## Directi Interview Question Software Engineer / Developers

- 0of 0 votes
He gave me an array of Integers, each integer allows me to make at max its value jumps. If i am at zero, i'm stuck i cannot move forword. He asked me to find,

1). If the last index was reachable from the first index.

2). Minimum number of jumps required to reach the last index, given any index as the starting index.

3). Total number of ways one can reach the last index.

I was asked to write a code for this.

ex: 1 3 5 8 9 2 6 7 6 8 9

initially at one i can make only one jump to 3, from 3 i can jump either 1 step reaching 5, or 2 steps reaching 8, or 3 steps reaching 9. Carrying on in the same way till i can hit the last index.

Simple code to find out if its reachable :

#include<stdio.h>

int jump(int a,int b)

{

return a+b;

}

void Func(int n,int a[n],int start,int last)

{

int i,k=0,temp;

while(k<n)

{

for(i=1;i<=a[k];i++)

{

temp=jump(k,i);

if(temp==last)

{

printf("Reachable\n");

return;

}

}

k++;

}

printf("Not reachable\n");

return;

}

main()

{

int n,i;

scanf("%d",&n);

int a[n];

for(i=0;i<n;i++)

scanf("%d",&a[i]);

Func(n,a,0,n-1);

}

Backtracking + Recursion :

1). If the last index was reachable from the first index.

n=1

Take jumps of n, if current number is 0, backtrack and jump n+1 if possible, else backtrack. If you reach the end, then print reachable.

2). Minimum number of jumps required to reach the last index, given any index as the starting index.

n = biggest possible step

Take jumps of n, if current number is 0, backtrack and jump n-1 if possible, else backtrack. Keep a count of jumps.

3). Total number of ways one can reach the last index.

Aha ! variation of (1), when you reach end, do not exit from the program, rather increase the count. so you will get the count of all possible ways to reach the end.

i think this code is working..

#include<stdio.h>

int n,s[100];

int min(int a,int b)

{

return(a<b?a:b);

}

int fun(int i,int count)

{

int j,max1=n+1;

if(i>=n)

{

return max1;

}

else

{

if(i==n-1)

{

return count;

}

for(j=1;j<=s[i];j++)

{

max1=min(max1,fun(i+j,count+1));

}

}

return max1;

}

main()

{

int i;

scanf("%d",&n);

for(i=0;i<n;i++)

{

scanf("%d",&s[i]);

}

if((i=fun(0,0))==n+1)

{

printf("\ncould not reachable");

}

else

{

printf("\n\n\nreachable in %d steps ",i);

}

}

Using BFS :

```
private static int BFS(Queue<Node> q) {
while(!q.isEmpty()) {
Node node = q.remove();
int curInd = node.getIndex();
int curJump = node.getJump();
if(curInd == N)
return curJump;
int value = node.getValue();
for(int i = 1; i <= value; ++i) {
int index = curInd+i;
int jump = curJump+1;
if(isSafe(nodes, index)) {
nodes[index].setColor(COLOR.GREY);
nodes[index].setJump(jump);
nodes[index].setParent(curInd);
q.add(nodes[index]);
}
}
node.setColor(COLOR.BLACK);
}
return -1;
}
private static int getMinJump(Node[] nodes, int start, int end) {
Queue<Node> q = new LinkedList<Node>();
nodes[start].setColor(COLOR.GREY);
nodes[start].setJump(0);
nodes[start].setParent(-1);
q.add(nodes[start]);
return BFS(q);
}
private static boolean isSafe(Node[] nodes, int index) {
return index >= 1 && index <= N && nodes[index].getColor() == COLOR.WHITE;
}
```

You can approach the problem in the following way -

- Anonymous on September 21, 2010 Edit | Flag ReplyConstruct a Directed Graph where max No of jumps will be the no of leaving edges from that specific node.After constructing the Graph do a BFS tree traversal,u will get the min path and to find all possible path modify the standard BFS algo....