Coding Interview Questions: No. 42 - Three Increasing Elements in an Array


Problem: Given an array of integers A, please find three indexes i, j, k, such that i<j<k and A[i]<A[j]<A[k].
Solution 1: O(n) time efficiency with O(n) space consumption
we could construct an auxiliary array B. The element B[j] stores the index of the smallest element of elements from the leftmost element to A[j]. The array B can be constructed based on elements in A from left to right.
Similarly, we could also construct another auxiliary array C. The element C[j] stores the index of the greatest element of elements from the rightmost element to A[j]. The array C can be constructed based on elements in A from right to left.
When an element A[j] is scanned, the index j is compared with B[j] and C[j]. if B[j]<j (there is a smaller element on the left side) and j<C[j] (there is a greater element on the right side), three increasing elements have been found.
void increasingIndex_1(int* nums, int length, int* i, int* j, int* k)
{
    if(nums == NULL || length <= 0 || i == NULL || j == NULL || k == NULL)
        return;

    int* minIndex = new int[length];
    int index = 0;
    minIndex[0] = 0;
    int t;
    for(t = 1; t < length; ++t)
    {
        if(nums[t] < nums[index])
            index = t;
        minIndex[t] = index;
    }

    int* maxIndex = new int[length];
    index = length - 1;
    for(t = length - 1; t >= 0; --t)
    {
        if(nums[t] > nums[index])
            index = t;
        maxIndex[t] = index;
    }

    for(t = 1; t < length - 1; ++t)
    {
        if(minIndex[t] < t && maxIndex[t] > t)
            break;
    }
    if(t < length - 1)
    {
        *i = minIndex[t];
        *j = t;
        *k = maxIndex[t];
    }
    else
    {
        *i = *j = *k = -1;
    }

    delete[] minIndex;
    delete[] maxIndex;
}
Solution 2: O(n) time efficiency with O(1) space consumption
The strategy of this solution is to store as less value to A[i] and A[j] as possible, in order to enlarge the value range for steps in the future.

void increasingIndex_2(int* nums, int length, int* i, int* j, int* k)
{
    if(nums == NULL || length <= 0 || i == NULL || j == NULL || k == NULL)
        return;

    *i = *j = *k = -1;
    int backup = -1;

    int index;
    for(index = 0; index < length; ++index)
    {
        if(*i == -1)
        {
            *i = index;
        }
        else if(*j == -1)
        {
            if(nums[index] > nums[*i])
                *j = index;
            else
                *i = index;
        }
        else if(nums[index] > nums[*j])
        {
            *k = index;
            break;
        }
        else if(nums[index] < nums[*j])
        {
            if(backup != -1)
            {
                if(nums[index] > nums[backup])
                {
                    *i = backup;
                    *j = index;
                    backup = -1;
                }
                else if (nums[index] < nums[backup])
                {
                    backup = index;
                }
            }
            else if(nums[index] < nums[*j])
                backup = index;
        }
    }
    if(index == length)
        *i = *j = *k = -1;
}
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