Description
Input
输入文件的第1行包含两个数N和M，N表示初始时数列中数的个数，M表示要进行的操作数目。第2行包含N个数字，描述初始时的数列。以下M行，每行一条命令，格式参见问题描述中的表格。
Output
对于输入数据中的GET-SUM和MAX-SUM操作，向输出文件依次打印结果，每个答案（数字）占一行。
Sample Input
9 8
2 -6 3 5 1 -5 -3 6 3
GET-SUM 5 4
MAX-SUM
INSERT 8 3 -5 7 2
DELETE 12 1
MAKE-SAME 3 3 2
REVERSE 3 6
GET-SUM 5 4
MAX-SUM
Sample Output
-1
10
1
10
HINT
Source
这题也是醉了～拍了两三天。。。看上去也就是个splay裸题。
最大字段和的维护：splay每个节点i记录从i的左子树最左起的最大字段和lb，右子树最右起的最大字段和rb，以及它所表示的整个区间的最大字段和。 lb[i]=max(lb[lc],sum[lc]+key[i]+lb[rc])，rb[i]=max(rb[rc],sum[rc]+key[i]+rb[lc])，wb[i]=max(wb[lc],wb[rc],rb[lc]+lb[rc]+key[i])，其中sum表示区间和，key表示该点的权值，lc与rc分别表示左右孩子。有许多细节请自己脑补。。。
1 #include<queue>
2 #include<iostream>
3 #include<cstring>
4 #include<cstdio>
5 #include<cstdlib>
6 using namespace std;
7
8 #define maxn 500010
9 #define inf (1 << 20)
10 int n,m,TEMP[maxn],stack[maxn];
11 queue <int> team;
12
13 inline int Max(int a,int b) {if (a > b) return a; return b;}
14
15 struct node
16 {
17 int fa[maxn],ch[maxn][2],key[maxn],sum[maxn],lm[maxn],rm[maxn],wm[maxn],size[maxn],cnt,root;
18 bool rev[maxn],change[maxn];
19
20 inline int newnode()
21 {
22 if (team.empty()) return ++cnt;
23 int ret = team.front(); team.pop();
24 return ret;
25 }
26
27 inline void updata(int a)
28 {
29 int lc = ch[a][0],rc = ch[a][1];
30 pushdown(a); pushdown(lc); pushdown(rc);
31 size[a] = size[lc] + size[rc] + 1;
32 {
33 sum[a] = sum[lc] + sum[rc] + key[a];
34 lm[a] = rm[a] = wm[a] = -inf;
35 lm[a] = Max(lm[a],sum[lc]+key[a]);
36 lm[a] = Max(lm[a],sum[lc]+lm[rc]+key[a]);
37 if (lc) lm[a] = Max(lm[a],lm[lc]);
38 rm[a] = Max(rm[a],sum[rc]+key[a]);
39 rm[a] = Max(rm[a],sum[rc]+rm[lc]+key[a]);
40 if (rc) rm[a] = Max(rm[a],rm[rc]);
41 wm[a] = Max(lm[a],rm[a]);
42 wm[a] = Max(wm[a],rm[lc]+lm[rc]+key[a]);
43 wm[a] = Max(wm[a],key[a]);
44 wm[a] = Max(wm[a],rm[lc]+key[a]);
45 wm[a] = Max(wm[a],lm[rc]+key[a]);
46 if (rc) wm[a] = Max(wm[a],Max(lm[rc],wm[rc]));
47 if (lc) wm[a] = Max(wm[a],Max(rm[lc],wm[lc]));
48 }
49 }
50
51 inline void pushdown(int a)
52 {
53 if (a == 0) { rev[a] = false; change[a] = false; return; }
54 else
55 {
56 int lc = ch[a][0],rc = ch[a][1];
57 if (rev[a])
58 {
59 rev[a] = false;
60 swap(lm[a],rm[a]); swap(ch[a][0],ch[a][1]);
61 if (lc) rev[lc] ^= 1; if (rc) rev[rc] ^= 1;
62 }
63 if (change[a])
64 {
65 change[a] = false;
66 if (lc) key[lc] = key[a],change[lc] = true;
67 if (rc) key[rc] = key[a],change[rc] = true;
68 sum[a] = key[a] * size[a];
69 if (key[a] >= 0) wm[a] = lm[a] = rm[a] = sum[a];
70 else wm[a] = lm[a] = rm[a] = key[a];
71 }
72 }
73 }
74
75 inline int find(int rank,int have,int now)
76 {
77 pushdown(now);
78 if (have+size[ch[now][0]]+1==rank) return now;
79 if (have+size[ch[now][0]]+1>rank) return find(rank,have,ch[now][0]);
80 else return find(rank,have+size[ch[now][0]]+1,ch[now][1]);
81 }
82
83 inline void rotate(int x)
84 {
85 int y = fa[x],z = fa[y],l,r;
86 if (ch[y][0] == x) l = 0; else l = 1; r = l ^ 1;
87 if (z != 0)
88 {
89 if (ch[z][0] == y) ch[z][0] = x; else ch[z][1] = x;
90 }
91 fa[x] = z; fa[y] = x; fa[ch[x][r]] = y;
92 ch[y][l] = ch[x][r]; ch[x][r] = y;
93 updata(y); updata(x);
94 }
95
96 inline void splay(int x,int aim)
97 {
98 int t = fa[aim],top = 0;
99 for (int i = x;i != t;i = fa[i]) stack[++top] = i;
100 while (top) pushdown(stack[top--]);
101 while (fa[x] != t)
102 {
103 int y = fa[x],z = fa[y];
104 if (fa[y] != t)
105 {
106 if ((ch[y][0] == x)^(ch[z][0] == y)) rotate(x);
