解題區/解題區 - UVa

UVa 1402 - Robotic Sort

contents

  1. 1. Problem
  2. 2. Sample Input
  3. 3. Sample Output
  4. 4. Solution

Problem

機器人要排序序列，每一次會將第 i 小元素放置到正確位置，機器人每一次操作都會翻轉一個區間。請問每一步運行時，要翻轉的元素位置分別在哪裡。

Sample Input

1
2
3
4
5
6 
3 4 5 1 6 2 
4 
3 3 2 1 
0

Sample Output

1
2
4 6 4 5 6 6 
4 2 4 4

Solution

我想這一題的做法偏向 treap、splay tree 來維護區間反轉。

這裡用 塊狀鏈表 來試試，為了解決元素查找位置，紀錄該元素所在的堆、該堆的哪個位置。再利用 $O(\sqrt{n})$ 的時間去計算實際位置。還好速度沒有卡很緊，勉強能拿到 AC。弄個內存池說不定可以更快一點。但是常常需要刪除跟增加，必須寫額外的記憶體管理部分 (用一個 set 維護)。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
#include <stdio.h>
#include <math.h>
#include <stack>
#include <assert.h>
#include <vector>
#include <map>
#include <algorithm>
using namespace std;
// Unrolled Linked List
const int MAXPILE = 512;
const int MAXN = 131072;
class UnrolledLinkedList{
public:
    struct Node {
        int v[MAXPILE], vn;
        int rev_label, pid;
        Node *next;
        Node() {
            vn = rev_label = 0;
            next = NULL;
        }
        void relax() {
            if (rev_label) {
                for(int i = 0, j = vn-1; i < j; i++, j--)
        			swap(v[i], v[j]);
        		rev_label = 0;
        	}
        }
    };
    Node *head;
    int PSIZE, pid;
    int e_pos[MAXN], e_id[MAXN];
    void init() {
        free();
        head = NULL, PSIZE = MAXPILE /2;
        pid = 0;
    }
    Node* getNode() {
        Node* p = new Node();
        p->pid = pid++;
        return p;
    }
    void remap(Node *u) {
        for (int i = 0; i < u->vn; i++) 
            e_pos[u->v[i]] = i, e_id[u->v[i]] = u->pid;
    }
    int find(int e_val) {
        int pid = e_id[e_val];
        int sum_element = 0;
        Node *u, *v;
        
        for (u = head; u != NULL && u->pid != pid; u = u->next)
            sum_element += u->vn;
            
//		printf("find %d - %d\n", e_val, pid);
        assert(u != NULL);
        if (u->rev_label)
            return sum_element + u->vn - 1 - e_pos[e_val];
        else
            return sum_element + e_pos[e_val];
    }
    void set(int A[], int n) {
        init();
        Node *u, *v;
        
        head = getNode();
        u = head, v = NULL;
        PSIZE = min(PSIZE, (int) sqrt(n));
        for (int i = 0; i < n; i++) {
            if (u->vn == PSIZE) {
                u->next = getNode();
                v = u, u = u->next;
            }
            u->v[u->vn++] = A[i];
        }
        for (u = head; u != NULL; u = u->next)
            remap(u);
    }
    void shrinkList() {
        Node *u, *v;
        u = head;
        for (u = head; u != NULL && u->next != NULL; u = u->next) {
            if (u->vn + u->next->vn <= 2 * PSIZE) { // merge
                v = u->next;
                u->relax(), v->relax();
                for (int i = u->vn, j = 0; j < v->vn; i++, j++)
                    u->v[i] = v->v[j];
                u->vn += v->vn;
                remap(u);
                u->next = v->next;
                delete v;
            }
        }
    }
    void splitNode(Node *u, int left_size) { // length(left) = v
        Node *v = getNode();
        u->relax();
        v->next = u->next;
        u->next = v;
        v->vn = u->vn - left_size;
        for(int i = left_size, j = 0; i < u->vn; i++, j++)
            v->v[j] = u->v[i];
        u->vn = left_size;
        remap(u), remap(v);
    }
    void reverse(int l, int r) { // [l, r] = [0, n-1]
        Node *lptr, *rptr, *u, *v;
    	Node *lpre, *rpre, *rnext;
    	int sum_element = 0;
    	
    	u = head, v = NULL;
    	for (u = head, v = NULL; u != NULL; v = u, u = u->next) {
    		if (sum_element < l && l < sum_element + u->vn) 
            	splitNode(u, l - sum_element); // left[...l-1], right[l...]
        	if (sum_element <= r && r < sum_element + u->vn)
            	splitNode(u, r - sum_element + 1);
            	
            if (sum_element == l)
        		lptr = u, lpre = v;
            if (sum_element + u->vn - 1 == r)
        		rptr = u, rpre = v;
        	
        	sum_element += u->vn;
    	}
    	    	
//    	debug();
    	
    	rnext = rptr->next;
    	stack<Node*> stk;
    	for (u = lptr; u != rnext; u = u->next) {
    		u->rev_label = !u->rev_label;
    		stk.push(u);
    	}
    	
    	if (lpre == NULL) {
    		head = stk.top();
        	u = head, stk.pop();
        	while (!stk.empty()) {
            	u->next = stk.top(), stk.pop();
            	u = u->next;
        	}
        	u->next = rnext;
    	} else {
    		u = lpre;
    		while (!stk.empty()) {
    			u->next = stk.top(), stk.pop();
            	u = u->next;
        	}
        	u->next = rnext;
    	}
    	
    	shrinkList();
    }
    void debug() {
        Node *u = head;
    	while (u != NULL) {
        	printf("%d : %d, ", u->pid, u->rev_label);
        	for(int i = 0; i < u->vn; i++)
            	printf("%d ", u->v[i]);
        	puts("");
        	u = u->next;
    	}
    	puts("====");
    }
    void free() {
        Node *u = head, *v = NULL;
    	while(u != NULL) {
        	v = u, u = u->next;
        	delete v;
    	}
    }
} g;
int A[MAXN];
int main() {
    int n;
    while (scanf("%d", &n) == 1 && n) {
        vector< pair<int, int> > B;
        for (int i = 0; i < n; i++) {
            scanf("%d", &A[i]);
            B.push_back(make_pair(A[i], i));
        }
        
        sort(B.begin(), B.end());
        
        map< pair<int, int>, int > C;
        for (int i = 0; i < B.size(); i++)
            C[B[i]] = i;
        
        for (int i = 0; i < n; i++)
            A[i] = C[make_pair(A[i], i)];
        
        g.set(A, n);
//		g.debug();
        
        vector<int> ret;
        for (int i = 0; i < n; i++) {
            int pos = g.find(i);
            g.reverse(i, pos);
            ret.push_back(pos);
//			g.debug();
        }
        
        for (int i = 0; i < n; i++)
            printf("%d%c", ret[i] + 1, i == n-1 ? '\n' : ' ');
        
    }
    return 0;
}
/*
6 
3 4 5 1 6 2 
4 
3 3 2 1 
0
10
5 18 19 12 7 12 0 2 11 9
1
4
19
5 17 8 10 13 18 10 5 3 15 2 19 12 10 2 14 18 0 6
12
15 13 7 14 15 7 12 15 4 10 6 3
15
18 7 5 6 5 5 10 9 2 4 9 10 7 13 19
5
3 4 1 1 3
6
8 0 6 2 6 16
7
17 5 12 1 3 9 13
1
8
10
15 19 17 19 17 18 2 12 0 10
10
5 1 14 6 7 12 15 17 5 11
0
*/