UVa 11922 - Permutation Transformer （Splay）

UVA - 11922

Permutation Transformer

Time Limit: 2000MS Memory Limit: Unknown 64bit IO Format: %lld & %llu

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Description

  Permutation Transformer 

Write a program to transform the permutation 1, 2, 3,..., n according to m instructions. Each instruction (a, b) means to take out the subsequence from the a-th to the b-th element, reverse it, then append it to the end.

Input 

There is only one case for this problem. The first line contains two integers n and m ( 1n, m100, 000). Each of the next m lines contains an instruction consisting of two integers a and b ( 1abn).

Output 

Print n lines, one for each integer, the final permutation.

Explanation of the sample below

Instruction (2,5): Take out the subsequence {2,3,4,5}, reverse it to {5,4,3,2}, append it to the remaining permutation {1,6,7,8,9,10}

Instruction (4,8): The subsequence from the 4-th to the 8-th element of {1,6,7,8,9,10,5,4,3,2} is {8,9,10,5,4}. Take it out, reverse it, and you'll get the sample output.

Warning: Don't use cin, cout for this problem, use faster i/o methods e.g scanf, printf.

Sample Input 

10 22 54 8

Sample Output 

16732451098

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Source

Root :: Prominent Problemsetters :: Rujia Liu
Root :: AOAPC I: Beginning Algorithm Contests -- Training Guide (Rujia Liu) :: Chapter 3. Data Structures :: Binary Search Trees ::Examples

