Hello,as I am beginner in dp ,I am facing problem with [this](http://lightoj.com/volume_showproblem.php?problem=1223) problem.Anyone help me understand the states and base cases for this problem?↵
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The statement:↵
When monkeys are given some fire-crackers, they have only thing in the mind — to blow things up. Small boxes were easy to blow up, and thus mailboxes became a popular target. Now, a small mailbox manufacturer is interested in how many fire-crackers his new mailbox prototype can withstand without exploding and has hired you to help him. He will provide you with k identical mailbox prototypes each fitting up to m fire-crackers. However, he is not sure of how many fire-crackers he needs to provide you with in order for you to be able to solve his problem, so he asks your help.↵
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The constraints are:↵
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1. If you blow up a mailbox, you can't use the mailbox again, so if you have only k = 1 mailboxes, you would have to start testing with 1 fire-cracker, then 2 fire-crackers, and so on until it finally exploded. In the worst case, that is if it does not blow up even when filled with m fire-crackers, you would need 1 + 2 + 3 + ... + m = m * (m + 1)/2 fire-crackers.↵
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2. If a mailbox can withstand x fire-crackers, it can also withstand x-1 fire-crackers.↵
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3. Upon an explosion, a mailbox is either totally destroyed (blown up) or unharmed, which means that it can be reused in another test explosion.↵
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Now the manufacturer wants you to find the maximum number of fire-crackers that his mailboxes can withstand. Before doing that you have to buy some fire-crackers to test that. So, you need to find the minimum number of fire-crackers you need to buy to test the mailboxes.
↵
The statement:↵
When monkeys are given some fire-crackers, they have only thing in the mind — to blow things up. Small boxes were easy to blow up, and thus mailboxes became a popular target. Now, a small mailbox manufacturer is interested in how many fire-crackers his new mailbox prototype can withstand without exploding and has hired you to help him. He will provide you with k identical mailbox prototypes each fitting up to m fire-crackers. However, he is not sure of how many fire-crackers he needs to provide you with in order for you to be able to solve his problem, so he asks your help.↵
↵
The constraints are:↵
↵
1. If you blow up a mailbox, you can't use the mailbox again, so if you have only k = 1 mailboxes, you would have to start testing with 1 fire-cracker, then 2 fire-crackers, and so on until it finally exploded. In the worst case, that is if it does not blow up even when filled with m fire-crackers, you would need 1 + 2 + 3 + ... + m = m * (m + 1)/2 fire-crackers.↵
↵
2. If a mailbox can withstand x fire-crackers, it can also withstand x-1 fire-crackers.↵
↵
3. Upon an explosion, a mailbox is either totally destroyed (blown up) or unharmed, which means that it can be reused in another test explosion.↵
↵
Now the manufacturer wants you to find the maximum number of fire-crackers that his mailboxes can withstand. Before doing that you have to buy some fire-crackers to test that. So, you need to find the minimum number of fire-crackers you need to buy to test the mailboxes.
