# For each element in 1st array count elements less than or equal to it in 2nd array

Given two unsorted arrays arr1[] and arr2[]. They may contain duplicates. For each element in arr1[] count elements less than or equal to it in array arr2[].
Source: Amazon Interview Experience | Set 354 (For SDE-2)
Examples:

```Input : arr1[] = [1, 2, 3, 4, 7, 9]
arr2[] = [0, 1, 2, 1, 1, 4]
Output : [4, 5, 5, 6, 6, 6]
So the number of elements less than or equal to
1 is 4, 2 is 5, 3 is 5, 4 is 6, 7 is 6 and 9 is 6.

Input : arr1[] = [5, 10, 2, 6, 1, 8, 6, 12]
arr2[] = [6, 5, 11, 4, 2, 3, 7]
Output : [4, 6, 1, 5, 0, 6, 5, 7]
So the number of elements less than or equal to
5 is 4, 10 is 6, 2 is 1, 6 is 5, 1 is 0, 8 is 6,
6 is 5 and 12 is 7 ```

Naive Approach:
Approach: The idea is to use two loops, the outer loop for elements of array arr1[] and an inner loop for elements of array arr2[]. Then for each element of arr1[], count elements less than or equal to it in arr2[].
Algorithm :

1. Traverse through the elements of the first array from start to end.
2. For every element in the first array.
3. Traverse through the elements in the second array and find the count of elements that are less than or equal to the element of the first array.
4. Print the count for every index.

 `// C++ code for the above algorithm` `#include ` `using` `namespace` `std;`   `// Function to count for each` `// element in 1st array,` `// elements less than or equal` `// to it in 2nd array` `void` `countEleLessThanOrEqual(``int` `arr1[], ``int` `arr2[],` `                             ``int` `m, ``int` `n)` `{` `    ``// Run two loops to count` `    ``// First loop to traverse the first array` `    ``// Second loop to traverse the second array` `    ``for` `(``int` `i = 0; i < m; i++) {` `        ``int` `count = 0;`   `        ``// Traverse through second array` `        ``for` `(``int` `j = 0; j < n; j++)` `            ``if` `(arr2[j] <= arr1[i])` `                ``count++;`   `        ``cout << count << ``" "``;` `    ``}` `}`   `// Driver program to test above` `int` `main()` `{` `    ``int` `arr1[] = { 1, 2, 3, 4, 7, 9 };` `    ``int` `arr2[] = { 0, 1, 2, 1, 1, 4 };` `    ``int` `m = ``sizeof``(arr1) / ``sizeof``(arr1);` `    ``int` `n = ``sizeof``(arr2) / ``sizeof``(arr2);` `    ``countEleLessThanOrEqual(arr1, arr2, m, n);` `    ``return` `0;` `}`

 `import` `java.util.Arrays;`   `class` `GFG {`   `    ``// function to count for each` `    ``// element in 1st array,` `    ``// elements less than or equal` `    ``// to it in 2nd array` `    ``static` `int` `countEleLessThanOrEqual(` `        ``int` `arr1[], ``int` `arr2[],` `        ``int` `m, ``int` `n)` `    ``{` `        ``// Run two loops to count` `        ``// First loop to traverse the first array` `        ``// Second loop to traverse the second array` `        ``for` `(``int` `i = ``0``; i < m; i++) {` `            ``int` `count = ``0``;`   `            ``// Traverse through second array` `            ``for` `(``int` `j = ``0``; j < n; j++)` `                ``if` `(arr2[j] <= arr1[i])` `                    ``count++;` `            ``System.out.print(count + ``" "``);` `        ``}` `        ``return` `m;` `    ``}`   `    ``// Driver method` `    ``public` `static` `void` `main(String[] args)` `    ``{`   `        ``int` `arr1[] = { ``1``, ``2``, ``3``, ``4``, ``7``, ``9` `};` `        ``int` `arr2[] = { ``0``, ``1``, ``2``, ``1``, ``1``, ``4` `};` `        ``countEleLessThanOrEqual(` `            ``arr1, arr2, arr1.length, arr2.length);` `    ``}` `}`   `// This code is contributed by shivanisinghss2110`

