[8.3] Magic Index

A magic index in an array A[0...n-1] is defined to be an index such that A[i] = i. Given a sorted array of distinct integers, write a method to find a magic index, if one exists, in array A.

FOLLOW UP

What if the values are not distinct?

    public int getMagicIndex(int[] inputs) {
        return helper(0, inputs.length - 1, inputs);
    }

    private int helper(int start, int end, int[] inputs) {
        if(end < start)
             return -1;
        int mid = (end - start) / 2 + start;
        if(mid == inputs[mid]) {
            return mid;
        } else if (mid > inputs[mid]) {
            return helper(mid + 1, end, inputs);
        } else {
            return helper(start, mid - 1, inputs);
        }
    }

Follow Up: 看答案的

    /**
     * 
     * A magic index in an array A[0...n-1] is defined to be an index such that A[i] = i. 
     * Given a sorted array of distinct integers, write a method to find a magic index, if one exists, in array A.
     * 
     * FOLLOW UP
     * What if the values are not distinct?
     * 
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[] inputs = {-11, -9, -3, -3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 16};
        System.out.println(getMagicIndex(inputs));
    }

    public static int getMagicIndex(int[] inputs) {
        return helper(0, inputs.length - 1, inputs);
    }

    private static int helper(int start, int end, int[] inputs) {
        if(end < start)
             return -1;

        int midIndex = (end - start) / 2 + start;
        int midValue = inputs[midIndex];
        
        if(midIndex == midValue) {
            return midIndex;
        } else {
            // Search left
            int leftIndex = Math.min(midIndex - 1, midValue);
            int left = helper(start, leftIndex, inputs);
            if(left > 0) {
                return left;
            }
            // Search right
            int rightIndex = Math.max(midIndex + 1, midValue);
            return helper(rightIndex, end, inputs);
        }
    }