# Split List - Microsoft Top Interview Questions

### Problem Statement :

```Given a list of integers nums, return whether you can partition the list into two non-empty sublists such that every number in the left sublist is strictly less than every number in the right sublist.

Constraints

n ≤ 100,000 where n is the length of nums.

Example 1

Input

nums = [5, 3, 2, 7, 9]

Output

True

Explanation

We can split the list into left = [5, 3, 2] and right = [7, 9]```

### Solution :

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

bool solve(vector<int>& nums) {
if (nums.size() <= 1) return false;

int max = nums[0];      // max seen so far
int leftMax = nums[0];  // max in the left sublist
int leftSize = 1;

for (int i = 1; i < nums.size(); i++) {
// update max seen so far
max = nums[i] > max ? nums[i] : max;

if (nums[i] <= leftMax) {
// expand left
leftSize = i + 1;
leftMax = max;
}
}

// true if leftSize is not numsSize
return leftSize < nums.size();
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public boolean solve(int[] nums) {
int rmin[] = new int[nums.length];
rmin[nums.length - 1] = nums[nums.length - 1];
for (int i = nums.length - 2; i > -1; i--) {
if (nums[i] < rmin[i + 1])
rmin[i] = nums[i];
else
rmin[i] = rmin[i + 1];
}
int max = 0;
for (int i = 0; i < rmin.length - 1; i++) {
if (max < nums[i])
max = nums[i];
if (max < rmin[i + 1])
return true;
}
return false;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, nums):
n = len(nums)

right_mins = [math.inf] * n
for i, num in enumerate(reversed(nums)):
right_mins[~i] = min(num, right_mins[~i + 1])

left_max = -math.inf
for left_num, right_min in zip(nums, right_mins[1:]):
left_max = max(left_max, left_num)
if left_max < right_min:
return True

return False```
```

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