首页 > 代码库 > POJ 3468 A Simple Problem with Integers
POJ 3468 A Simple Problem with Integers
链接:http://poj.org/problem?id=3468
A Simple Problem with Integers
Time Limit: 5000MS Memory Limit: 131072K
Total Submissions: 77302 Accepted: 23788
Case Time Limit: 2000MS
Description
You have N integers, A1, A2, ... , AN. You need to deal with two kinds of operations. One type of operation is to add some given number to each number in a given interval. The other is to ask for the sum of numbers in a given interval.
Input
The first line contains two numbers N and Q. 1 ≤ N,Q ≤ 100000.
The second line contains N numbers, the initial values of A1, A2, ... , AN. -1000000000 ≤ Ai ≤ 1000000000.
Each of the next Q lines represents an operation.
"C a b c" means adding c to each of Aa, Aa+1, ... , Ab. -10000 ≤ c ≤ 10000.
"Q a b" means querying the sum of Aa, Aa+1, ... , Ab.
Output
You need to answer all Q commands in order. One answer in a line.
Sample Input
10 51 2 3 4 5 6 7 8 9 10
Q 4 4
Q 1 10
Q 2 4
C 3 6 3
Q 2 4
Sample Output
455
9
15
Hint
The sums may exceed the range of 32-bit integers.
Source
POJ Monthly--2007.11.25, Yang Yi
大意——给你n个数字组成的序列。
你将可以对它们进行两种操作,一种是对于当前给定区间里的数字都加上一个数,还有一种是对于当前给定区间里的数字进行求和。
思路——表面上看起来是用线段树解决,但实际上将问题略微处理一下就能够用树状数组来解决。并且效率更高。
处理例如以下:假设给区间[l,r]都加上一个数x的话,我们令s(i)=加上x之前的前i项和,s’(i)=加上x之后的前i项和,那么就有当i<l时,s’(i)=s(i);当l<=i<=r时。s’(i)=s(i)+x*(i-l+1)=s(i)+x*i
-x*(l-1);当i>r时,s’(i)=s(i)+x*(r-l+1)。那么我们就能够建立两个树状数组,从而将问题简化。详细參见:csdn博客:http://blog.csdn.net/u013068502/article/details/47252335。
复杂度分析——时间复杂度:O(log(n!)+q*log(ab)),空间复杂度:O(n)
附上AC代码:
#include <iostream> #include <cstdio> #include <string> #include <cmath> #include <iomanip> #include <ctime> #include <climits> #include <cstdlib> #include <cstring> #include <algorithm> #include <queue> #include <vector> #include <set> #include <map> using namespace std; typedef unsigned int UI; typedef long long LL; typedef unsigned long long ULL; typedef long double LD; const double pi = acos(-1.0); const double e = exp(1.0); const double eps = 1e-8; const int maxn = 100005; LL bit1[maxn], bit2[maxn]; // 代表两个树状数组。数组1用来存储初始值, // 数组2用来存储变化的值 int n, query; // 初始数组大小。问题的个数 char op[5]; // 选择哪种操作 int lowbit(int x); void update(LL * bit, int x, int add); LL sum(LL * bit, int x); int main() { ios::sync_with_stdio(false); int a, b, c, x; while (~scanf("%d%d", &n, &query)) { memset(bit1, 0, sizeof(bit1)); memset(bit2, 0, sizeof(bit2)); // 上面清空数组。避免上次结果干扰 for (int i=1; i<=n; i++) { scanf("%d", &x); update(bit1, i, x); // 将初始值存入数组1 } while (query--) { scanf("%s%d%d", op, &a, &b); if (op[0] == 'C') { scanf("%d", &c); update(bit1, a, (-c)*(a-1)); update(bit2, a, c); // 上面更新改变状态 update(bit1, b+1, c*b); update(bit2, b+1, (-c)); // 上面去掉反复状态 } else { LL ans = 0; ans += sum(bit1, b)+sum(bit2, b)*b; ans -= sum(bit1, a-1)+sum(bit2, a-1)*(a-1); printf("%lld\n", ans); } } } return 0; } int lowbit(int x) // 求2^k,k表示x为二进制时末尾的0的个数 { return (x&(-x)); } void update(LL * bit, int x, int add) { // 更新节点信息(加上数add) while (x!=0 && x<=n) { bit[x] += add; x += lowbit(x); } } LL sum(LL * bit, int x) { // 区间求和(求1~x之间数组的和) LL res = 0; while (x > 0) { res += bit[x]; x -= lowbit(x); } return res; }
POJ 3468 A Simple Problem with Integers
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。