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CodeForces 1053C Putting Boxes Together

Source:Source:Codeforces Round #512 (Div. 1, based on Technocup 2019 Elimination Round 1) Probelm:Probelm:n=2e5個物品從左到右排列,第i個物品的位置pos[i],重量w[i]。每次詢問如果將pos[l]…pos[r]這段物品移到某個連續區間[x, x+(r-l)],且物品不能重疊,物品移動d米需要d*w[i]的費用,問最少需要多少費用。並且有修改物品重量的操作。 Idea:Idea:如果將每個物品pos[i]-=i,問題轉化為把物品移動到同一個點,變成了帶權中位數問題,由於pos是有序的,二分s

umL<sumRsumL<sumR找到MM點,Ans=w[i]abs(pos[M]pos[i])Ans = w[i]*abs(pos[M]-pos[i]),維護w[i]w[i]pos[i]w[i]和w[i]*pos[i]Code:Code:

#include<bits/stdc++.h>
using namespace std;

#define I inline
typedef long long LL;

const int N = 2e5+10;
const int MOD = 1e9+7;

I void add(LL &a, const LL &b) { if((a+=b) >= MOD) a -= MOD; }

int a[N], w[N];
LL c1[N], c2[N];
I LL sum1(int x) { LL ret=0; while(x) ret+=c1[x], x-=(x&-x); return ret; }
I void add1(int x, LL d) { while(x<N) c1[x]+=d, x+=(x&-x); }
I LL sum2(int x) { LL ret=0; while(x) add(ret, c2[x]), x-=(x&-x); return ret; }
I void add2(int x, LL d) { while(x<N) add(c2[x], d), x+=(x&-x); }

I void work() {
    int n, q;
    scanf("%d%d", &n, &q);
    for(int i = 1; i <= n; i++) {
        scanf("%d", a+i);
        a[i] -= i;
    }
    for(int i = 1; i <= n; i++) {
        scanf("%d", w+i);
        add1(i, w[i]);
        add2(i, 1LL*w[i]*a[i]%MOD);
    }
    while(q--) {
        int x, y;
        scanf("%d%d", &x, &y);
        if(x < 0) {
            add1(-x, -w[-x]+y);
            add2(-x, (1LL*(-w[-x]+y)*a[-x]%MOD+MOD)%MOD);
            w[-x] = y;
        }
        else {
            int L = x, R = y;
            LL t = sum1(L-1), sum = sum1(R)-t;
            while(L < R) {
                int M = (L+R)>>1;
                if(2*(sum1(M)-t) < sum) L = M+1;
                else R = M;
            }
            LL t1 = ((sum1(L)-t)%MOD*a[L]%MOD-(sum2(L)-sum2(x-1))%MOD)%MOD;
            LL t2 = (-(sum1(y)-sum1(L))%MOD*a[L]%MOD+(sum2(y)-sum2(L))%MOD)%MOD;
            LL ans = (t1+t2)%MOD;
            printf("%lld\n", (ans+MOD)%MOD);
        }
    }
}

int main() {
    work();
    return 0;
}