# Saitama’s Punch ### CONCEPTS USED:

Basic Mathematics

Hard

### PROBLEM STATEMENT`(`SIMPLIFIED`)`:

Given an array `A` which contains the sorted time points at which a hero named `Saitama` punches and paralyzes his enemy `Garou`, also given time interval `K` for the time, his enemy is paralyzed with each punch. Your task is to determine the total time for which `Garou` is paralyzed.

See original problem statement here

#### For Example:

``````Input :

N = 3, K = 2
A = [1 4 6]

Output : 6

Explanation :

1st punch on time point = 1, paralyzes him for 2 units of time [1 to 2]

2nd punch on time point = 4, paralyzes him for another 2 units of time [4 to 5]

3rd punch on time point = 6, paralyzes him for another 2 units of time [6 to 7]

Therefore, Saitama paralyzes Garou for 6 units of time.``````
``````Input :

N = 3, K = 2
A = [1 2 6]

Output : 5

Explanation :

1st punch on time point = 1, paralyzes him for 2 units of time [1 to 2].

2nd punch on time point = 2, Garou is already paralyzed at this point of time, so he was only paralyzed for 2 - 1 = 1 unit of time with the first punch, now again he is paralyzed for another 2 units of time [2 to 3].

3rd punch on time point = 6, paralyzes him for another 2 units of time [6 to 7].

Therefore, Saitama paralyzes Garou for 5 units of time.``````

### SOLVING APPROACH:

1. Start by adding `K` to the first time point in the array and store it in `palalyze_till` variable, this will give us the time point till when the `Garou` is paralyzed by the first punch of `Saitama`.

2. Now traverse the array starting from the second element and check whether the calculated `paralyze_till` is less than or equal to current element, `A[i]` of the array. This implies `Garou` was paralyzed for `K` units of time and now is awake. If `Yes`, increment the value of `total_time` by `K` and update `paralyze_till = A[i] + K`.

3. If `paralyze_till` is greater than current element, `A[i]`. This implies that `Garou` is still paralyzed and again we need to paralyze it for `K` units of time. So we add the time for which it was paralyzed till now and move ahead, updating `total_time = A[i] - A[i]` and `paralyze_till = A[i] + K`.

4. Finally add the time for which `Garou` was paralyzed by the last punch i.e. `K` units of time.

### SOLUTIONS:

```#include

int main()
{
int t; scanf("%d", &t);
while(t--){
int n, k; scanf("%d %d", &n, &k);
int arr[n];
for(int i=0; i

```
```#include
using namespace std;

int main()
{
int t; cin>>t;
while(t--){
int n, k; cin>>n>>k;
int arr[n];
for(int i=0; i>arr[i];

long long sum = 0;
long long curr_time = arr + k;
for(int i=1; i
```
```import java.util.*;
import java.io.*;

public class Main {
public static void main(String args[]) throws IOException {

Scanner sc = new Scanner(System.in);
int t = sc.nextInt();

while(t --> 0){
int n = sc.nextInt();
int k = sc.nextInt();
int arr[] = new int[n];

for(int i=0; i
```
```n, k = map(int,input().split())
arr = list(map(int,input().split()))
sum = 0
curr_time = arr + k

for i in range(1, n):

if curr_time <= arr[i]:
sum += k
else:
sum += arr[i] - arr[i - 1]
curr_time = arr[i] + k

sum += k

print(sum)
```

Space Complexity: O(1)

[forminator_quiz id="558"]

This article tried to discuss the concept of Basic Mathematics. Hope this blog helps you understand and solve the problem. To practice more problems on Basic Mathematics you can check out MYCODE | Competitive Programming.