032. Prison Break

Codeforces

IDCF10269032

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Unfortunately, you have been sent to prison because you solved too many problems at CodeQuest 2021. Now, you're trying to break out. Your cell has a combination lock with $n$ dials. You're planning to try all of the possible combinations of the lock, and you want to know how many possible combinations the lock has. The first line of input contains a positive integer $n$: the number of dials on the lock. The next $n$ lines each contain two space-separated integers: the lower and upper limits of each lock dial. For example, if the lower and upper limits were $3$ and $7$, respectively, then the lock dial could turn to 3, 4, 5, 6, or 7. Output a single integer $c$: the total number of possible lock combinations. ## Input The first line of input contains a positive integer $n$: the number of dials on the lock. The next $n$ lines each contain two space-separated integers: the lower and upper limits of each lock dial. For example, if the lower and upper limits were $3$ and $7$, respectively, then the lock dial could turn to 3, 4, 5, 6, or 7. ## Output Output a single integer $c$: the total number of possible lock combinations. [samples]

**Definitions** Let $ n \in \mathbb{Z}^+ $ be the number of dials. For each dial $ i \in \{1, \dots, n\} $, let $ [l_i, u_i] \subseteq \mathbb{Z} $ denote the range of possible values, where $ l_i $ and $ u_i $ are the lower and upper limits, respectively. **Constraints** For each $ i \in \{1, \dots, n\} $: $ l_i \leq u_i $ **Objective** Compute the total number of combinations: $$ c = \prod_{i=1}^{n} (u_i - l_i + 1) $$

API Response (JSON)

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