[Solution] Two Trains CodeChef Solution | Solution CodeChef

Problem

There are $2$ trains $A$ and $B$ and $N$ stations in a line from $1$ to $N$ in order. There is also an array $P$ of length $N-1$ such that $P_i$ $(1\le i \lt N)$ denotes the amount of time any train takes to go from the $i$-th station to the $(i+1)$-th station.

Initially, both trains are at station $1$. Train $A$ departs from station $1$ and stops directly at station $N$. For safety purposes, it is maintained that train $B$ cannot depart from station $i$ unless train $A$ has already reached station $(i+1)$ $(1 \le i \lt N)$.

Find the minimum time after which train $B$ reaches station $N$, once train $A$ departs from station $1$.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of two lines of input.
• The first line of each test case contains an integer $N$, denoting number of stations.
• The next line contains $N-1$ space-separated integers, $P_1,P_2,\ldots ,P_{N-1}$.

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Output Format

For each test case, output on a new line the minimum time after which train $B$ reaches station $N$.

Explanation:

Test case $1$: $A$ reaches station $2$ at $t=4$ and at this time $B$ departs from station $1$ and reaches station $2$ at $t=4+4=8$.

Test case $1$: Following is the timeline of two trains-

• At $t=3$, $A$ reaches station $2$ and $B$ departs from station $1$.
• At $t=6$, $B$ reaches station $2$ but $A$ has not yet reached station $3$, so train $B$ will wait at station $2$.
• At $t=8$, $A$ reaches station $3$ and $B$ departs from station $2$.
• At $t=8+5=13$, train $B$ reaches station $3$.