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ambitious

Given two slices of sorted arrays, find the median. Repeat for many such slices, return the median of the results.

Programming language:
Spoken language:

The *median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Note that sequences of odd length have only one median, which is equal to X[N/2] after sorting X. In this problem we consider medians of sequences of odd length only.

Write a function:

int solution(int A[], int N, int B[], int M, int P[], int Q[], int R[], int S[], int K);

that, given:

- two non-empty zero-indexed arrays, A (consisting of N integers) and B (consisting of M integers), both sorted in ascending order

- two zero-indexed arrays P and Q, each consisting of K indices of array A, such that 0 ≤ P[I] ≤ Q[I] < N for 0 ≤ I < K

- two zero-indexed arrays R and S, each consisting of K indices of array B, such that 0 ≤ R[I] ≤ S[I] < M for 0 ≤ I < K

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));
- expected worst-case space complexity is O(K), beyond input storage (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

The *median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Note that sequences of odd length have only one median, which is equal to X[N/2] after sorting X. In this problem we consider medians of sequences of odd length only.

Write a function:

int solution(vector<int> &A, vector<int> &B, vector<int> &P, vector<int> &Q, vector<int> &R, vector<int> &S);

that, given:

- two non-empty zero-indexed arrays, A (consisting of N integers) and B (consisting of M integers), both sorted in ascending order

- two zero-indexed arrays P and Q, each consisting of K indices of array A, such that 0 ≤ P[I] ≤ Q[I] < N for 0 ≤ I < K

- two zero-indexed arrays R and S, each consisting of K indices of array B, such that 0 ≤ R[I] ≤ S[I] < M for 0 ≤ I < K

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));
- expected worst-case space complexity is O(K), beyond input storage (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

The *median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Note that sequences of odd length have only one median, which is equal to X[N/2] after sorting X. In this problem we consider medians of sequences of odd length only.

Write a function:

class Solution { public int solution(int[] A, int[] B, int[] P, int[] Q, int[] R, int[] S); }

that, given:

- two non-empty zero-indexed arrays, A (consisting of N integers) and B (consisting of M integers), both sorted in ascending order

- two zero-indexed arrays P and Q, each consisting of K indices of array A, such that 0 ≤ P[I] ≤ Q[I] < N for 0 ≤ I < K

- two zero-indexed arrays R and S, each consisting of K indices of array B, such that 0 ≤ R[I] ≤ S[I] < M for 0 ≤ I < K

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));
- expected worst-case space complexity is O(K), beyond input storage (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

func Solution(A []int, B []int, P []int, Q []int, R []int, S []int) int

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

class Solution { public int solution(int[] A, int[] B, int[] P, int[] Q, int[] R, int[] S); }

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

function solution(A, B, P, Q, R, S);

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

function solution(A, B, P, Q, R, S)

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

int solution(NSMutableArray *A, NSMutableArray *B, NSMutableArray *P, NSMutableArray *Q, NSMutableArray *R, NSMutableArray *S);

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

function solution(A: array of longint; N: longint; B: array of longint; M: longint; P: array of longint; Q: array of longint; R: array of longint; S: array of longint; K: longint): longint;

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

function solution($A, $B, $P, $Q, $R, $S);

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

sub solution { my ($A, $B, $P, $Q, $R, $S)=@_; my @A=@$A; my @B=@$B; my @P=@$P; my @Q=@$Q; my @R=@$R; my @S=@$S; ... }

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

def solution(A, B, P, Q, R, S)

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

def solution(a, b, p, q, r, s)

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

object Solution { def solution(a: Array[Int], b: Array[Int], p: Array[Int], q: Array[Int], r: Array[Int], s: Array[Int]): Int }

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

public func solution(inout A : [Int], inout _ B : [Int], inout _ P : [Int], inout _ Q : [Int], inout _ R : [Int], inout _ S : [Int]) -> Int

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

public func solution(_ A : inout [Int], _ B : inout [Int], _ P : inout [Int], _ Q : inout [Int], _ R : inout [Int], _ S : inout [Int]) -> Int

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

*median* of a sequence of numbers X[0], X[1], ..., X[N] is the middle element in terms of their values. More formally, the median of X[0], X[1], ..., X[N] is an element X[I] of the sequence, such that at most half of the elements are larger than X[I] and at most half of the elements are smaller than X[I]. For example, the median of the following sequence:

is 5; the median of the following sequence:

is 2; and the following sequence:

has two medians: 4 and 5.

Write a function:

Private Function solution(A As Integer(), B As Integer(), P As Integer(), Q As Integer(), R As Integer(), S As Integer()) As Integer

that, given:

computes medians of K sequences of the form:

for 0 ≤ I < K, and returns the median of all such medians.

For example, given the following arrays:

the function should return 8, since:

- the median of [10, 13, 5, 6, 8, 12, 13] equals 10,
- the median of [4, 10, 5] equals 5,
- the median of [−2, 4, 10, 13, 6, 8, 12] equals 8, and
- the median of [10, 5, 8] equals 8.

Assume that:

- N and M are integers within the range [1..100,000];
- K is an integer within the range [1..10,000];
- each element of arrays A, B is an integer within the range [−1,000,000,000..1,000,000,000];
- array A is sorted in non-decreasing order;
- array B is sorted in non-decreasing order;
- each element of arrays P, Q is an integer within the range [0..N−1];
- each element of arrays R, S is an integer within the range [0..M−1];
- P[i] ≤ Q[i] and R[i] ≤ S[i] for 0 ≤ i < K;
- K is odd and so is Q[i]−P[i]+R[i]−S[i] for 0 ≤ i < K.

Complexity:

- expected worst-case time complexity is O(K*log(K+N+M));

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