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December 2010

PrefixSet edition (2010-10)

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

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 arrays, A (consisting of N integers) and B (consisting of M integers), both sorted in ascending order

- two 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 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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

Copyright 2009–2024 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 arrays, A (consisting of N integers) and B (consisting of M integers), both sorted in ascending order

- two 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 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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

Copyright 2009–2024 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 arrays, A (consisting of N integers) and B (consisting of M integers), both sorted in ascending order

- two 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 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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

Copyright 2009–2024 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:

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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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(List<int> A, List<int> B, List<int> P, List<int> Q, List<int> R, List<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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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:

fun solution(A: IntArray, B: IntArray, P: IntArray, Q: IntArray, R: IntArray, S: IntArray): 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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use `#A` to get the length of the array A.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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: number[], B: number[], P: number[], Q: number[], R: number[], S: number[]): number;

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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.

*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.

Write an ** efficient** algorithm for the following assumptions:

- 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 and 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 and Q is an integer within the range [0..
N-1];- each element of arrays R and 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.