HDU 1890 Robotic Sort

Description

Somewhere deep in the Czech Technical University buildings, there are laboratories for examining mechanical and electrical properties of various materials. In one of yesterday’s presentations, you have seen how was one of the laboratories changed into a new multimedia lab. But there are still others, serving to their original purposes. 

In this task, you are to write software for a robot that handles samples in such a laboratory. Imagine there are material samples lined up on a running belt. The samples have different heights, which may cause troubles to the next processing unit. To eliminate such troubles, we need to sort the samples by their height into the ascending order. 

Reordering is done by a mechanical robot arm, which is able to pick up any number of consecutive samples and turn them round, such that their mutual order is reversed. In other words, one robot operation can reverse the order of samples on positions between A and B. 

A possible way to sort the samples is to find the position of the smallest one (P1) and reverse the order between positions 1 and P1, which causes the smallest sample to become first. Then we find the second one on position P and reverse the order between 2 and P2. Then the third sample is located etc. 



The picture shows a simple example of 6 samples. The smallest one is on the 4th position, therefore, the robot arm reverses the first 4 samples. The second smallest sample is the last one, so the next robot operation will reverse the order of five samples on positions 2�6. The third step will be to reverse the samples 3�4, etc. 

Your task is to find the correct sequence of reversal operations that will sort the samples using the above algorithm. If there are more samples with the same height, their mutual order must be preserved: the one that was given first in the initial order must be placed before the others in the final order too.

 

Input

The input consists of several scenarios. Each scenario is described by two lines. The first line contains one integer number N , the number of samples, 1 ≤ N ≤ 100 000. The second line lists exactly N space-separated positive integers, they specify the heights of individual samples and their initial order. 

The last scenario is followed by a line containing zero.

 

Output

For each scenario, output one line with exactly N integers P1 , P1 , . . . PN ,separated by a space. 
Each Pi must be an integer (1 ≤ Pi ≤ N ) giving the position of the i-th sample just before the i-th reversal operation. 

Note that if a sample is already on its correct position Pi , you should output the number Pi anyway, indicating that the “interval between Pi and Pi ” (a single sample) should be reversed. 

 

Sample Input

63 4 5 1 6 243 3 2 10 

 

Sample Output

4 6 4 5 6 6
4 2 4 4 
作为splay区间反转的第一题，这道题并不难，然而我却花了整整一下午调试还是wa，直到晚上再床上转辗反侧时
才回忆起，是我题意没读清楚，何等sb的错误啊，其实早早就写对了的。顺便一提，第一次做区间反转我直接把整个区间的坐标都算出来了，后来我以为是wa在这，又去网上参考了不少人的想法，后来发现splay本身是平衡树，无论怎么样旋转是不会改变节点之间的相对大小的，所以根本不用算出坐标，反转只要打标记然后交换左右子树就好了，这样写方便一点。此题有重复值，先离散化一发在做。
第一次写的计算标号的
#include<cstdio>#include<cstring>#include<cmath>#include<queue>#include<vector>#include<iostream>#include<algorithm>#include<bitset>#include<functional>using namespace std;typedef unsigned long long ull;typedef long long LL;const int maxn = 1e5 + 10;int n, m, l, r, c, root, a[maxn];char s[10];struct point{int x, id;bool operator<(const point&a)const{ return x == a.x ? id < a.id : x < a.x; }}b[maxn];struct Splays{const static int maxn = 1e5 + 10;const static int INF = 0x7FFFFFFF;int ch[maxn][2], F[maxn], U[maxn], C[maxn], A[maxn], sz, G[maxn], S[maxn];int Node(int f, int u, int c) { S[sz] = 1; C[sz] = A[sz] = c; G[sz] = ch[sz][0] = ch[sz][1] = 0; F[sz] = f; U[sz] = u; return sz++; }void clear(){ sz = 1; ch[0][0] = ch[0][1] = A[0] = U[0] = F[0] = G[0] = 0; C[0] = INF; S[0] = 1; }void Pushdown(int x){if (!G[x]) return;if (ch[x][0]) { U[ch[x][0]] = G[x] + S[x] * U[ch[x][0]]; G[ch[x][0]] = G[x] + S[x] * G[ch[x][0]]; S[ch[x][0]] *= S[x]; }if (ch[x][1]) { U[ch[x][1]] = G[x] + S[x] * U[ch[x][1]]; G[ch[x][1]] = G[x] + S[x] * G[ch[x][1]]; S[ch[x][1]] *= S[x]; }if (S[x] < 0) swap(ch[x][0], ch[x][1]);G[x] = 0;S[x] = 1;}void rotate(int x, int k){int y = F[x]; ch[y][!k] = ch[x][k]; F[ch[x][k]] = y;if (F[y]) ch[F[y]][y == ch[F[y]][1]] = x;F[x] = F[y];    F[y] = x;ch[x][k] = y;C[x] = C[y];C[y] = min(A[y], min(C[ch[y][1]], C[ch[y][0]]));}void Splay(int x, int r){for (int fa = F[r]; F[x] != fa;){if (F[F[x]] == fa) { rotate(x, x == ch[F[x]][0]); return; }int y = x == ch[F[x]][0], z = F[x] == ch[F[F[x]]][0];y^z ? (rotate(x, y), rotate(x, z)) : (rotate(F[x], z), rotate(x, y));}}void insert(int &x, int u){for (int i = x; i; i = ch[i][U[i] < u]){Pushdown(i);if (u == U[i]){ Splay(i, x); x = i; break; }}}void find(int &x, int u){insert(x, u - 1);int now = 0;for (int i = ch[x][1]; i;){Pushdown(i);if (C[ch[i][1]] == C[i]) { i = ch[i][1]; continue; }if (A[i] == C[i]) { now = i; break; }if (C[ch[i][0]] == C[i]) { i = ch[i][0]; continue; }}printf("%d", U[now]);insert(ch[x][1], U[now] + 1);G[ch[ch[x][1]][0]] = (u + U[now]) - G[ch[ch[x][1]][0]];S[ch[ch[x][1]][0]] *= -1;U[ch[ch[x][1]][0]] = (u + U[now]) - U[ch[ch[x][1]][0]];}void build(int fa, int &x, int l, int r){if (l > r) return;if (l == r) { x = Node(fa, l, a[l]); return; }int mid = l + r >> 1;x = Node(fa, mid, a[mid]);build(x, ch[x][0], l, mid - 1);build(x, ch[x][1], mid + 1, r);C[x] = min(A[x], min(C[ch[x][0]], C[ch[x][1]]));}}solve;int main(){while (scanf("%d", &n) != EOF, n){solve.clear();a[0] = root = 0;a[n + 1] = 0x7FFFFFFF;for (int i = 1; i <= n; i++) scanf("%d", &b[i].x), b[i].id = i;sort(b + 1, b + n + 1);for (int i = 1; i <= n; i++) a[b[i].id] = i;solve.build(0, root, 0, n + 1);for (int i = 1; i <= n; i++) { solve.find(root, i); printf("%s", i == n ? "\n" : " "); }}return 0;}