 `# Python3 code for the above algorithm`   `# function to count for each element in 1st array,` `# elements less than or equal to it in 2nd array` `def` `countEleLessThanOrEqual(arr1, arr2, m, n):` `    `  `    ``# Run two loops to count ` `    ``# First loop to traverse the first array` `    ``# Second loop to traverse the second array` `    ``for` `i ``in` `range``(m):` `        `  `        ``count ``=` `0` `        ``# Traverse through second array` `        ``for` `j ``in` `range``(n):` `            ``if` `(arr2[j] <``=` `arr1[i]):` `                ``count``+``=` `1` `            `  `        ``print``(count, end ``=``" "``)`   `# Driver program to test above` `arr1 ``=` `[``1``, ``2``, ``3``, ``4``, ``7``, ``9``]` `arr2 ``=` `[``0``, ``1``, ``2``, ``1``, ``1``, ``4``]` `m ``=` `len``(arr1)` `n ``=` `len``(arr2)` `countEleLessThanOrEqual(arr1, arr2, m, n)` ` `  `# This code is contributed by shubhamsingh10`

 `// C# implementation of For each element` `using` `System;`   `class` `GFG {`   `    ``// function to count for each element in 1st array,` `    ``// elements less than or equal to it in 2nd array` `    ``static` `void` `countEleLessThanOrEqual(` `        ``int``[] arr1, ``int``[] arr2,` `        ``int` `m, ``int` `n)` `    ``{` `        ``// Run two loops to count` `        ``// First loop to traverse the first array` `        ``// Second loop to traverse the second array` `        ``for` `(``int` `i = 0; i < m; i++) {` `            ``int` `count = 0;`   `            ``// Traverse through second array` `            ``for` `(``int` `j = 0; j < n; j++)` `                ``if` `(arr2[j] <= arr1[i])` `                    ``count++;` `            ``Console.Write((count) + ``" "``);` `        ``}` `    ``}`   `    ``// Driver method` `    ``public` `static` `void` `Main()` `    ``{` `        ``int``[] arr1 = { 1, 2, 3, 4, 7, 9 };` `        ``int``[] arr2 = { 0, 1, 2, 1, 1, 4 };`   `        ``countEleLessThanOrEqual(arr1,` `                                ``arr2, arr1.Length, arr2.Length);` `    ``}` `}`   `// This code is contributed by mohit kumar 29.`

 ``

Output:

`4 5 5 6 6 6 `

Complexity Analysis:

• Time complexity: O(m * n).
Considering arr1[] and arr2[] are of sizes m and n respectively.
• Space Complexity: O(1).
As no extra space is required

Efficient Solution:
Approach: Sort the elements of 2nd array, i.e., array arr2[]. Then perform a modified binary search on array arr2[]. For each element x of array arr1[], find the last index of the largest element smaller than or equal to x in sorted array arr2[]. The index of the largest element will give the count of elements.
Algorithm:

1. Sort the second array.
2. Traverse through the elements of the first array from start to end.
3. For every element in the first array.
4. Do a binary search on the second array and find the index of the largest element smaller than or equal to the element of the first array.
