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Hi, everyone.

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So in this video, we are going to solve this question, so we need to find out.

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We need to find out the number of ways to reach and from zero.

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So basically, these are the steps.

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So I want to reach step and starting from ground and ground zero.

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OK, so ground zero, I want to step in and I can take a jump off.

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When I can take a jump of two, I can take a jump of three.

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So from here I can take a jump of one, I can take a jump of two and I can take a jump of three.

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So we need to find out how many number of bees are there, for example, if we want to reach three.

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So number of ways to reach trees, basically, you can take a jump of one, one and one.

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Similarly, it can take a jump of one, then take a jump of the first trigger, jump of two, then take

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a jump of one and one more directly.

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Take a jump of three from zero DIKLA take a jump of three.

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So to reach three from zero.

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I have four of his.

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OK, so for viewers out there, if the value of an E t.

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So I hope you understood my question.

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So given the value, often you have to tell me how many number of these are there.

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So this question can be easily solved with the help of recursion.

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So what resurgences?

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See, you want to reach an.

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You want to reach in and you can take a jump of 120 so you can reach in from minus one.

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You can reach in from Minnesota, you can reach GNR from ministry.

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So the number of ways to reach in will basically be the addition of these three to a number of ways

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to reach and is basically number of ways to reach and minus one, because if you are standing at 10

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minus one, you will take a jump of one plus the number of ways to reach.

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And minus two, if you are standing at minus two, you will take a jump of two and you will reach and

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if you will take a jump of one, then that will be counted in the number of ways to reach and minus

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one, which we have already counted.

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Similarly, number of ways to reach.

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And minus three, if you are standing at then minus three, then you need to take a jump of three to

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reach and OK, you do not have any choice.

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You will take a jump of tea if you will.

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See I am standing at then minus three and I take a jump of one.

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It will take a jump of one, then it will be counted as number of ways to reach and minus two and it

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is already there.

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So a number of ways to reach and is basically number of ways to reach and minus one number of ways to

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reach and minus two and number of ways to reach and minus three.

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And the addition of these three will give you the number of ways to reach.

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And so, for example, let's take one example.

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So a number of ways to reach one is one.

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Take one step from zero.

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Number of ways to each two is basically I can take a jump of 21 and I can take a jump of the number

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of ways to reach two is two and above.

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We calculated that number of ways to each three is basically four.

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Simple.

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And what is the number of ways to reach zero?

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Basically you are standing at zero and you want to reach zero.

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So there is only one.

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We do not do anything.

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So now let's try to find out how many number of ways to reach for.

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I want to reach Stepha's, how many of these are there?

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So you want to reach for so you can reach for and the gems allow this one to entry so you can reach

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Plumtree, you can reach from two and you can reach from one to four three.

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You can reach from two, you can reach three from one and you can reach three from zero.

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Simple.

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So what we will do, we will make it as a base case.

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We know a number of ways to each do is to.

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So I will return to a number of ways to each one is basically one.

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So I will return one number of ways to reach zero.

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And you are standing at zero.

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So do not do anything.

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There's only one way.

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So two plus three plus the number of ways to reach three is four I will return for.

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Number of ways to reach do is to so I will return to a number of ways, each one is basically one,

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so I will return one.

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So what I will do, I will take the additional four plus two, six and seven.

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So a number of ways to reach 47.

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It is seven simple, so a number of ways to reach for this number of mysteries, three plus number of

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ways to reach to less number of ways to reach one.

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So a number of ways to ease trees for a number of ways to each tool is basically do a number of ways

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to each one is one.

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So four plus two plus one is seven.

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Seven is the right answer.

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And what are those ways you want to reach for.

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So one, two, three and four.

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One, two and four.

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One, one, three and four.

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Similar to one one.

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And one entry, three, anyone, one, two, one, two.

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So let's count one, two, three, four, five, six, seven.

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So seven ways are there to each step four.

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So this question can easily be solved with the help of the.

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So what do you want to reach and write?

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So to reach in, you can reach from minus one, you can reach from minus two and you can reach from

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minus three.