后来写的直接反转区间，然后把之前节点删除的做法
#include<cstdio>#include<cstring>#include<cmath>#include<queue>#include<vector>#include<iostream>#include<algorithm>#include<bitset>#include<functional>using namespace std;typedef unsigned long long ull;typedef long long LL;const int maxn = 2e5 + 10;int n, m, l, r, c, root, a[maxn];char s[10];struct point{int x, id;bool operator<(const point&a)const{ return x == a.x ? id < a.id : x < a.x; }}b[maxn];struct Splays{const static int maxn = 2e5 + 10;const static int INF = 0x7FFFFFFF;int ch[maxn][2], F[maxn], sz;int C[maxn], A[maxn], R[maxn], S[maxn];int Node(int f, int c) { R[sz] = ch[sz][0] = ch[sz][1] = 0; F[sz] = f; C[sz] = A[sz] = c; S[sz] = 1; return sz++; }void clear(){ sz = 1; ch[0][0] = ch[0][1] = F[0] = 0; C[0] = INF; S[0] = 0; }void pushdown(int x){if (!R[x]) return;R[ch[x][0]] ^= 1;R[ch[x][1]] ^= 1;swap(ch[x][0], ch[x][1]);R[x] = 0;}void rotate(int x, int k){int y = F[x]; ch[y][!k] = ch[x][k]; F[ch[x][k]] = y;if (F[y]) ch[F[y]][y == ch[F[y]][1]] = x;F[x] = F[y];    F[y] = x;ch[x][k] = y;C[x] = C[y];C[y] = min(min(C[ch[y][0]], C[ch[y][1]]), A[y]);S[x] = S[y];S[y] = S[ch[y][0]] + S[ch[y][1]] + 1;}void Splay(int x, int r){for (int fa = F[r]; F[x] != fa;){if (F[F[x]] == fa) { rotate(x, x == ch[F[x]][0]); return; }int y = (x == ch[F[x]][0]), z = (F[x] == ch[F[F[x]]][0]);y^z ? (rotate(x, y), rotate(x, z)) : (rotate(F[x], z), rotate(x, y));}}void build(int f, int&x, int l, int r){if (l > r) return;int mid = l + r >> 1;x = Node(f, a[mid]);build(x, ch[x][0], l, mid - 1);build(x, ch[x][1], mid + 1, r);C[x] = min(min(C[ch[x][0]], C[ch[x][1]]), A[x]);S[x] += S[ch[x][0]] + S[ch[x][1]];}void find(int &x, int k){for (int i = x; i;){pushdown(i);if (C[i] == C[ch[i][1]]) { i = ch[i][1]; continue; }if (C[i] == A[i]) { Splay(i, x); x = i; break; }i = ch[i][0];}printf("%d%s", k + S[ch[x][0]], k == n ? "\n" : " ");if (!ch[x][0]) { x = ch[x][1]; F[x] = 0; return; }R[ch[x][0]] ^= 1;for (int i = ch[x][0]; i; i = ch[i][1]){pushdown(i);if (!ch[i][1]) { Splay(i, x); x = i; break; }}ch[x][1] = ch[ch[x][1]][1];F[ch[x][1]] = x;S[x]--;C[x] = min(min(C[ch[x][0]], C[ch[x][1]]), A[x]);}}solve;int main(){while (scanf("%d", &n) != EOF, n){solve.clear();root = 0;for (int i = 1; i <= n; i++) scanf("%d", &b[i].x), b[i].id = i;sort(b + 1, b + n + 1);for (int i = 1; i <= n; i++) a[b[i].id] = i;solve.build(0, root, 1, n);for (int i = 1; i <= n; i++) solve.find(root, i);}return 0;}