5. The index of the largest element will give the count of elements. Print the count for every index.

 `// C++ implementation of For each element in 1st` `// array count elements less than or equal to it` `// in 2nd array` `#include `   `using` `namespace` `std;`   `// function returns the index of largest element` `// smaller than equal to 'x' in 'arr'. For duplicates` `// it returns the last index of occurrence of required` `// element. If no such element exits then it returns -1.` `int` `binary_search(``int` `arr[], ``int` `l, ``int` `h, ``int` `x)` `{` `    ``while` `(l <= h) {` `        ``int` `mid = (l + h) / 2;`   `        ``// if 'x' is greater than or equal to arr[mid],` `        ``// then search in arr[mid+1...h]` `        ``if` `(arr[mid] <= x)` `            ``l = mid + 1;`   `        ``// else search in arr[l...mid-1]` `        ``else` `            ``h = mid - 1;` `    ``}`   `    ``// required index` `    ``return` `h;` `}`   `// function to count for each element in 1st array,` `// elements less than or equal to it in 2nd array` `void` `countEleLessThanOrEqual(` `    ``int` `arr1[], ``int` `arr2[],` `    ``int` `m, ``int` `n)` `{` `    ``// sort the 2nd array` `    ``sort(arr2, arr2 + n);`   `    ``// for each element of 1st array` `    ``for` `(``int` `i = 0; i < m; i++) {` `        ``// last index of largest element` `        ``// smaller than or equal to x` `        ``int` `index = binary_search(` `            ``arr2, 0, n - 1, arr1[i]);`   `        ``// required count for the element arr1[i]` `        ``cout << (index + 1) << ``" "``;` `    ``}` `}`   `// Driver program to test above` `int` `main()` `{` `    ``int` `arr1[] = { 1, 2, 3, 4, 7, 9 };` `    ``int` `arr2[] = { 0, 1, 2, 1, 1, 4 };` `    ``int` `m = ``sizeof``(arr1) / ``sizeof``(arr1);` `    ``int` `n = ``sizeof``(arr2) / ``sizeof``(arr2);` `    ``countEleLessThanOrEqual(arr1, arr2, m, n);` `    ``return` `0;` `}`

 `// Java implementation of For` `// each element in 1st` `// array count elements less` `// than or equal to it` `// in 2nd array`   `import` `java.util.Arrays;`   `class` `GFG {` `    ``// method returns the index` `    ``// of largest element` `    ``// smaller than equal to 'x'` `    ``// in 'arr'. For duplicates` `    ``// it returns the last index` `    ``// of occurrence of required` `    ``// element. If no such element` `    ``// exits then it returns -1.` `    ``static` `int` `binary_search(` `        ``int` `arr[], ``int` `l,` `        ``int` `h, ``int` `x)` `    ``{` `        ``while` `(l <= h) {` `            ``int` `mid = (l + h) / ``2``;`   `            ``// if 'x' is greater than or equal` `            ``// to arr[mid], then search in` `            ``// arr[mid+1...h]` `            ``if` `(arr[mid] <= x)` `                ``l = mid + ``1``;`   `            ``// else search in arr[l...mid-1]` `            ``else` `                ``h = mid - ``1``;` `        ``}`   `        ``// Required index` `        ``return` `h;` `    ``}`   `    ``// Method to count for each` `    ``// element in 1st array,` `    ``// elements less than or equal` `    ``// to it in 2nd array` `    ``static` `void` `countEleLessThanOrEqual(` `        ``int` `arr1[], ``int` `arr2[],` `        ``int` `m, ``int` `n)` `    ``{` `        ``// Sort the 2nd array` `        ``Arrays.sort(arr2);`   `        ``// for each element of 1st array` `        ``for` `(``int` `i = ``0``; i < m; i++) {` `            ``// Last index of largest element` `            ``// smaller than or equal to x` `            ``int` `index = binary_search(` `                ``arr2, ``0``, n - ``1``, arr1[i]);`   `            ``// Required count for the element arr1[i]` `            ``System.out.print((index + ``1``) + ``" "``);` `        ``}` `    ``}`   `    ``// Driver method` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `arr1[] = { ``1``, ``2``, ``3``, ``4``, ``7``, ``9` `};` `        ``int` `arr2[] = { ``0``, ``1``, ``2``, ``1``, ``1``, ``4` `};`   `        ``countEleLessThanOrEqual(` `            ``arr1, arr2, arr1.length,` `            ``arr2.length);` `    ``}` `}`

