Saturday, January 18, 2014

How many possible ways the child can run up the ladder

A child is running up a ladder with n steps, and can hop either 1 step or 2 steps at a time. Calculate how many possible ways the child can run up the ladder.

This problem is similar to Fibonacci Problem. Each step n can be reached from either two steps below (n-2) or one step below (n-1), thus the number of possibilities to reach that step is the sum of the possibilities to reach those other two steps. Base cases would be:

1. If there is only 1 step then child can run up the ladder only one way by taking 1 step.
2. If there are 2 steps then child can run up the ladder 2 ways by taking a single 2 step or taking two 1 steps.

int countWays(int n)
{
    if(n==0)
        return 0;
    else if(n==1||n==2)
        return n;
    else
        return countWays(n-1)+countWays(n-2);
}

Like the Fibonacci problem,the runtime of this problem is exponential O(2^n)

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