【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。

  1 /* 3468 */
  2 #include <iostream>
  3 #include <sstream>
  4 #include <string>
  5 #include <map>
  6 #include <queue>
  7 #include <set>
  8 #include <stack>
  9 #include <vector>
 10 #include <deque>
 11 #include <algorithm>
 12 #include <cstdio>
 13 #include <cmath>
 14 #include <ctime>
 15 #include <cstring>
 16 #include <climits>
 17 #include <cctype>
 18 #include <cassert>
 19 #include <functional>
 20 #include <iterator>
 21 #include <iomanip>
 22 using namespace std;
 23 //#pragma comment(linker,"/STACK:102400000,1024000")
 24 
 25 #define sti                set<int>
 26 #define stpii            set<pair<int, int> >
 27 #define mpii            map<int,int>
 28 #define vi                vector<int>
 29 #define pii                pair<int,int>
 30 #define vpii            vector<pair<int,int> >
 31 #define rep(i, a, n)     for (int i=a;i<n;++i)
 32 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 33 #define clr                clear
 34 #define pb                 push_back
 35 #define mp                 make_pair
 36 #define fir                first
 37 #define sec                second
 38 #define all(x)             (x).begin(),(x).end()
 39 #define SZ(x)             ((int)(x).size())
 40 #define lson            l, mid, rt<<1
 41 #define rson            mid+1, r, rt<<1|1
 42 
 43 typedef struct {
 44     __int64 s, ss;
 45 } node_t;
 46 
 47 const int maxn = 1e5+5;
 48 int a[maxn];
 49 __int64 tot[maxn];
 50 node_t nd[maxn];
 51 int n, q;
 52 
 53 int lowest(int x) {
 54     return -x & x;
 55 }
 56 
 57 __int64 sum(int x) {
 58     __int64 s = 0, ss = 0;
 59     int xx = x;
 60     
 61     while (x) {
 62         s += nd[x].s;
 63         ss += nd[x].ss;
 64         x -= lowest(x);
 65     }
 66     
 67     return (xx+1) * s - ss;
 68 }
 69 
 70 void update(int x, int delta) {
 71     __int64 tmp = 1LL * x * delta;
 72     
 73     while (x <= n) {
 74         nd[x].s += delta;
 75         nd[x].ss += tmp;
 76         x += lowest(x);
 77     }
 78 }
 79 
 80 int main() {
 81     ios::sync_with_stdio(false);
 82     #ifndef ONLINE_JUDGE
 83         freopen("data.in", "r", stdin);
 84         freopen("data.out", "w", stdout);
 85     #endif
 86     
 87     scanf("%d %d", &n, &q);
 88     rep(i, 1, n+1) {
 89         scanf("%d", &a[i]);
 90         tot[i] = tot[i-1] + a[i];
 91     }
 92     
 93     __int64 ans;
 94     char op[4];
 95     int l, r, d;
 96     
 97     while (q--) {
 98         scanf("%s %d %d", op, &l, &r);
 99         if (op[0] == 'Q') {
100             ans = tot[r] - tot[l-1] + sum(r) - sum(l-1);
101             printf("%I64d\n", ans);
102         } else {
103             scanf("%d", &d);
104             update(l, d);
105             update(r+1, -d);
106         }
107     }
108     
109     #ifndef ONLINE_JUDGE
110         printf("time = %d.\n", (int)clock());
111     #endif
112     
113     return 0;
114 }

数据发生器。

 1 from copy import deepcopy
 2 from random import randint, shuffle
 3 import shutil
 4 import string
 5 
 6 
 7 def GenDataIn():
 8     with open("data.in", "w") as fout:
 9         t = 1
10         bound = 10**3
11         # fout.write("%d\n" % (t))
12         for tt in xrange(t):
13             n = randint(100, 200)
14             q = randint(100, 200)
15             fout.write("%d %d\n" % (n, q))
16             L = []
17             for i in xrange(n):
18                 x = randint(1, bound)
19                 L.append(x)
20             fout.write(" ".join(map(str, L)) + "\n")
21             for i in xrange(q):
22                 op = randint(0, 1)
23                 if op:
24                     l = randint(1, n)
25                     r = randint(l, n)
26                     k = randint(1, bound)
27                     fout.write("C %d %d %d\n" % (l, r, k))
28                 else:
29                     l = randint(1, n)
30                     r = randint(l, n)
31                     fout.write("Q %d %d\n" % (l, r))
32             
33                 
34 def MovDataIn():
35     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
36     shutil.copyfile("data.in", desFileName)
37 
38     
39 if __name__ == "__main__":
40     GenDataIn()
41     MovDataIn()