划分树 poj2104 hdu5249
KPI
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 616 Accepted Submission(s): 261
每组数据第一行有一个 n(1≤n≤10000) ，代表服务记录数。
接下来有n行。每一行有3种形式
"in x": 代表重要值为 x(0≤x≤109
)
的请求被推进管道。
"out": 代表服务拉取了管道头部的请求。
"query: 代表我想知道当前管道内请求重要值的中间值. 那就是说，假设当前管道内有m条请求, 我想知道。升序排序后第 floor(m/2)+1th
条请求的重要值.
为了让题目简单，全部的x都不同。而且假设管道内没有值。就不会有"out"和"query"操作。
Case #i:
然后每一次"query"。输出当前管道内重要值的中间值。
6
in 874
query
out
in 24622
in 12194
query
Case #1:
874
24622
| Time Limit: 20000MS | Memory Limit: 65536K | |
| Total Submissions: 41138 | Accepted: 13447 | |
| Case Time Limit: 2000MS | ||
Description
That is, given an array a[1...n] of different integer numbers, your program must answer a series of questions Q(i, j, k) in the form: "What would be the k-th number in a[i...j] segment, if this segment was sorted?
"
For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question be Q(2, 5, 3). The segment a[2...5] is (5, 2, 6, 3). If we sort this segment, we get (2, 3, 5, 6), the third number is 5, and therefore the answer to the question is 5.
Input
The second line contains n different integer numbers not exceeding 10 9 by their absolute values --- the array for which the answers should be given.
The following m lines contain question descriptions, each description consists of three numbers: i, j, and k (1 <= i <= j <= n, 1 <= k <= j - i + 1) and represents the question Q(i, j, k).
Output
Sample Input
7 3 1 5 2 6 3 7 4 2 5 3 4 4 1 1 7 3
Sample Output
5 6 3
Hint
This problem has huge input,so please use c-style input(scanf,printf),or you may got time limit exceed.
这两题都 要求子区间的第k大数，假设用快排之后，再查，复杂度太大。不能过，就要用到划分树了，划分树。事实上，就是线段树的
一个变种了，当然，这样做查询是lg(n)级别，建树是n * lg(n),再加上一次快排，也是n * lg(n),差点儿相同就能够过了！
先来看看划分树，我们在线段树的基础上，假设每一个结点都保存了。当前子段向左子树走的个数。假设，查询的k要小于，查询段向左走的个数，自然，我们向左子树就能够查到结果。假设，k>向左走的个数，当然要向右找k-midcount个数，区间的变换。我们能够
推一下向左走就是l + scount, l + ecount - 1。向右走就是mid + 1 + s - l - scount, mid + 1 + e - l - ecount，当中scount就是s之前向左走的个数。 ecount，就是e之前向左走的个数。
上核心代码
#define MID(a,b) (((a)+(b))>>1)
#define N 100050
int num[20][N], val[20][N];
//第i层，向左包含自已，向左子树的个数，当前的值
int pri[N], sorted[N];
//原始和排序后的数列
char str[20];
void build(int l, int r, int layer){
if (l >= r){
return;
}
int mid = MID(l, r);
int ql = l, qr = mid + 1, leftCount = mid, eqCount = 0;
for (int i = l; i <= r; i++)
leftCount -= val[layer][i] < sorted[mid];
for (int i = l; i <= r; i++){
if (i == l){
num[layer][i] = 0;
}
else{
num[layer][i] = num[layer][i - 1];
}
if (val[layer][i] < sorted[mid]){
num[layer][i]++;
val[layer + 1][ql++] = val[layer][i];
}
else if (val[layer][i] > sorted[mid]){
val[layer + 1][qr++] = val[layer][i];
}
else {
if (eqCount < leftCount){
eqCount++;
num[layer][i]++;
val[layer + 1][ql++] = val[layer][i];
}
else {
val[layer + 1][qr++] = val[layer][i];
}
}
}
build(l, mid, layer + 1);
build(mid + 1, r, layer + 1);
}
//在layer层l到r间，找s-e之间的第k大数
int query(int l, int r, int layer, int s, int e, int k){
if (l >= r || s >= e){
return val[layer][s];
}
int scount, ecount, mid = MID(l, r);
if (s == l){
scount = 0, ecount = num[layer][e];
}
else {
scount = num[layer][s - 1], ecount = num[layer][e];
}
int midcount = ecount - scount;
if (k <= midcount){
return query(l, mid, layer + 1, l + scount, l + ecount - 1, k);
}
else {
return query(mid + 1, r, layer + 1, mid + 1 + s - l - scount, mid + 1 + e - l - ecount, k - midcount);
}
}
int main()
{
int tcase, tcasenum = 0;
int n, k, q, s, e, begin = 1, nn, qcount, m;
while (S2(n, m) != EOF)
{
FI(n){
S(val[0][i+1]);
}
FI(n){
sorted[i + 1] = val[0][i + 1];
}
sort(sorted + 1, sorted + n + 1);
build(1, n, 0);
FI(m){
S2(s, e); S(q);
Prn(query(1, n, 0, s,e,q));
}
}
return 0;
}