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So what you will do, you will apply recursion for then minus one applied equation, applied equation.

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And of course it will give me the number of ways to reach and minus one, let's call it X and of course

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it will give you the number of ways to reach and minus two, let's call it Y because it will give you

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the number of ways to reach and minus three, let's call it Z and with a number of ways to reach an

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addition of X plus Y plussed.

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Simple.

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So let's write the code.

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So in, let's say, the name of the function, this count is.

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So I want to reach in from zero what will the case, because it's very simple, if you are standing

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at zero.

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Or us standing at one.

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So in that case, do not do anything.

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So there is only one way I will return one.

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Otherwise, what will my answer?

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My answer will be.

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Number of ways to reach and minus one, plus number of ways to reach and minus two.

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Plus, a number of ways to reach and ministry.

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And I think our function will be OK, so let's test our function.

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So integer and it's taken Porten.

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And let's call the function see out.

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Countries need to give an.

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So our function will work, but there's one slight problem with our function and what is that slight

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problem?

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So let's take this example.

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So, for example.

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Number of ways to reach to the value of any number of ways to reach to this one and one and to take

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a jump of two or take a jump of one on one, simple.

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So if the value of it is to let supply and so who is not and is not and is not one.

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So we will call on one.

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We will call on zero and two will call on minus one.

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So this is a case we know the answer is one, this is a base case, we know the answer is one.

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But you are calling one minus one.

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So what will happen minus one is not a biscuit, so it will call on this, it will call on minus two,

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it will go on minus three, and it will call on minus four.

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And similarly, these are not biscuits.

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So, again, it will call.

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On three.

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So Tuticorin, Colin Taseko also, it will call on minus three, minus four, minus five, similarly

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minus four, minus five, minus six and minus five, minus six, minus seven.

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So it will continue.

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OK.

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So this will become infinite.

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So what we need to do.

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So we need to make it as a base case, we need to take it as a base case, OK?

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So we need to make it as our base case so that we do not reach minus one.

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So we need to make it as our base case.

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So it is compulsion here.

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We need to take to as our base case.

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So this is the first option to handle the situation.

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The second option is to handle the situation is basically you can write one condition.

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If the value of it becomes less than zero, return zero.

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So this is the second we saw minus one is basically zero, so I will return zero, so I will return

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zero from you so you can make two as your best case or you can use this condition.

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So what I want to say to is calling on when we know the answer to is calling on zero.

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We know the answer because both our base case, but who is also calling one minus one?

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So I told you, there are two ways to handle the situation.

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First, make two as our base case so I can write one condition here.

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I can add one more base case if the value of any two I know.

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What is the answer?

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Answer is two.

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I know the answer.

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So I can make it as a base case, so then I will reach out to I will directly answer to Sorto will act

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as a base case.

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The second situation is we can right this condition if the value is less than zero.

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So basically, this is invalid value.

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OK, this is invalid value.

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So for the invalid value, my answer will be zero.

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So if you recall, and minus and minus one is invalid value, so I will return zero from here.

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So you have both options.

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You can make it you can make a call like this or you can make a call like this.

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It's your choice.

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So first, which is basically you can write like this, you need to make to your best case.

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And we know the answer.

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Answer is to.

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Answer is.

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So now your code will work, so let's test our function.

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So a number of ways to reach three is basically Ford, so Ford is the right answer.

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Similarly, the number of ways to reach forty seven, so a number of ways to reach four is seven, so

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seven is the right answer and we already discussed it here.

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So a number of ways to Utah is basically seven.

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So this is the first way of making your record correct, the second way of making your record correct

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is if you do not want to make it as your best case, what you can do, you can add one condition.

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And what is that condition?

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If.

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The value often is basically invested.

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If the value of wine is invalid, then in that case, that answer will be zero for anybody to value.

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My answer will be zero.

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I want to search for for no obvious reason for this seven, it is working.

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Similarly, I want to reach out to a number of races, too, and it is working, so you have the option.

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You can use this or you can use this.

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Or you can use both of them.

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So this is it from this video, I will see you in the next one.