# Target Number with Operations - Google Top Interview Questions

### Problem Statement :

```Given positive integers start and end (start < end), return the minimum number of operations needed to convert start to end using these operations:

Increment by 1

Multiply by 2

Constraints

start < end < 2 ** 31

Example 1

Input

start = 2

end = 9

Output

3

Explanation

We can multiply 2 to get 4, and then again to get 8, then add 1 to get 9.```

### Solution :

```                        ```Solution in C++ :

int solve(int start, int end) {
int ops = 0;
for (; start * 2 <= end; ops++) {
if (end % 2)
end--;
else
end /= 2;
}
return ops + end - start;
}```
```

```                        ```Solution in Java :

class Solution {
public int solve(int start, int end) {
int ops = 0;
while (end / 2 >= start) {
ops += 1 + (end % 2);
end /= 2;
}
return ops + end - start;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, start, end):
c = 0
if start <= 0:
return None
while end != start:
if end & 1:  # Odd number
end -= 1
else:
res = end // 2
if res < start:
c += end - start
return c
end = res
c += 1
return c```
```

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