2860. Sum of integers on the interval

Find the sum of all integers from a to b.

Input. Two integers а and b, no more than 2 * 10⁹ by absolute value.

Output. Print the sum of all integers from a to b.

Sample input	Sample output
2 5	14

SOLUTION

elementary evaluations

Algorithm analysis

If we calculate the result with the loop, in the worst case (for a = -2 * 10⁹, b = 2 * 10⁹) we need to make up to 4 * 10⁹ iterations, this gives Time Limit. Let’s use the formula of the sum of an arithmetic progression. The first term equals to a, the last equas to b, and number of terms is b – a + 1. Then the required sum is

It should also be noted that the received sum could not fit in an int. Therefore, when calculating you should use 64-bit integer type long long.

Algorithm realization

Read the input data. Calculate and print the answer.

scanf("%lld %lld",&a,&b);

res = (a + b) * (b - a + 1) / 2;

printf("%lld\n",res);

Java realization

import java.util.*;

public class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in);

long a = con.nextLong();

long b = con.nextLong();

long res = (a + b) * (b - a + 1) / 2;

System.out.println(res);

}

}

Python realization

a,b = map(int,input().split())

res = (a + b) * (b - a + 1) // 2

print (res)