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题意：

维护序列1,2,3...n。只有一种操作：

a b 表示把[a, b]翻转后放到序列尾部

Splay的基本操作

#include <cstdio>#include <iostream>#include <vector>#include <algorithm>#include <cstring>#include <string>#include <map>#include <cmath>#include <queue>#include <set>using namespace std;//#define WIN#ifdef WINtypedef __int64 LL;#define iform "%I64d"#define oform "%I64d\n"#define oform1 "%I64d"#elsetypedef long long LL;#define iform "%lld"#define oform "%lld\n"#define oform1 "%lld"#endif#define S64I(a) scanf(iform, &(a))#define P64I(a) printf(oform, (a))#define P64I1(a) printf(oform1, (a))#define REP(i, n) for(int (i)=0; (i)<n; (i)++)#define REP1(i, n) for(int (i)=1; (i)<=(n); (i)++)#define FOR(i, s, t) for(int (i)=(s); (i)<=(t); (i)++)#define keyTree (ch[ch[root][1]][0])const int INF = 0x3f3f3f3f;const double eps = 1e-9;const double PI = (4.0*atan(1.0));const int maxn = 100000 + 20;int ch[maxn][2], val[maxn], pre[maxn], size[maxn], S[maxn];int root, top1, top2;LL sumv[maxn], addv[maxn];int rev[maxn];// debugvoid push_down(int );void Treaval(int x) {    if(x) {        Treaval(ch[x][0]);        printf("结点%2d : 左儿子 %2d 右儿子 %2d 父结点 %2d size = %2d ,val = %2d\n",x,ch[x][0],ch[x][1],pre[x],size[x],val[x]);        Treaval(ch[x][1]);    }}void debug() {    printf("root=%d\n",root);    Treaval(root);}void New(int & r, int fa, int v) {    if(top2) r = S[--top2];    else r = ++top1;    pre[r] = fa;    size[r] = 1;    ch[r][0] = ch[r][1] = 0;    sumv[r] = val[r] = v;    addv[r] = 0;    rev[r] = 0;}void Reversed(int r) {    if(!r) return ;    rev[r] ^= 1;    swap(ch[r][0], ch[r][1]);}void push_up(int r) {    size[r] = size[ch[r][0]] + size[ch[r][1]] + 1;    sumv[r] = sumv[ch[r][0]] + sumv[ch[r][1]] + val[r];}void push_down(int r) {    if(addv[r]) {        int lson = ch[r][0], rson = ch[r][1];        addv[lson] += addv[r];        val[lson] += addv[r];        addv[rson] += addv[r];        val[rson] += addv[r];        sumv[lson] += addv[r] * size[lson];        sumv[rson] += addv[r] * size[rson];        addv[r] = 0;    }    if(rev[r]) {        Reversed(ch[r][0]);        Reversed(ch[r][1]);        rev[r] = 0;    }}void Rotate(int x, int d) {    int y = pre[x];    push_down(x);    push_down(y);    ch[y][!d] = ch[x][d];    pre[ch[x][d]] = y;    if(pre[y]) ch[pre[y]][ch[pre[y]][1] == y] = x;    pre[x] = pre[y];    ch[x][d] = y;    pre[y] = x;    push_up(y);}void Splay(int x, int goal) {    push_down(x);    while(pre[x] != goal) {        if(pre[pre[x]] == goal)            Rotate(x, ch[pre[x]][0] == x);        else {            int y = pre[x];            int d = ch[pre[y]][0] == y;            if(ch[y][d] == x) {                Rotate(x, !d);                Rotate(x, d);            } else {                Rotate(y, d);                Rotate(x, d);            }        }    }    push_up(x);    if(goal == 0) root = x;}void RotateTo(int k, int goal) {    int r = root;    push_down(r);    while(size[ch[r][0]] != k) {        if(k < size[ch[r][0]]) r = ch[r][0];        else {            k -= size[ch[r][0]] + 1;            r = ch[r][1];        }        push_down(r);    }    Splay(r, goal);}int que[maxn];void erase(int x) {    int y = pre[x];    int head = 0, tail = 0;    for(que[tail++] = x; head < tail; head++) {        int r = que[head];        S[top2++] = r;        if(ch[r][0]) que[tail++] = ch[r][0];        if(ch[r][1]) que[tail++] = ch[r][1];    }    ch[y][ch[y][1] == x] = 0;    push_up(y);}void build(int & r, int L, int R, int fa) {    if(L > R) return ;    int M = (L + R) / 2;    New(r, fa, M);    if(L < M) build(ch[r][0], L, M-1, r);    if(M < R) build(ch[r][1], M+1, R, r);    push_up(r);}void init(int n) {    root = top1 = top2 = 0;    ch[0][0] = ch[0][1] = size[0] = pre[0] = 0;    addv[0] = sumv[0] = 0;    New(root, 0, -1);    New(ch[root][1], root, -1);    size[root] = 2;    build(keyTree, 1, n, ch[root][1]);    push_up(ch[root][1]);    push_up(root);}int getPre(int r) {    int t = ch[r][0];    if(!t) return INF;    while(ch[t][1]) t = ch[t][1];    return val[t];}int getNext(int r) {    int t = ch[r][1];    if(!t) return INF;    while(ch[t][0]) t = ch[t][0];    return val[t];}LL query(int L, int R) {    RotateTo(L-1, 0);    RotateTo(R+1, root);    return sumv[keyTree];}void update(int L, int R, int v) {    RotateTo(L-1, 0);    RotateTo(R+1, root);    addv[keyTree] += v;    val[keyTree] += v;    sumv[keyTree] += (LL) v * size[keyTree];}void print(int x) {    if(!x) return ;    push_down(x);    print(ch[x][0]);    printf("%d\n", val[x]);    print(ch[x][1]);}char str[10];int main() {    int n, m;    while(scanf("%d%d", &n, &m) != EOF) {        init(n);        while(m--) {            int a, b;            scanf("%d%d", &a, &b);            RotateTo(a-1, 0);            RotateTo(b+1, root);            Reversed(keyTree);            int t = keyTree;            keyTree = 0;            push_up(ch[root][1]);            push_up(root);            int nn = n - (b-a+1);            RotateTo(nn, 0);            RotateTo(nn+1, root);            keyTree = t;            pre[t] = ch[root][1];            push_up(ch[root][1]);            push_up(root);        }        RotateTo(0, 0);        RotateTo(n+1, root);        print(keyTree);    }    return 0;}