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 :



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                        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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