Question

Use C++. The game of “Jump It” consists of a board with n positive integers in a row, except for the first
column, which always contains zero. These numbers represent the cost to enter each column.
Here is a sample game board where n is 6:

0 3 80 6 57 10

The object of the game is to move from the first column to the last column with the lowest total
cost.
The number in each column represents the cost to enter that column. You always start the game
in the first column and have two types of moves. You can either move to the adjacent column or
jump over the adjacent column to land two columns over. The cost of a game is the sum of the
costs of the visited columns.
In the board shown above, there are several ways to get to the end. Starting in the first column,
our cost so far is 0. We could jump to 80, then jump to 57, and then move to 10 for a total cost
of 80 + 57 + 10 = 147. However, a cheaper path would be to move to 3, jump to 6, then jump to
10, for a total cost of 3 + 6 + 10 = 19.
Write a recursive function that solves this problem and returns the lowest cost of a game board
represented and passed as an array.
Note: your function shouldn’t output the actual sequence of jumps, only the lowest cost of this
sequence.

Answer 1

/*Algo: In each step we have two options either we can choose
adjacent column or next to adjacent column .
In both the case which value leads to minimum jump cost that will be selected.
So, recursion would be
R(x)=arr[x]+min(R(x+1)+R(x+2)) where arr: array of jump cost
R: Recursion equation */

Solution:

#include <iostream>
using namespace std;
int minJumpCost(int arr[],int start,int n)
{
if(start==n-1) //if we reached at destination
return arr[start];
if(start>=n) //out of destination
return INT_MAX;
//either select adjacent or next to adjacent
return arr[start]+min(minJumpCost(arr,start+1,n),minJumpCost(arr,start+2,n));
}
int main()
{
int n;//size of array
cout<<"Enter Size of array: ";
cin>>n;
int arr[n]; //jump cost array
cout<<"Enter jump cost:";
for(int i=0;i<n;i++)
cin>>arr[i];
cout<<"Minimum jump cost: "<<minJumpCost(arr,0,n);
return 0;
}

Output