uva 1400 - "Ray, Pass me the dishes!"(线段树)

题目链接：uva 1400 - "Ray, Pass me the dishes!"

题目大意：给定一个长度为n个整数序列，对m次询问作出回答，对于每次询问(a,b),找到两个下标x，y使得x到y的连续和为区间a，b中最大的连续和，如果存在多解优先x小，然后y小。

解题思路：线段树，对于每个节点维护三个线段值：

• max_sub：区间连续最大和
• max_prefix：区间连续前缀最大和
• max_suffix：区间连续后缀最大和

  建树的过程维护三个值，查询时只需考虑左右子节点的max_sub，以及两边max_suffix+max_prefix

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
#define lson(x) ((x)<<1)
#define rson(x) (((x)<<1)+1)
typedef long long ll;
const int maxn = 500005;
const ll INF = 0x3f3f3f3f3f3f3f3f;

struct segment {
    int l, r;
    ll val;
    segment (int l = 0, int r = 0, ll val = 0) {
        this->set(l, r, val);
    }
    void set (int l, int r, ll val) {
        this->l = l;
        this->r = r;
        this->val = val;
    }
    segment operator + (const segment& u) {
        return segment(min(l, u.l), max(r, u.r), val + u.val);
    }
    bool operator < (const segment& u) const {
        if (val != u.val)
            return val < u.val;
        if (l != u.l)
            return l > u.l;
        return r > u.r;
    }
};

struct Node {
    int l, r;
    segment max_sub, max_prefix, max_suffix;
} node[4*maxn];
int N, M;
ll arr[maxn], s[maxn];

Node seg_push (Node a, Node b) {

    Node ret;

    ll suml = s[a.r] - s[a.l-1];
    ll sumr = s[b.r] - s[b.l-1];

    ret.l = a.l;
    ret.r = b.r;
    ret.max_sub = max(a.max_suffix + b.max_prefix, max(a.max_sub, b.max_sub));
    ret.max_prefix = max(a.max_prefix, segment(a.l, a.r, suml) + b.max_prefix);
    ret.max_suffix = max(b.max_suffix, a.max_suffix + segment(b.l, b.r, sumr));
    return ret;
}

void build_segTree (int root, int l, int r) {

    if (l == r) {
        node[root].l = node[root].r = l;
        node[root].max_sub.set(l, r, (ll)arr[l]);
        node[root].max_prefix.set(l, r, (ll)arr[l]);
        node[root].max_suffix.set(l, r, (ll)arr[l]);
        return;
    }

    int mid = (l + r) / 2;
    build_segTree(lson(root), l, mid);
    build_segTree(rson(root), mid + 1, r);

    node[root] = seg_push(node[lson(root)], node[rson(root)]);
}

Node query (int root, int l, int r) {

    if (l <= node[root].l && r >= node[root].r)
        return node[root];

    int mid = (node[root].l + node[root].r) / 2;
    if (l <= mid && r > mid)
        return seg_push(query(lson(root), l, r), query(rson(root), l, r));
    else if (r <= mid)
        return query(lson(root), l, r);
    else
        return query(rson(root), l, r);
}

int main () {
    int cas = 1;
    while (scanf("%d%d", &N, &M) == 2) {
        s[0] = 0;
        for (int i = 1; i <= N; i++) {
            scanf("%lld", &arr[i]);
            s[i] = s[i-1] + arr[i];
        }

        build_segTree(1, 1, N);
        printf("Case %d:\n", cas++);

        int l, r;
        for (int i = 0; i < M; i++) {
            scanf("%d%d", &l, &r);
            Node u = query(1, l, r);
            printf("%d %d\n", u.max_sub.l, u.max_sub.r);
        }
    }
    return 0;
}