 `# python implementation of For each element in 1st ` `# array count elements less than or equal to it` `# in 2nd array`   `# function returns the index of largest element ` `# smaller than equal to 'x' in 'arr'. For duplicates` `# it returns the last index of occurrence of required` `# element. If no such element exits then it returns -1` `def` `bin_search(arr, n, x):` `    `  `l ``=` `0` `h ``=` `n ``-` `1` `while``(l <``=` `h):` `    ``mid ``=` `int``((l ``+` `h) ``/` `2``)` `    ``# if 'x' is greater than or equal to arr[mid], ` `    ``# then search in arr[mid + 1...h]` `    ``if``(arr[mid] <``=` `x):` `    ``l ``=` `mid ``+` `1``;` `    ``else``:` `    ``# else search in arr[l...mid-1]` `    ``h ``=` `mid ``-` `1` `# required index` `return` `h`   `# function to count for each element in 1st array,` `# elements less than or equal to it in 2nd array` `def` `countElements(arr1, arr2, m, n):` `# sort the 2nd array` `arr2.sort()`   `# for each element in first array` `for` `i ``in` `range``(m):` `    ``# last index of largest element ` `    ``# smaller than or equal to x` `    ``index ``=` `bin_search(arr2, n, arr1[i])` `    ``# required count for the element arr1[i]` `    ``print``(index ``+` `1``)`   `# driver program to test above function` `arr1 ``=` `[``1``, ``2``, ``3``, ``4``, ``7``, ``9``]` `arr2 ``=` `[``0``, ``1``, ``2``, ``1``, ``1``, ``4``]` `m ``=` `len``(arr1)` `n ``=` `len``(arr2)` `countElements(arr1, arr2, m, n)`   `# This code is contributed by Aditi Sharma`

 `// C# implementation of For each element` `// in 1st array count elements less than` `// or equal to it in 2nd array` `using` `System;`   `public` `class` `GFG {`   `    ``// method returns the index of` `    ``// largest element smaller than` `    ``// equal to 'x' in 'arr'. For` `    ``// duplicates it returns the last` `    ``// index of occurrence of required` `    ``// element. If no such element` `    ``// exits then it returns -1.` `    ``static` `int` `binary_search(``int``[] arr,` `                             ``int` `l, ``int` `h, ``int` `x)` `    ``{` `        ``while` `(l <= h) {` `            ``int` `mid = (l + h) / 2;`   `            ``// if 'x' is greater than or` `            ``// equal to arr[mid], then` `            ``// search in arr[mid+1...h]` `            ``if` `(arr[mid] <= x)` `                ``l = mid + 1;`   `            ``// else search in` `            ``// arr[l...mid-1]` `            ``else` `                ``h = mid - 1;` `        ``}`   `        ``// required index` `        ``return` `h;` `    ``}`   `    ``// method to count for each element` `    ``// in 1st array, elements less than` `    ``// or equal to it in 2nd array` `    ``static` `void` `countEleLessThanOrEqual(` `        ``int``[] arr1, ``int``[] arr2,` `        ``int` `m, ``int` `n)` `    ``{`   `        ``// sort the 2nd array` `        ``Array.Sort(arr2);`   `        ``// for each element of 1st array` `        ``for` `(``int` `i = 0; i < m; i++) {` `            ``// last index of largest` `            ``// element smaller than or` `            ``// equal to x` `            ``int` `index = binary_search(` `                ``arr2, 0, n - 1, arr1[i]);`   `            ``// required count for the` `            ``// element arr1[i]` `            ``Console.Write((index + 1) + ``" "``);` `        ``}` `    ``}`   `    ``// Driver method` `    ``public` `static` `void` `Main()` `    ``{` `        ``int``[] arr1 = { 1, 2, 3, 4, 7, 9 };` `        ``int``[] arr2 = { 0, 1, 2, 1, 1, 4 };`   `        ``countEleLessThanOrEqual(arr1,` `                                ``arr2, arr1.Length, arr2.Length);` `    ``}` `}`   `// This code is contributed by Sam007.`

 ``

 ``

Output:

`4 5 5 6 6 6`

Complexity Analysis:

• Time Complexity: O(mlogn + nlogn).
Considering arr1[] and arr2[] of sizes m and n respectively.
• Space Complexity: O(1).
As no extra space is required

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