PROBLEM LINK:

http://www.codechef.com/ICL2015/problems/ACMICL5

Author:

Jaiwant Rawat

Tester:

Ankit Sultana

DIFFICULTY:

HARD

PREREQUISITES:

Dynamic Programming

EXPLANATION:

For solving it we will keep track of state as ( a , b ). In the state ( a , b ) 1) a - denotes the sum 2) b - denotes the sum formed from only using the first b numbers from the interval [ k1 , k2 ] where k1 = minimum value of the start of all the intervals k2 = maximum value of the end of all the intervals

Example -

Taking the test case given in question 2 0 2 2 5 1 2

Here we have two intervals [ 0 , 2 ] & [ 2 , 5 ] and we have to find the sum from 1 to 3 . so following the above approach we have k1 = 0 ( min of ( 0 , 2 ) ) k2 = 5 ( max of ( 2 , 5 ) ) Now all the values that i can take will lie in this interval only and how many times i can take them is equal to the number of intervals in which that value lies . Now according to the question k1 minimum value can be 0 and k2 maximum value can be 500 so i can have only 501 distinct numbers for consideration in worst case Now the state is ( a , b ) where a is one of the number belonging to the interval [ N , N + x ] b is one of the number belonging to interval in [ k1 , k2 ]

Now the transition of the states will be like ( a , b + 1 ) -> ( a , b ) if i am not using the b + 1 in my sum or ( a , b + 1 ) -> ( y , b ) where y be one of depending on how many b i am considering for the sum .