# The Maximum Subarray

### Problem Statement :

```We define subsequence as any subset of an array. We define a subarray as a contiguous subsequence in an array.

Given an array, find the maximum possible sum among:

1.all nonempty subarrays.
2.all nonempty subsequences.
Print the two values as space-separated integers on one line.

Note that empty subarrays/subsequences should not be considered.

Example
arr = [-1, 2, 3, -4, 5,10]
The maximum subarray sum is comprised of elements at inidices [1-5]. Their sum is 2 + 3 + -4 +5 + 10 = 16. The maximum subsequence sum is comprised of elements at indices [1,2,4,5] and their sum is 2 + 3 + 5 + 10 = 20.

Function Description

Complete the maxSubarray function in the editor below.

maxSubarray has the following parameter(s):

int arr[n]: an array of integers
Returns

int[2]: the maximum subarray and subsequence sums
Input Format

The first line of input contains a single integer t, the number of test cases.

The first line of each test case contains na single integer n.
The second line contains  space-separated integers arr[i] where 0 <= i < n.

Constraints

1 <= t <= 10
1 <= n <= 10^5
-10^4 <= arr[i] <= 10^4
The subarray and subsequences you consider should have at least one element.```

### Solution :

```                            ```Solution in C :

In C++ :

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

int main()
{
/* Enter your code here. Read input from STDIN. Print output to STDOUT */
int loop;
cin >> loop;
while (loop--) {
int size;
cin >> size;
vector<int> data(size, 0);
for (int i = 0; i < size; ++i) {
cin >> data[i];
}

vector<int> dp(size, 0);
int big = 0;
int sum = 0;
int start = -1;
for (int i = 0; i < size; i++) {
int val = sum + data[i];

if (val > 0) {
if (sum == 0) {
start = i;
}
sum = val;
} else {
sum = 0;
}

if (sum > big) {
big = sum;
}
}

if (start == -1) {
cout << data[0] << " ";
} else {
cout << big << " ";
}

sum = 0;
start = -1;
for (int i = 0; i < size; ++i) {
if (data[i] > 0) {
start = i;
sum += data[i];
}
}

if (start == -1) {
cout << data[0] << endl;
} else {
cout << sum << endl;
}
}
return 0;
}

In Java :

import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {

public static void main(String[] args) {
Scanner myScan = new Scanner(System.in);
int T = myScan.nextInt();
while(T--!=0){
int N = myScan.nextInt();
int[] arr = new int[N];
for(int i=0; i<N; i++){
arr[i]=myScan.nextInt();
}
int curr_sum=0;
int best_sum=0;
int non_cont_sum=0;
for(int j=0; j<N; j++){
curr_sum += arr[j];
if(curr_sum>0){
if(curr_sum>best_sum){
best_sum=curr_sum;
}
}else{
curr_sum=0;
}
if(arr[j]>0){
non_cont_sum +=arr[j];
}
}
if(best_sum ==0 && non_cont_sum==0){
int max = arr[0];
for(int l=1; l<N; l++){
if(arr[l]>max){
max=arr[l];
}
}
best_sum=max;
non_cont_sum=max;
}
System.out.print(best_sum+" "+non_cont_sum);
System.out.println();
}
}
}

In C :

#include <stdio.h>
#include <stdlib.h>
long long dp[100000];

int main(){
long long a,T,N,ans1,ans2,max,i;
scanf("%lld",&T);
while(T--){
ans1=ans2=0;
max=-999999;
scanf("%lld",&N);
for(i=0;i<N;i++){
scanf("%lld",&a);
if(a>max)
max=a;
if(a>0)
ans2+=a;
dp[i]=a;
if(i && dp[i-1]>0)
dp[i]+=dp[i-1];
if(dp[i]>ans1)
ans1=dp[i];
}
if(ans1==0)
ans1=max;
if(ans2==0)
ans2=max;
printf("%lld %lld\n",ans1,ans2);
}
return 0;
}

In Pyhton3 :

test = int(input())
while test:
test -= 1
input()
num_list = [int(x) for x in input().split()]
max_sum = 0
tmp_sum = 0
max_non_contg = 0
flg = False
mx = max(num_list)
if mx < 0:
print(str(mx) + " " + str(mx))
continue
for i in range(len(num_list)):
if tmp_sum < 0:
tmp_sum = 0
tmp_sum += num_list[i]
if tmp_sum > max_sum:
max_sum = tmp_sum
if num_list[i] > 0:
max_non_contg += num_list[i]
print(str(max_sum) + " " + str(max_non_contg))```
```

## Balanced Brackets

A bracket is considered to be any one of the following characters: (, ), {, }, [, or ]. Two brackets are considered to be a matched pair if the an opening bracket (i.e., (, [, or {) occurs to the left of a closing bracket (i.e., ), ], or }) of the exact same type. There are three types of matched pairs of brackets: [], {}, and (). A matching pair of brackets is not balanced if the set of bra

## Equal Stacks

ou have three stacks of cylinders where each cylinder has the same diameter, but they may vary in height. You can change the height of a stack by removing and discarding its topmost cylinder any number of times. Find the maximum possible height of the stacks such that all of the stacks are exactly the same height. This means you must remove zero or more cylinders from the top of zero or more of

## Game of Two Stacks

Alexa has two stacks of non-negative integers, stack A = [a0, a1, . . . , an-1 ] and stack B = [b0, b1, . . . , b m-1] where index 0 denotes the top of the stack. Alexa challenges Nick to play the following game: In each move, Nick can remove one integer from the top of either stack A or stack B. Nick keeps a running sum of the integers he removes from the two stacks. Nick is disqualified f

## Largest Rectangle

Skyline Real Estate Developers is planning to demolish a number of old, unoccupied buildings and construct a shopping mall in their place. Your task is to find the largest solid area in which the mall can be constructed. There are a number of buildings in a certain two-dimensional landscape. Each building has a height, given by . If you join adjacent buildings, they will form a solid rectangle

## Simple Text Editor

In this challenge, you must implement a simple text editor. Initially, your editor contains an empty string, S. You must perform Q operations of the following 4 types: 1. append(W) - Append W string to the end of S. 2 . delete( k ) - Delete the last k characters of S. 3 .print( k ) - Print the kth character of S. 4 . undo( ) - Undo the last (not previously undone) operation of type 1 or 2,

## Poisonous Plants

There are a number of plants in a garden. Each of the plants has been treated with some amount of pesticide. After each day, if any plant has more pesticide than the plant on its left, being weaker than the left one, it dies. You are given the initial values of the pesticide in each of the plants. Determine the number of days after which no plant dies, i.e. the time after which there is no plan