107 else rotate(y);
108 }
109 rotate(x);
110 }
111 if (aim == root) root = x;
112 }
113
114 inline int build(int l,int r)
115 {
116 int now = newnode(),mid = (l + r) >> 1;
117 ch[now][0] = ch[now][1] = 0;
118 rev[now] = change[now] = false;
119 if (l == r)
120 {
121 key[now] = TEMP[l]; updata(now);
122 return now;
123 }
124 if (l < mid)
125 {
126 ch[now][0] = build(l,mid - 1);
127 fa[ch[now][0]] = now;
128 }
129 if (mid < r)
130 {
131 ch[now][1] = build(mid + 1,r);
132 fa[ch[now][1]] = now;
133 }
134 key[now] = TEMP[mid];
135 updata(now);
136 return now;
137 }
138
139 inline void init(int l,int r)
140 {
141 root = build(l,r); int p;
142 p = find(n,0,root);
143 splay(p,root);
144 key[++cnt] = -inf;
145 fa[cnt] = p; ch[p][1] = cnt;
146 updata(cnt); updata(p);
147 p = find(1,0,root);
148 splay(p,root);
149 key[++cnt] = -inf;
150 fa[cnt] = p; ch[p][0] = cnt;
151 updata(cnt); updata(p);
152 }
153
154 inline void insert(int a,int b)
155 {
156 int p = find(a + 1,0,root),q = find(a + 2,0,root);
157 splay(p,root); splay(q,ch[p][1]);
158 int tr = build(1,b);
159 fa[tr] = q; ch[q][0] = tr;
160 updata(q); updata(p);
161 }
162
163 inline void rec(int now)
164 {
165 if (now == 0) return;
166 team.push(now);
167 rec(ch[now][0]); rec(ch[now][1]);
168 }
169
170 inline void del(int a,int b)
171 {
172 int p = find(a,0,root),q = find(a+b+1,0,root);
173 splay(p,root); splay(q,ch[p][1]);
174 rec(ch[q][0]);
175 fa[ch[q][0]] = 0; ch[q][0] = 0;
176 updata(q); updata(p);
177 }
178
179 inline void reverse(int a,int b)
180 {
181 int p = find(a,0,root),q = find(a+b+1,0,root);
182 splay(p,root); splay(q,ch[p][1]);
183 rev[ch[q][0]] ^= 1; pushdown(ch[q][0]);
184 updata(q); updata(p);
185 }
186
187 inline int getsum(int a,int b)
188 {
189 int p = find(a,0,root),q = find(a+b+1,0,root);
190 splay(p,root); splay(q,ch[p][1]);
191 return sum[ch[q][0]];
192 }
193
194 inline int maxsum() { updata(root); return wm[root];}
195
196 inline void modify(int a,int b,int c)
197 {
198 int p = find(a,0,root),q = find(a+b+1,0,root);
199 splay(p,root); splay(q,ch[p][1]);
200 key[ch[q][0]] = c; change[ch[q][0]] = true;
201 pushdown(ch[q][0]);
202 updata(ch[q][0]); updata(q); updata(p);
203 return;
204 }
205 }tree;
206
207 inline int read()
208 {
209 int x=0,f=1;char ch=getchar();
210 while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
211 while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
212 return x*f;
213 }
214
215 int main()
216 {
217 freopen("1500.in","r",stdin);
218 freopen("1500.out","w",stdout);
219 n = read(); m = read();
220 for (int i = 1;i <= n;++i) TEMP[i] = read();
221 tree.init(1,n);
222 char opt[20];
223 while (m--)
224 {
225 scanf("%s",opt);
226 if (opt[0] == ‘I‘)
227 {
228 int a = read(),b = read();
229 for (int i = 1;i <= b;++i) TEMP[i] = read();
230 tree.insert(a,b);
231 }
232 else if (opt[0] == ‘D‘)
233 {
234 int a = read(),b =read();
235 tree.del(a,b);
236 }
237 else if (opt[0] == ‘R‘)
238 {
239 int a = read(),b = read();
240 tree.reverse(a,b);
241 }
242 else if (opt[0] == ‘G‘)
243 {
244 int a = read(),b = read();
245 printf("%d\n",tree.getsum(a,b));
246 }
247 else if (opt[0] == ‘M‘&&opt[2] == ‘K‘)
248 {
249 int a = read(),b = read(),c = read();
250 tree.modify(a,b,c);
251 }
252 else printf("%d\n",tree.maxsum());
253 }
254 fclose(stdin); fclose(stdout);
255 return 0;
256 }
时间： 2024-12-25 20:53:17