# Permutation of an array that has smaller values from another array

Given two arrays **A** and **B** of equal size. The task is to print **any permutation of array A** such that the number of indices **i** for which **A[i] > B[i]** is **maximized**.

**Examples:**

Input: A = [12, 24, 8, 32], B = [13, 25, 32, 11] Output: 24 32 8 12 Input: A = [2, 7, 11, 15], B = [1, 10, 4, 11] Output: 2 11 7 15

If the **smallest** element in **A** beats the smallest element in **B**, we should pair them. Otherwise, it is useless for our score, as it can’t beat any other element of **B**.

With above strategy we make two **vector of pairs**, **Ap** for **A **and **Bp** for **B **with their **element** and respective **index**. Then **sort **both vectors and simulate them. Whenever we found any element in vector **Ap** such that** Ap[i].first > Bp[j].first** for some **(i, j)** we pair them i:e we update our answer array to **ans[Bp[j].second] = Ap[i].first**. However if **Ap[i].first < Bp[j].first** for some **(i, j)** then we store them in vector **remain** and finally pair them with any one.

**Below is the implementation of above approach:**

## C++

`// CPP program to find permutation of an array that ` `// has smaller values from another array ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to print required permutation ` `void` `anyPermutation(` `int` `A[], ` `int` `B[], ` `int` `n) ` `{ ` ` ` `// Storing elements and indexes ` ` ` `vector<pair<` `int` `, ` `int` `> > Ap, Bp; ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `Ap.push_back(make_pair(A[i], i)); ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `Bp.push_back(make_pair(B[i], i)); ` ` ` ` ` `sort(Ap.begin(), Ap.end()); ` ` ` `sort(Bp.begin(), Bp.end()); ` ` ` ` ` `int` `i = 0, j = 0, ans[n] = { 0 }; ` ` ` ` ` `// Filling the answer array ` ` ` `vector<` `int` `> remain; ` ` ` `while` `(i < n && j < n) { ` ` ` ` ` `// pair element of A and B ` ` ` `if` `(Ap[i].first > Bp[j].first) { ` ` ` `ans[Bp[j].second] = Ap[i].first; ` ` ` `i++; ` ` ` `j++; ` ` ` `} ` ` ` `else` `{ ` ` ` `remain.push_back(i); ` ` ` `i++; ` ` ` `} ` ` ` `} ` ` ` ` ` `// Fill the remaining elements of answer ` ` ` `j = 0; ` ` ` `for` `(` `int` `i = 0; i < n; ++i) ` ` ` `if` `(ans[i] == 0) { ` ` ` `ans[i] = Ap[remain[j]].first; ` ` ` `j++; ` ` ` `} ` ` ` ` ` `// Output required permutation ` ` ` `for` `(` `int` `i = 0; i < n; ++i) ` ` ` `cout << ans[i] << ` `" "` `; ` `} ` ` ` `// Driver program ` `int` `main() ` `{ ` ` ` `int` `A[] = { 12, 24, 8, 32 }; ` ` ` `int` `B[] = { 13, 25, 32, 11 }; ` ` ` `int` `n = ` `sizeof` `(A) / ` `sizeof` `(A[0]); ` ` ` `anyPermutation(A, B, n); ` ` ` `return` `0; ` `} ` ` ` `// This code is written by Sanjit_Prasad ` |

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## Python3

`# Python3 program to find permutation of ` `# an array that has smaller values from ` `# another array ` ` ` `# Function to print required permutation ` `def` `anyPermutation(A, B, n): ` ` ` ` ` `# Storing elements and indexes ` ` ` `Ap, Bp ` `=` `[], [] ` ` ` ` ` `for` `i ` `in` `range` `(` `0` `, n): ` ` ` `Ap.append([A[i], i]) ` ` ` `for` `i ` `in` `range` `(` `0` `, n): ` ` ` `Bp.append([B[i], i]) ` ` ` ` ` `Ap.sort() ` ` ` `Bp.sort() ` ` ` ` ` `i, j ` `=` `0` `, ` `0` `, ` ` ` `ans ` `=` `[` `0` `] ` `*` `n ` ` ` ` ` `# Filling the answer array ` ` ` `remain ` `=` `[] ` ` ` `while` `i < n ` `and` `j < n: ` ` ` ` ` `# pair element of A and B ` ` ` `if` `Ap[i][` `0` `] > Bp[j][` `0` `]: ` ` ` `ans[Bp[j][` `1` `]] ` `=` `Ap[i][` `0` `] ` ` ` `i ` `+` `=` `1` ` ` `j ` `+` `=` `1` ` ` ` ` `else` `: ` ` ` `remain.append(i) ` ` ` `i ` `+` `=` `1` ` ` ` ` `# Fill the remaining elements ` ` ` `# of answer ` ` ` `j ` `=` `0` ` ` `for` `i ` `in` `range` `(` `0` `, n): ` ` ` `if` `ans[i] ` `=` `=` `0` `: ` ` ` `ans[i] ` `=` `Ap[remain[j]][` `0` `] ` ` ` `j ` `+` `=` `1` ` ` ` ` `# Output required permutation ` ` ` `for` `i ` `in` `range` `(` `0` `, n): ` ` ` `print` `(ans[i], end ` `=` `" "` `) ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `A ` `=` `[ ` `12` `, ` `24` `, ` `8` `, ` `32` `] ` ` ` `B ` `=` `[ ` `13` `, ` `25` `, ` `32` `, ` `11` `] ` ` ` `n ` `=` `len` `(A) ` ` ` `anyPermutation(A, B, n) ` ` ` `# This code is contributed ` `# by Rituraj Jain ` |

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**Output:**

24 32 8 12

**Time Complexity:** O(N*log(N)), where N is the length of array.

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