Answer
It takes more heat to boil the water.
Work Step by Step
First, recall that the heat required to melt ice is $334 KJ/kg$. Since there is a gram of ice, it will take: $\frac{334}{1000} = .334 kJ$.
Now, we consider the specific heat of water to see how much energy it takes to increase the temperature of water by 100 Kelvin:
$ Q = mC \Delta t \\ Q = (.001)(4.184)(100) = .4184 kJ$
This is more energy than melting the ice, so it will take more energy to boil water.
