Sure! Here's a randomized quicksort algorithm in C++ to sort an array of unsorted integers:

```cpp
#include <iostream>
#include <cstdlib>
#include <ctime>
using namespace std;

// Function to swap two elements
void swap(int& a, int& b) {
    int temp = a;
    a = b;
    b = temp;
}

// Partition function for randomized quicksort
int partition(int arr[], int low, int high) {
    int pivotIndex = low + rand() % (high - low + 1);
    int pivot = arr[pivotIndex];
    swap(arr[pivotIndex], arr[high]);

    int i = low - 1;

    for (int j = low; j <= high - 1; j++) {
        if (arr[j] < pivot) {
            i++;
            swap(arr[i], arr[j]);
        }
    }
    swap(arr[i + 1], arr[high]);
    return i + 1;
}

// Randomized Quicksort function
void randomizedQuicksort(int arr[], int low, int high) {
    if (low < high) {
        int pi = partition(arr, low, high);
        randomizedQuicksort(arr, low, pi - 1);
        randomizedQuicksort(arr, pi + 1, high);
    }
}

int main() {
    int arr[] = {10, 7, 8, 9, 1, 5};
    int size = sizeof(arr) / sizeof(arr[0]);

    cout << "Original array: ";
    for (int i = 0; i < size; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;

    srand(time(NULL)); // Seed the random number generator
    randomizedQuicksort(arr, 0, size - 1);

    cout << "Sorted array: ";
    for (int i = 0; i < size; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;

    return 0;
}
```

The `randomizedQuicksort` function is similar to the regular quicksort but with a random pivot selection. Instead of always choosing the last element as the pivot, it selects a random element within the subarray, swapping it with the last element, and then proceeds with the partitioning and sorting.

For the given example array `{10, 7, 8, 9, 1, 5}`, the output will be `1 5 7 8 9 10` after