【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+5;
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 = 0, ss = 0;
    int xx = x;
    
    while (x) {
        s += nd[x].s;
        ss += nd[x].ss;
        x -= lowest(x);
    }
    
    return (xx+1) * 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, 1, n+1) {
        scanf("%d", &a[i]);
        tot[i] = tot[i-1] + a[i];
    }
    
    __int64 ans;
    char op[4];
    int l, r, d;
    
    while (q--) {
        scanf("%s %d %d", op, &l, &r);
        if (op[0] == 'Q') {
            ans = tot[r] - tot[l-1] + sum(r) - sum(l-1);
            printf("%I64d
", ans);
        } else {
            scanf("%d", &d);
            update(l, d);
            update(r+1, -d);
        }
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}

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
" % (t))
        for tt in xrange(t):
            n = randint(100, 200)
            q = randint(100, 200)
            fout.write("%d %d
" % (n, q))
            L = []
            for i in xrange(n):
                x = randint(1, bound)
                L.append(x)
            fout.write(" ".join(map(str, L)) + "
")
            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
" % (l, r, k))
                else:
                    l = randint(1, n)
                    r = randint(l, n)
                    fout.write("Q %d %d
" % (l, r))
            
                
def MovDataIn():
    desFileName = "F:eclipse_prjworkspacehdojdata.in"
    shutil.copyfile("data.in", desFileName)

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