版权声明:蒟蒻的博文,dalao转载标明出处就好吖 https://blog.csdn.net/jokingcoder/article/details/81477253
区间最大子段和
You are given a sequence
. A query is defined as follows:
.
Given M queries, your program must output the results of these queries.
Input
The first line of the input file contains the integer
.
In the second line,
numbers follow.
The third line contains the integer
.
M lines follow, where line
contains
numbers
and
.
Output
Your program should output the results of the M queries, one query per line.
Example
Input:
3
-1 2 3
1
1 2
Output:
2
Solution
对于每一个每个区间,保存一个Node,记录这个区间的sum(总和),maxsum(最大子段和),lmax(最大前缀和),rmax(最大后缀和),有了这四个标记,就可以随意转移,为所欲为了。。。
这里我们把核心代码拉出来讲一讲
ans.sum = lo.sum + ro.sum;//sum直接相加
ans.maxsum = max(max(lo.maxsum, ro.maxsum), lo.rmax + ro.lmax);//左右两半的最大子段和,合并起来的最大子段和
ans.lmax = max(lo.lmax, lo.sum + ro.lmax);//左边的最大前缀和,左边整段+右边最大前缀
ans.rmax = max(ro.rmax, ro.sum + lo.rmax);//右边的最大后缀和,右边整段+左边最大后缀
Code
#include <cstdio>
#include <algorithm>
#define N 50010
using namespace std;
struct Node{
int sum, maxsum, lmax, rmax;
}tr[N << 2];
int a[N];
void build(int l, int r, int id) {
if (l == r) {
tr[id].sum = tr[id].maxsum = tr[id].lmax = tr[id].rmax = a[l];
return;
}
int mid = (l + r) >> 1, ls = id << 1, rs = id << 1 | 1;
build(l, mid, ls);
build(mid + 1, r, rs);
tr[id].sum = tr[ls].sum + tr[rs].sum;
tr[id].maxsum = max(max(tr[ls].maxsum, tr[rs].maxsum), tr[ls].rmax + tr[rs].lmax);
tr[id].lmax = max(tr[ls].lmax, tr[ls].sum + tr[rs].lmax);
tr[id].rmax = max(tr[rs].rmax, tr[rs].sum + tr[ls].rmax);
}
Node query(int l, int r, int ll, int rr, int id) {
if (ll <= l && r <= rr) {
return tr[id];
}
int mid = (l + r) >> 1, ls = id << 1, rs = id << 1 | 1;
if (rr <= mid) return query(l, mid, ll, rr, ls);
if (mid < ll) return query(mid + 1, r, ll, rr, rs);
Node lo = query(l, mid, ll, rr, ls), ro = query(mid + 1, r, ll, rr, rs), ans;
ans.sum = lo.sum + ro.sum;
ans.maxsum = max(max(lo.maxsum, ro.maxsum), lo.rmax + ro.lmax);
ans.lmax = max(lo.lmax, lo.sum + ro.lmax);
ans.rmax = max(ro.rmax, ro.sum + lo.rmax);
return ans;
}
int main() {
int n, m;
scanf("%d", &n);
for (int i = 1; i <= n; ++i) {
scanf("%d", &a[i]);
}
build(1, n, 1);
scanf("%d", &m);
for (int i = 1; i <= m; ++i) {
int x, y;
scanf("%d%d", &x, &y);
printf("%d\n", query(1, n, x, y, 1).maxsum);
}
return 0;
}