3155: Preprefix sum

3155: Preprefix sum

https://www.lydsy.com/JudgeOnline/problem.php?id=3155

分析：

　　区间修改，区间查询，线段树就好了。

　　然后，这题有树状数组！

代码：

线段树620ms

/*
一个数修改影响后面的数，使后面的数都增加或者减少多少，所以线段树维护区间和，区间修改  
*/
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;

inline int read() {
    int x=0,f=1;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-1;
    for (;isdigit(ch);ch=getchar())x=x*10+ch-'0';return x*f;
}

const int N = 100010;

#define Root 1,n,1
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1

LL sum[N<<2],tag[N<<2],a[N],s[N];
void pushup(int rt) {
    sum[rt] = sum[rt<<1] + sum[rt<<1|1];
}
void pushdown(int rt,int len) {
    if (tag[rt]) {
        tag[rt<<1] += tag[rt]; sum[rt<<1] += tag[rt] * 1ll * (len-len/2);
        tag[rt<<1|1] += tag[rt]; sum[rt<<1|1] += tag[rt] * 1ll * (len/2);
        tag[rt] = 0; //--忘记1 
    }
}
void build(int l,int r,int rt) {
    if (l == r) {
        sum[rt] = s[l];
        return ;
    }
    int mid = (l + r) >> 1;
    build(lson);
    build(rson);
    pushup(rt);
}
void update(int l,int r,int rt,int L,int R,LL val) {
    if (L <= l && r <= R) {
        sum[rt] += val*1ll*(r-l+1);tag[rt] += val;
        return ;
    }
    int mid = (l + r) >> 1;
    pushdown(rt,r-l+1);
    if (L <= mid) update(lson,L,R,val);
    if (R > mid)  update(rson,L,R,val);
    pushup(rt);
}
LL query(int l,int r,int rt,int L,int R) {
    if (L <= l && r <= R) {
        return sum[rt];
    }
    int mid = (l + r) >> 1;
    LL res = 0;
    pushdown(rt,r-l+1);
    if (L <= mid) res += query(lson,L,R);
    if (R > mid)  res += query(rson,L,R);
    return res;//--忘记2
}
int main() {
    int n = read(),m = read();
    for (int t,i=1; i<=n; ++i) {
        a[i] = read();
        s[i] = s[i-1] + a[i];
    }
    build(Root);
    char opt[10];
    while (m--) {
        scanf("%s",opt);
        if (opt[0]=='Q') {
            int p = read();
            printf("%lld
",query(Root,1,p));
        }
        else {
            int p = read(); LL v = read();
            update(Root,p,n,v-a[p]);
            a[p] = v;
        }
    }
    return 0;
}

树状数组392ms

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

inline int read() {
    int x=0,f=1;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-1;
    for (;isdigit(ch);ch=getchar())x=x*10+ch-'0';return x*f;
}

const int N = 100010;
LL a[N];

struct BIT{
    int n;LL c1[N],c2[N];
    void update(int p,LL v) {
        for (int i=p; i<=n; i+=(i&(-i))) c1[i] += v,c2[i] += 1ll*p*v; // long long
    }
    LL query(int p) {
        LL ans = 0;
        for (int i=p; i; i-=(i&(-i))) ans += 1ll*(p+1)*c1[i]-c2[i];
        return ans;
    }
}bit;

int main() {
    int n = read(),m = read();
    bit.n = n;  // ---
    for (int i=1; i<=n; ++i) {
        a[i] = read();
        bit.update(i,a[i]);
    }
    char opt[10];
    while (m--) {
        scanf("%s",opt);
        if (opt[0]=='Q') {
            int p = read();
            printf("%lld
",bit.query(p));
        }
        else {
            int p = read(); LL v = read();
            bit.update(p,v-a[p]);
            a[p] = v;
        }
    }
    return 0;
}