解題區/解題區 - 其他題目

BZOJ 3065 帶插入區間 K 小值

contents

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

Problem

詢問區間 K 小，額外支持插入一個元素到序列中。

Sample Input

1
2
3
4
5
6
7
8
9
10
11
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13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
10
10 5 8 28 0 19 2 31 1 22 
30
I 6 9
M 1 11
I 8 17
M 1 31
M 6 26
Q 2 7 6
I 23 30
M 31 7
I 22 27
M 26 18
Q 26 17 31
I 5 2
I 18 13
Q 3 3 3
I 27 19
Q 23 23 30
Q 5 13 5
I 3 0
M 15 27
Q 0 28 13
Q 3 29 11
M 2 8
Q 12 5 7
I 30 19
M 11 19
Q 17 8 29
M 29 4
Q 3 0 12
I 7 18
M 29 27

Sample Output

1
2
3
4
5
6
7
8
9
10
28
2
31
0
14
15
14
27
15
14

Solution

直接修改可持久化塊狀鏈表的那一題 Zerojudge b411 記憶中的序列 2，把可持久化的記憶體拔掉，這樣就免得記憶體需求過大。出題者是想用替罪羊樹掛另一個平衡樹下去做。應該沒設想到塊狀鏈表在此題的速度也不算差。時限 60 秒大概跑了 30 秒，還不比樹套樹來得慢。

因為有插入操作，不管是主席樹還是函數式線段樹 (這兩個應該是同一個傢伙)，都無法辦到，只能靠可插入的平衡樹。

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#include <stdio.h>
#include <math.h>
#include <stack>
#include <assert.h>
#include <vector>
#include <limits.h>
#include <map>
#include <algorithm>
using namespace std;
const int MAXN = 65536;
const int MAXQ = 262144;
class UnrolledLinkedList {
public:
    struct Node {
        vector<int> A, B;
        Node *next, *alias;
        Node() {
            A.clear(), B.clear(), next = alias = NULL;
        }
        Node* real() {
            if (alias)	return alias;
            return this;
        }
        void insert(int x, int val) {
            if (alias) {
                A = alias->A, B = alias->B;
                alias = NULL;
            }
            A.insert(A.begin() + x, val);
            B.resize(A.size());
            B[A.size()-1] = val;
            for (int i = (int) A.size()-1; i > 0 && B[i] < B[i-1]; i--)
                swap(B[i], B[i-1]);
        }
        void erase(int x) {
            int val = A[x];
            A.erase(A.begin()+x);
            B.erase(lower_bound(B.begin(), B.end(), val));
        }
        void change(int x, int val) {
            int t = A[x];
            A[x] = val;
            B.erase(lower_bound(B.begin(), B.end(), t));
            B.resize(A.size());
            B[A.size()-1] = val;
            for (int i = (int) A.size()-1; i > 0 && B[i] < B[i-1]; i--)
                swap(B[i], B[i-1]);
        }
        void relax() {
            B = A;
            sort(B.begin(), B.end());
        }
    };
    int PSIZE;
    stack<Node*> mem;
    Node* init(int A[], int n) { // A[1:n]
        free();
        PSIZE = max((int) sqrt(n), 2);
        for (int i = 1; ; i <<= 1) {
            if (i >= PSIZE) {
                PSIZE = i;
                break;
            }
        }
        
        Node *u, *v, *head;
        
