given an array, for each element, find out the total number of elements lesser than it, which appear to the right of it

Question

I had previously posted a question, Given an array, find out the next smaller element for each element now, i was trying to know , if there is any way to find out \"given an ar

Answer 1

Modified Merge sort: (Already tested code)

Takes O(nlogn) time.

public class MergeSort {
    static HashMap valueToLowerCount = new HashMap();

    public static void main(String[] args) {
        int []                 arr = new int[] {50, 33, 37, 26, 58, 36, 59};
        int [] lowerValuesOnRight  = new int[] {4,   1,  2,  0,  1,  0,  0};

        HashMap expectedLowerCounts = new HashMap();
        idx = 0;
        for (int x: arr) {
            expectedLowerCounts.put(x, lowerValuesOnRight[idx++]);
        }
        
        for (int x : arr) valueToLowerCount.put(x, 0);
        
        mergeSort(arr, 0, arr.length-1);
        
        //Testing       
        Assert.assertEquals("Count lower values on right side", expectedLowerCounts, valueToLowerCount);
    }
    public static void mergeSort(int []arr, int l, int r) {
        if (r <= l) return;
        int mid = (l+r)/2;
        mergeSort(arr, l, mid);
        mergeSort(arr, mid+1, r);
        mergeDecreasingOrder(arr, l, mid, r);
    }
    public static void mergeDecreasingOrder(int []arr, int l, int lr, int r) {
        int []leftArr = Arrays.copyOfRange(arr, l, lr+1);
        int []rightArr = Arrays.copyOfRange(arr, lr+1, r+1);
        int indexArr = l;
        int i = 0, j = 0;
        while (i < leftArr.length && j < rightArr.length) {
            if (leftArr[i] > rightArr[j]) {
                valueToLowerCount.put(leftArr[i], valueToLowerCount.get(leftArr[i]) + rightArr.length - j);
                arr[indexArr++] = leftArr[i++];
            }else {
                arr[indexArr++] = rightArr[j++];
            }
        }
        while (i < leftArr.length)  { 
            arr[indexArr++] = leftArr[i++]; 
        }
        while (j < rightArr.length) {
            arr[indexArr++] = rightArr[j++];
        }
    }   
}

To find the total number of values on right-side which are greater than an array element, simply change single line of code:

if (leftArr[i] > rightArr[j])

to

if (leftArr[i] < rightArr[j])