【POJ】3468 A Simple Problem with Integers

这题用线段树轻松解了，重新用树状数组解，关键点是区间更新。
公式推导如下：
sum[x] = org_sum[x] + delta[1]*x + delta[2]*(x-1) + delta[x]*1
           = org_sum[x] + Sigma(delta[1..x]) * (x+1) - Sigma(delta[i]*i)
树状数组增加两个结点信息分别存delta[i] 和 delta[i] * i就好了。

 /* 3468 */
 #include <iostream>
 #include <sstream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1

 typedef struct {
     __int64 s, ss;
 } node_t;

 const int maxn = 1e5+;
 int a[maxn];
 __int64 tot[maxn];
 node_t nd[maxn];
 int n, q;

 int lowest(int x) {
     return -x & x;
 }

 __int64 sum(int x) {
     __int64 s = , ss = ;
     int xx = x;

     while (x) {
         s += nd[x].s;
         ss += nd[x].ss;
         x -= lowest(x);
     }

     return (xx+) * s - ss;
 }

 void update(int x, int delta) {
     __int64 tmp = 1LL * x * delta;

     while (x <= n) {
         nd[x].s += delta;
         nd[x].ss += tmp;
         x += lowest(x);
     }
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     scanf("%d %d", &n, &q);
     rep(i, , n+) {
         scanf("%d", &a[i]);
         tot[i] = tot[i-] + a[i];
     }

     __int64 ans;
     char op[];
     int l, r, d;

     while (q--) {
         scanf("%s %d %d", op, &l, &r);
         if (op[] == 'Q') {
             ans = tot[r] - tot[l-] + sum(r) - sum(l-);
             printf("%I64d\n", ans);
         } else {
             scanf("%d", &d);
             update(l, d);
             update(r+, -d);
         }
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }

数据发生器。

 from copy import deepcopy
 from random import randint, shuffle
 import shutil
 import string

 def GenDataIn():
     with open("data.in", "w") as fout:
         t = 1
         bound = 10**3
         # fout.write("%d\n" % (t))
         for tt in xrange(t):
             n = randint(100, 200)
             q = randint(100, 200)
             fout.write("%d %d\n" % (n, q))
             L = []
             for i in xrange(n):
                 x = randint(1, bound)
                 L.append(x)
             fout.write(" ".join(map(str, L)) + "\n")
             for i in xrange(q):
                 op = randint(0, 1)
                 if op:
                     l = randint(1, n)
                     r = randint(l, n)
                     k = randint(1, bound)
                     fout.write("C %d %d %d\n" % (l, r, k))
                 else:
                     l = randint(1, n)
                     r = randint(l, n)
                     fout.write("Q %d %d\n" % (l, r))

 def MovDataIn():
     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
     shutil.copyfile("data.in", desFileName)

 if __name__ == "__main__":
     GenDataIn()
     MovDataIn()