        head = newNode();
        u = head, v = NULL;
        for (int i = 1; i <= n; i++) {
            if (u->A.size() == PSIZE) {
                u->next = newNode();
                v = u, u = u->next;
            }
            u->A.push_back(A[i]);
        }
        for (u = head; u != NULL; u = u->next)
            u->relax();
        return head;
    }
    Node* newNode() {
        Node* p = new Node();
        mem.push(p);
        return p;
    }
    Node* cloneNode(Node *u) {
        Node *t = u->real();
        Node *p = new Node();
        *p = *t, p->next = u->next, mem.push(p);
        return p; 
    }
    Node* aliasNode(Node *u) {
        Node *t = u->real();
//		Node* p = new Node();
//		p->alias = t, p->next = u->next, mem.push(p);
//		return p;
        return u;
    }
    Node* erase(Node *ver, int x) {
        Node *a, *b, *u, *v, *t;
        u = ver, a = NULL;
        for (int l = 1, r; u; l = r+1, u = u->next) {
            r = l + u->real()->A.size() - 1;
            if (l <= x && x <= r) {
                t = cloneNode(u);
                if (a == NULL)
                    a = t, b = a;
                else
                    b->next = t, b = b->next;
                t->erase(x - l);
                t->next = u->next;
                break;
            } else {
                if (a == NULL)
                    a = aliasNode(u), b = a;
                else
                    b->next = aliasNode(u), b = b->next;
            }
        }
        return relaxList(a);
    }
    Node* insert(Node *ver, int x, int val) {
        Node *a, *b, *u, *v, *t;
        u = ver, a = NULL;
        for (int l = 1, r; u; l = r+1, u = u->next) {
            r = l + u->real()->A.size() - 1;
            if (l-1 <= x && x <= r) {
                t = cloneNode(u);
                if (a == NULL)
                    a = t, b = a;
                else
                    b->next = t, b = b->next;
                t->insert(x - l + 1, val);
                t->next = u->next;
                break;
            } else {
                if (a == NULL)
                    a = aliasNode(u), b = a;
                else
                    b->next = aliasNode(u), b = b->next;
            }
        }
        return relaxList(a);
    }
    Node* change(Node *ver, int x, int val) {
        Node *a, *b, *u, *v, *t;
        u = ver, a = NULL;
        for (int l = 1, r; u; l = r+1, u = u->next) {
            r = l + u->real()->A.size() - 1;
            if (l <= x && x <= r) {
                t = cloneNode(u);
                if (a == NULL)
                    a = t, b = a;
                else
                    b->next = t, b = b->next;
                t->change(x - l, val);
                t->next = u->next;
                break;
            } else {
                if (a == NULL)
                    a = aliasNode(u), b = a;
                else
                    b->next = aliasNode(u), b = b->next;
            }
        }
        return a;
    }
    int findRank(Node *ver, int L, int R, int val, int threshold = INT_MAX) {
        Node *u, *v;
        int ret = 0;
        u = ver;
        for (int l = 1, r; u != NULL; u = u->next, l = r+1) {
            r = l + u->real()->A.size() - 1;
            if (L <= l && r <= R) {
                ret += upper_bound(u->real()->B.begin(), u->real()->B.end(), val) - u->real()->B.begin();
                L = r + 1;
            } else if ((l <= L && L <= r) || (l <= R && R <= r)) {
                int i = L - l;
                while (i < u->real()->A.size() && L <= R) {
                    if (u->real()->A[i] <= val)
                        ret++;
                    i++, L++;
                }
            }
            if (ret >= threshold)	return ret;
        }
        return ret;
    }
    int find(Node *ver, int L, int R, int k)  {	// kth-number
        int l = 0, r = 100005, mid, t = 0; // value in A[]
        while (l <= r) {
            mid = (l + r)/2;
            if (findRank(ver, L, R, mid, k) >= k)
                r = mid - 1, t = mid;
