Question

I am stuck in one interview question.. The question is,

*given two arrays A and B. A has integers unsorted. B has the same
length as A and its values are in the
set {-1,0,1}

you have to return an array C with the
following processing on A.

if B[i] has 0 then C[i] must have A[i]
if B[i] has -1 then A[i] must be in C
within the sub array C[0] – C[i-1] ie.
left subarray
if B[i] has 1 then A[i]
must be in C within the sub array
C[i+1] – C[length(A)] ie right
subarray.

if no such solution exists then
printf(“no solution”);*

I applied following logics:-

int indMinus1 = n-1;
int indPlus1 = 0;

//while(indPlus1 < n && indMinus1 > 0)
while(indPlus1 < indMinus1)
{
    while(b[indMinus1] != -1)   {
        if(b[indMinus1] == 0)
            c[indMinus1] = a[indMinus1];
        indMinus1--;
    }
    while(b[indPlus1] != +1)    {
        if(b[indPlus1] == 0)
            c[indPlus1] = a[indPlus1];
        indPlus1++;
    }

    c[indMinus1] = a[indPlus1];
    c[indPlus1] = a[indMinus1];
    b[indMinus1] = 0;
    b[indPlus1] = 0;
    indMinus1--;
    indPlus1++;
}

But this will not going to work,, for some cases like {1,2,3} >> {1,-1,-1}… One output is possible i.e. {2,3,1};

Please help…. does their any algorithm technique available for this problem?

Correct Solution Code

int arrange(int a[], int b[], int c[], int n)
{

for (int i = 0; i < n; ++i) {
    if(b[i] == 0)
        c[i] = a[i];
}

int ci = 0;
for (int i = 0; i < n; ++i) {
    if(b[i] == -1)  {
        while(c[ci] != 0 && ci < i)
            ci ++;
        if(c[ci] != 0 || ci >= i)
            return -1;
        c[ci] = a[i];
        ci++;
    }
}

for (int i = 0; i < n; ++i) {
    if(b[i] == 1)   {
        while(c[ci] != 0 && ci < n)
            ci ++;
        if(c[ci] != 0 || ci <= i)
            return -1;
        c[ci] = a[i];
        ci++;
    }
    }
    return 0;
}

Answer 1

I suggest the following algorithm:
1. Initially consider all C[ i ] as empty nests.
2. For each i where B[ i ] = 0 we put C[ i ] = A[ i ]
3. Go through array from left to right, and for each i where B[ i ] = -1 put
C[ j ] = A[ i ], where 0 <= j < i is the smallest index for which C[ j ] is still empty. If no such index exists, the answer is impossible.
4. Go through array from right to left, and for each i where B[ i ] = 1 put
C[ j ] = A[ i ], where i < j < n is the greatest index for which C[ j ] is still empty. If no such index exists, the answer is impossible.

Why do we put A[ i ] to the leftmost position in step 2 ? Well, we know that we must put it to some position j < i. On the other hand, putting it leftmost will increase our changes to not get stucked in step 3. See this example for illustration:

A: [ 1, 2, 3 ]
B: [ 1, 1,-1 ]

Initially C is empty: C:[ _, _, _ ]
We have no 0-s, so let’s pass to step 2.
We have to choose whether to place element A[ 2 ] to C[ 0 ] or to C[ 1 ].
If we place it not leftmost, we will get the following situation:
C: [ _, 3, _ ]
And… Oops, we are unable to arrange elements A[ 0 ] and A[ 1 ] due to insufficient place 🙁
But, if we put A[ 2 ] leftmost, we will get
C: [ 3, _, _ ],
And it is pretty possible to finish the algorithm with
C: [ 3, 1, 2 ] 🙂

Complexity:
What we do is pass three times along the array, so the complexity is O(3n) = O(n) – linear.

Further example:

A: [ 1, 2, 3 ]
B: [ 1, -1, -1 ]

Let’s go through the algorithm step by step:
1. C: [ _, _, _ ]
2. Empty, because no 0-s in B
3. Putting A[ 1 ] and A[ 2 ] to leftmost empty positions:

C: [ 2, 3, _ ]

4. Putting A[ 0 ] to the rightmost free (in this example the only one) free position:

C: [ 2, 3, 1 ]

Which is the answer.

Source code:

#include <iostream>
#include <string>
#include <vector>

using namespace std;


vector< int > a;
vector< int > b;
vector< int > c;
int n;

bool solve ()
{
    int i;
    for( i = 0; i < n; ++i )
        c[ i ] = -1;
    for( i = 0; i < n; ++i )
        if( b[ i ] == 0 )
            c[ i ] = a[ i ];
    int leftmost = 0;
    for( i = 0; i < n; ++i )
        if( b[ i ] == -1 )
        {
            for( ; leftmost < i && c[ leftmost ] != -1; ++leftmost ); // finding the leftmost free cell
            if( leftmost >= i )
                return false; // not found
            c[ leftmost++ ] = a[ i ];
        }
    int rightmost = n - 1;
    for( i = n - 1; i >= 0; --i )
        if( b[ i ] == 1 )
        {
            for( ; rightmost > i && c[ rightmost ] != -1; --rightmost ); // finding the rightmost free cell
            if( rightmost <= i )
                return false; // not found;
            c[ rightmost-- ] = a[ i ];
        }
    return true;
}


int main ()
{
    cin >> n;
    a.resize(n);
    b.resize(n);
    c.resize(n);
    int i;
    for( i = 0; i < n; ++i )
        cin >> a[ i ];
    for( i = 0; i < n; ++i )
        cin >> b[ i ];
    if( !solve() )
        cout << "Impossible";
    else
        for( i = 0; i < n; ++i )
            cout << c[ i ] << ' ';
    cout << endl;
    return 0;
}