);
    }

    write(ans);
    return 0;
}