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=,f=;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-;
     for (;isdigit(ch);ch=getchar())x=x*+ch-'';return x*f;
 }

 const int N = ;

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

 LL sum[N<<],tag[N<<],a[N],s[N];
 void pushup(int rt) {
     sum[rt] = sum[rt<<] + sum[rt<<|];
 }
 void pushdown(int rt,int len) {
     if (tag[rt]) {
         tag[rt<<] += tag[rt]; sum[rt<<] += tag[rt] * 1ll * (len-len/);
         tag[rt<<|] += tag[rt]; sum[rt<<|] += tag[rt] * 1ll * (len/);
         tag[rt] = ; //--忘记1
     }
 }
 void build(int l,int r,int rt) {
     if (l == r) {
         sum[rt] = s[l];
         return ;
     }
     int mid = (l + r) >> ;
     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+);tag[rt] += val;
         return ;
     }
     int mid = (l + r) >> ;
     pushdown(rt,r-l+);
     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) >> ;
     LL res = ;
     pushdown(rt,r-l+);
     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=; i<=n; ++i) {
         a[i] = read();
         s[i] = s[i-] + a[i];
     }
     build(Root);
     char opt[];
     while (m--) {
         scanf("%s",opt);
         if (opt[]=='Q') {
             int p = read();
             printf("%lld\n",query(Root,,p));
         }
         else {
             int p = read(); LL v = read();
             update(Root,p,n,v-a[p]);
             a[p] = v;
         }
     }
     return ;
 }

树状数组392ms

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

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

 const int N = ;
 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 = ;
         for (int i=p; i; i-=(i&(-i))) ans += 1ll*(p+)*c1[i]-c2[i];
         return ans;
     }
 }bit;

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