| <p> | |
| For this problem, a <i>possible median</i> is defined as: The median value of a set containing an odd number of values. -or- One of all the integers between, but not including, the two median values of a set containing an even number of values.<br><b>Examples:</b> 3 is the only possible median of the set (1, 5, 3, 2, 4). 2, 3 and 4 are all of the possible median values for the set (5, 1). There | |
| are <b>no</b> possible median values for the set (1, 2, 3, 4), since there are no integers between 2 and 3. | |
| <p> | |
| You are given an array <b>A</b> of <b>N</b> unique nonnegative integers, all of which are < <b>N</b> (i.e. a permutation of the numbers 0...<b>N-1</b>), where 3 ≤ <b>N</b> ≤ 200,000. You are | |
| also given a length <b>L</b> (1 ≤ <b>L</b> ≤ <b>N</b>). Additionally, you are given <b>Q</b> (1 ≤ <b>Q</b> ≤ 200,000) queries, each containing a number <b>x</b> (0 ≤ <b>x</b> < N) | |
| and two indices <b>i</b> and <b>j</b> (0 ≤ <b>i</b> < <b>j</b> ≤ <b>N</b>). | |
| <p> | |
| Each query returns TRUE if and only if there exists at least one subrange, of at least <b>L</b> elements, of the range <b>A[i]</b>...<b>A[j-1]</b> (where the array indices start at 0), with <b>x</b> as a possible median. In other words, the answer is TRUE precisely when there exist <b>a</b>, <b>b</b> with <b>i</b> ≤ <b>a</b> < <b>b</b> < <b>j</b> with <b>b</b> - <b>a</b> ≥ <b>L</b> - | |
| 1 and with <b>A[a]</b>...<b>A[b]</b> having <b>x</b> as a possible median. | |
| <p> | |
| You wish to determine the number of queries which will return TRUE. | |
| <h3>Input</h3> | |
| <p> | |
| The first line contains a positive integer <b>T</b> (1 ≤ <b>T</b> ≤ 20), the number of test cases. <b>T</b> test cases follow. | |
| <p> | |
| The first line of each test case consists of a single integer, <b>N</b>. The next line consists of <b>N</b> space-separated integers, the <b>A[i]</b>. The line after that contains two space-separate | |
| d integers, <b>L</b> and <b>Q</b>. | |
| <p> | |
| Each of the remaining <b>Q</b> lines in the test case contains three space-separated integers, <b>x</b>, <b>i</b> and <b>j</b>. | |
| <p> | |
| These inputs are all integers, and will be input in decimal form, with no leading zeros, and no decimal points. | |
| <h3>Output</h3> | |
| <p> | |
| For each of the test cases numbered in order from 1 to T, output "Case #", followed by the case number, followed by ": ", followed by a single integer, the number of passing queries. | |
| <p> | |
| These outputs are all integers, and must be output in decimal form, with no leading zeros, and no decimal points. | |