# Print direction of moves such that you stay within the [-k, +k] boundary in C++

In this problem, we have to find a valid way to move positive direction or negative direction in such a way that we stay within a certain limit that is provided by the user.

Here, We are given a certain maximum limit K, which is the maximum value to which we can move and an array of n positive values to move. We have to return the sequence i.e. positive or negative directions to move so that it never crosses K value.

Let’s take an example to understand the topic better,

Input : K = 56 and the array is [25 , 14 , 31 , 16 , 5].
Output : positive positive negative positive positive.

## Explanation

First we will check if 0 + a[0] = 0+25 = 25 < 56 yes, then we will move in positive direction.

Now, we will check if 25 + a[1] = 25+14 = 39 < 56 yes, then we will move in positive direction.

Now, we will check if 29 + a[2] = 39+31 = 70 < 56 No, then we will check if 39 - a[2] = 39 - 31 = 8 > 0, then we will move in a negative direction.

we will check if 8 + a[3] = 8+16 = 24 < 56 yes, then we will move in positive direction.

we will check if 16 + a[4] = 16 + 5 = 21 < 56 yes, then we will move in positive direction.

So, now let’s create the logic to solve this problem. We have to check if moving in a positive direction will reach the limit or not. If no, then move in a positive direction. Otherwise, check if moving in a negative direction will reach the lower limit i.e. 0. If no, then move in a negative direction. If both are Yes then return not possible.

Based on this logic the algorithm that we have to follow for creating our code is −

## Algorithm

Initially set position to 0.
Step 1 : for i -> 0 to n , n is the length of array. Follow step 2 - 4.
Step 2 : if initial_postition + a[i] < K, initial_position + = a[i]. Print “POSITIVE”.
Step 3 : else if initial_postition - a[i] > 0, initial_position - = a[i]. Print “NEGATIVE”.
Step 4 : else , print “NO MORE VALID MOVES”.

## Example

Now, let's create a program to show the implementation of the algorithm to solve the problem,

Live Demo

#include <iostream>
using namespace std;
void StepsTaken(int a[], int n, int k){
string res = "";
int position = 0;
int steps = 1;
for (int i = 0; i < n; i++) {
if (position + a[i] <= k && position + a[i] >= (-k)) {
position += a[i];
cout<<"POSITIVE \t";
}
else if (position - a[i] >= -k && position - a[i] <= k) {
position -= a[i];
cout<<"NEGATIVE \t";
} else {
cout << -1;
return;
}
}
cout << res;
}
int main(){
int a[] = { 12 , 24 , 9 , 17 , 8};
int n = sizeof(a) / sizeof(a[0]);
int k = 40;
StepsTaken(a, n, k);
return 0;
}

## Output

POSITIVE    POSITIVE    NEGATIVE
NEGATIVE    POSITIVE