# Find an integer array corresponding to the string specifying increase-decrease transitions

Given a string of size 'n' where each character can be either 'd' or 'i' and nothing else. If character 'd' denotes decrease in value and character 'i' denotes increase in value then how can we build an integer array of size 'n+1' created by using numbers from 1 to 'n+1' such that this array holds one to one correspondence with the input string.

For example, if the given string is "di" then because string size is 2, we need to use numbers 1,2,3 and build integer array [3,1,2] where first pair formed by first two elements 3,1 corresponds to character 'd' since there is decrease in value from 3 to 1 and then second pair 1,2 corresponds to character 'i' - increase in value from 1 to 2. Another way to build this could have been [2,1,3]. Now pair (2,1) corresponds to 'd' and second pair (1,3) corresponds to character 'i'.

When we consider 'n' such pairs formed out of adjacent elements from 'n+1' elements, 'n' pairs should correspond to 'n' characters of input string in the same sequence.

Another example could be for input string 'ddddi', one of the outputs could be [6,4,3,2,1,5].

Write a program to create any one of the correct output integer array given an input string having characters 'd' and 'i'.

## Algorithm/Insights

The idea is to use the higher numbers for satisfying 'i' transitions and remaining numbers for 'd' transitions.

Let's look at an example. Say we have a string consisting of only 2 'i's and 3 'd's - 'ddidi'
Then out of numbers 1,2,3,4,5,6 we reserve two higher numbers 6 and 5 for 'i' transitions because no matter what the current number we can always satisfy 'i' transitions using these higher numbers. The number next to reserved numbers for 'i' transitions is put at the 0th position. In this case, number next to 6 and 5 would be 4 hence we make output = 4. Note that out of 1,2,3,4,5,6 we have marked top 2 numbers that is 6 and 5 for 'i' transitions and next number to them that is 4 as a start value for output array - therefore remaining numbers(that is 3,2,1) would be used for 'd' transitions. Now we mark lowest number from the numbers reserved for 'i' transitions as increaseValue - in this case increaseValue would be 5. Similarly, we mark highest number from numbers that are going to used for 'd' transitions as decreaseValue - in this case decreaseValue would be 3.

Now the algorithm is very simple. Whenever we see a 'd' at string[i], we just put decreaseValue at output[i+1] and decrement decreaseValue by 1. And whenever we see a 'i' at string[i], we just put increaseValue at output[i+1] and increment increaseValue by 1. Output is already initilaized to the number next to numbers reserved for 'i' and 'd' transitions.

In this case, for string 'ddidi' we will be using numbers 1,2,3,4,5,6
Numbers reserved for 'i' - 6,5
StartValue to be put at output - 4
Numbers reserved for 'd' - 3,2,1
increaseValue marked at - 5
decreaseValue marked at - 3

output = 4
output = 3, decreaseValue updated to 2 (since 0th character for input is 'd')
output = 2, decreaseValue updated to 1 (first character is 'd')
output = 5, increaseValue updated to 6 (second character is 'i')
output = 1, decreaseValue updated to 0 (third character is 'd')
output = 6, increaseValue updated to 7 (fourth character is 'i')

Time taken by this algorithm is O(n).

## Code Snippet

```
package com.ideserve.questions.nilesh;

/**
* <b>IDeserve <br>
* Given an input string, finds corresponding decrease-increase sequence in O(n).
* @author Nilesh
*/

public class DecreaseIncreaseSequence
{

public void createSequence(String input, int[] output)
{
if (input.length() == 0)
{
return;
}

int iCount = 0;
// count the number of increases required
for (int i = 0;  i < input.length(); i++)
{
if (input.charAt(i) == 'i')
{
iCount += 1;
}
}

// now in numbers 1 to n+1 reserve 'iCount' higher numbers to be used for 'i'
// for example if there are 3 'i's in 6 character string,
// then reserve numbers 7,6 and 5 for 'i'

int n = input.length();

// if we see a 'i', put 'increaseValue' in the output array and increment 'increaseValue' by 1
int increaseValue = n + 2 - iCount;

// keep startValue fixed
int startValue = increaseValue - 1;

// if we see a 'd', put 'decreaseValue' in the output array and decrement 'decreaseValue' by 1
int decreaseValue = startValue - 1;

output = startValue;
for (int i = 0;  i < input.length(); i++)
{
if (input.charAt(i) == 'i')
{
output[i+1] = increaseValue;
increaseValue += 1;
}

if (input.charAt(i) == 'd')
{
output[i+1] = decreaseValue;
decreaseValue -= 1;
}
}
}

public static void main(String[] args)
{
DecreaseIncreaseSequence solution = new DecreaseIncreaseSequence();

String input = "idddii";
int[] output = new int[input.length() + 1];

solution.createSequence(input, output);

System.out.print("Output sequence corresponding to input string: ");
for (int i = 0; i < output.length; i++)
{
System.out.print(output[i] + ", ");
}
}
}
```

## Order of the Algorithm

Time Complexity is O(n)
Space Complexity is O(1)