            else
                l = mid + 1;
        }
        return t;
    }
    Node* mergeNode(Node *u, Node *v) {
        Node *p, *q;
        Node *a = newNode();
        p = u->real(), q = v->real();
        a->next = v->next;
        a->A.insert(a->A.end(), p->A.begin(), p->A.end());
        a->A.insert(a->A.end(), q->A.begin(), q->A.end());
        a->B.resize(a->A.size());
        merge(p->B.begin(), p->B.end(), q->B.begin(), q->B.end(), a->B.begin());
        return a;
    }
    Node* splitNode(Node *u) {
        Node *t = u->real();
        Node *a = newNode(), *b = newNode();
        int n = t->A.size()/2;
        a->next = b, b->next = u->next;
        a->A.insert(a->A.begin(), t->A.begin(), t->A.begin()+n);
        b->A.insert(b->A.begin(), t->A.begin()+n, t->A.end());
        a->relax(), b->relax();
        return a;
    }
    Node* relaxList(Node *ver) {
        Node *a, *b, *u, *v, *t;
        int need = 0;
        for (u = ver, a = NULL; !need && u != NULL; u = u->next) {
            if (u->next != NULL && u->real()->A.size() + u->next->real()->A.size() < (PSIZE<<1)) // merge
            	need = 1;
            if (u->real()->A.size() > (PSIZE<<1))	// split
            	need = 1;
        }
        if (!need)
        	return ver;
        stack<Node*> remove;	// static used 
        for (u = ver, a = NULL; u != NULL; u = u->next) {
            if (u->next != NULL && u->real()->A.size() + u->next->real()->A.size() < (PSIZE<<1)) {	// merge
            	if (a == NULL)
            		a = mergeNode(u, u->next), b = a;
            	else
            		b->next = mergeNode(u, u->next), b = b->next;
            	remove.push(u), remove.push(u->next); // static used  
                u = u->next;
            } else if (u->real()->A.size() > (PSIZE<<1)) {	// split
            	if (a == NULL)
            		a = splitNode(u), b = a->next;
            	else
            		b->next = splitNode(u), b = b->next->next;
            	remove.push(u); // static used  
            } else {
            	if (a == NULL)	
                    a = aliasNode(u), b = a;
            	else			
                    b->next = aliasNode(u), b = b->next;
            }
        }
        while (!remove.empty()) { // static used  
        	u = remove.top(), remove.pop();
        	delete u;
        }	    	
        return a;
    }
    void debug(Node *head) {
        Node *u = head;
        printf("[");
    	while (u != NULL) {
        	for(int i = 0; i < u->real()->A.size(); i++)
            	printf("%d%s", u->real()->A[i], i != u->real()->A.size()-1 ? " " : " ");
        	u = u->next;
    	}
    	puts("]");
    }
    void free() {
        return ;
        while (!mem.empty()) {
            Node *u = mem.top();
            mem.pop();
            delete u;
        }
    }
} dream; 
int A[MAXN], n, q;
UnrolledLinkedList::Node *ver[MAXQ];
int main() {
    int x, y, v;
    char cmd[10];
    while (scanf("%d", &n) == 1) {
        for (int i = 1; i <= n; i++)
            scanf("%d", &A[i]);
        ver[0] = dream.init(A, n);
//		dream.debug(ver[0]);
        int encrypt = 0;
        scanf("%d", &q);
        for (int i = 1; i <= q; i++) {
            scanf("%s", cmd);
            if (cmd[0] == 'I') {
                // insert A[x] = v
                scanf("%d %d", &x, &v);
                x ^= encrypt, v ^= encrypt;
                ver[i] = dream.insert(ver[i-1], x-1, v);
            } else if (cmd[0] == 'Q') {
                scanf("%d %d %d", &x, &y, &v);
                x ^= encrypt, y ^= encrypt, v ^= encrypt;
                int t = dream.find(ver[i-1], x, y, v);
                printf("%d\n", t);
                encrypt = t;
                ver[i] = ver[i-1];
            } else if (cmd[0] == 'M') {
                scanf("%d %d", &x, &v);
                x ^= encrypt, v ^= encrypt;
                ver[i] = dream.change(ver[i-1], x, v);
            }
//			dream.debug(ver[i]);
        }
    }
    return 0;
}
/*
5
1 2 3 4 5
9999
4 1 5 2
1 2 1
4 1 5 2
0 1
4 1 5 2
2 1
1 0 5
3 3 9
4 1 1 1
*/