Remove Sublist to Reach Equilibrium - Google Top Interview Questions
Problem Statement :
Given a list of integers nums and an integer k, you can remove any sublist at most once from the list. Return the length of the longest resulting list such that the amount of numbers strictly less than k and strictly larger than k is the same. Constraints n ≤ 100,000 where n is the length of nums Example 1 Input nums = [5, 9, 7, 8, 2, 4] k = 5 Output 5 Explanation If we remove the sublist [8] then we'd get [5, 9, 7, 2, 4] and there's two numbers [2, 4] that's smaller than 5 and two numbers [9, 7] larger than 5. Example 2 Input nums = [1, 2, 3] k = 4 Output 0 Explanation We need to remove the whole sublist to have the same amount of numbers greater than 4 as amount of numbers less than 4.
Solution :
Solution in C++ :
int find_sublist(vector<int>& nums, int target) {
if (target == 0) return 0;
// TO find sublist having sum, sum[i,j]=sum[0,j]-sum[0,i-1].
// so do prefix sum and keep index of all the sum appeared till now,
unordered_map<int, int> mp;
int pfsum = 0;
int len = INT_MAX;
for (int i = 0; i < nums.size(); i++) {
pfsum += nums[i];
if (pfsum == target) len = min(len, i + 1);
if (mp.count(pfsum - target) != 0) {
len = min(i - mp[pfsum - target], len);
}
mp[pfsum] = i;
}
return len;
}
int solve(vector<int>& nums, int k) {
// U need to find shortest sublist having sum=rem.
int sum = 0;
for (int i = 0; i < nums.size(); i++) {
if (nums[i] > k)
sum += 1, nums[i] = 1;
else if (nums[i] < k)
sum -= 1, nums[i] = -1;
else
nums[i] = 0;
}
int dlen = find_sublist(nums, sum);
return nums.size() - dlen;
}
Solution in Java :
import java.util.*;
class Solution {
public int solve(int[] nums, int k) {
if (nums == null || nums.length == 0)
return 0;
for (int i = 0; i < nums.length; i++) {
if (nums[i] > k)
nums[i] = 1;
else if (nums[i] < k)
nums[i] = -1;
else
nums[i] = 0;
}
int sum = 0;
int[] prefixSum = new int[nums.length + 1];
for (int i = 1; i < prefixSum.length; i++) {
prefixSum[i] = prefixSum[i - 1] + nums[i - 1];
sum += nums[i - 1];
}
if (sum == 0)
return nums.length;
Map<Integer, Integer> map = new HashMap();
int len = nums.length;
for (int i = 0; i < prefixSum.length; i++) {
int curr_sum = prefixSum[i];
int target = curr_sum - sum;
if (map.containsKey(target)) {
len = Math.min(len, i - map.get(target));
}
map.put(curr_sum, i);
}
return nums.length - len;
}
}
Solution in Python :
from itertools import accumulate
class Solution:
def solve(self, A, K):
N = len(A)
A = [(x > K) - (x < K) for x in A]
S = sum(A)
ans = 0
last = {0: 0}
for j, psum in enumerate(accumulate(A, initial=0)):
if (i := last.get(psum - S, -1)) >= 0:
ans = max(ans, N - (j - i))
last[psum] = j
return ans
View More Similar Problems
Fibonacci Numbers Tree
Shashank loves trees and math. He has a rooted tree, T , consisting of N nodes uniquely labeled with integers in the inclusive range [1 , N ]. The node labeled as 1 is the root node of tree , and each node in is associated with some positive integer value (all values are initially ). Let's define Fk as the Kth Fibonacci number. Shashank wants to perform 22 types of operations over his tree, T
View Solution →Pair Sums
Given an array, we define its value to be the value obtained by following these instructions: Write down all pairs of numbers from this array. Compute the product of each pair. Find the sum of all the products. For example, for a given array, for a given array [7,2 ,-1 ,2 ] Note that ( 7 , 2 ) is listed twice, one for each occurrence of 2. Given an array of integers, find the largest v
View Solution →Lazy White Falcon
White Falcon just solved the data structure problem below using heavy-light decomposition. Can you help her find a new solution that doesn't require implementing any fancy techniques? There are 2 types of query operations that can be performed on a tree: 1 u x: Assign x as the value of node u. 2 u v: Print the sum of the node values in the unique path from node u to node v. Given a tree wi
View Solution →Ticket to Ride
Simon received the board game Ticket to Ride as a birthday present. After playing it with his friends, he decides to come up with a strategy for the game. There are n cities on the map and n - 1 road plans. Each road plan consists of the following: Two cities which can be directly connected by a road. The length of the proposed road. The entire road plan is designed in such a way that if o
View Solution →Heavy Light White Falcon
Our lazy white falcon finally decided to learn heavy-light decomposition. Her teacher gave an assignment for her to practice this new technique. Please help her by solving this problem. You are given a tree with N nodes and each node's value is initially 0. The problem asks you to operate the following two types of queries: "1 u x" assign x to the value of the node . "2 u v" print the maxim
View Solution →Number Game on a Tree
Andy and Lily love playing games with numbers and trees. Today they have a tree consisting of n nodes and n -1 edges. Each edge i has an integer weight, wi. Before the game starts, Andy chooses an unordered pair of distinct nodes, ( u , v ), and uses all the edge weights present on the unique path from node u to node v to construct a list of numbers. For example, in the diagram below, Andy
View Solution →