/**
 * @file
 * \brief Implementation of an algorithm to solve the jumping game problem
 * \details
 * This algorithm is a greedy algorithm.
 * This solution takes in input as a vector and output as a boolean to check if you can reach the last position.
 * @author [Rakshaa Viswanathan](https://github.com/rakshaa2000)
*/

#include <vector>
#include<iostream>

//Implements the algorithm
/*We name the indices good and bad based on whether we can reach the destination if we start at that position.
 *We initialize the last index as lastPos.
 *Here, we start from the end of the array and check if we can ever reach the first index.
 *We check if the sum of the index and the maximum jump count given is greater than or equal to the lastPos.
 *If yes, then that is the last position you can reach starting from the back.
 *After the end of the loop, if we reach the lastPos as 0, then the destination can be reached from the start position.
*/
 /**
 * This function implements the above algorithm
 * @param vector of nums containing the maximum jump (in steps) from that index
 * @return returns bool value whether final index can be reached or not
 */  
bool canJump(std::vector<int> nums) {
    auto lastPos = nums.size() - 1;
    for (auto i = nums.size() - 1; i >= 0; i--) {
        if (i + nums[i] >= lastPos) {
            lastPos = i;
        }
    }
    return lastPos == 0;
}

/**
 * @brief Main function
 * @returns 0 on exit
 */
int main(){
    //Sample test case
    std::vector<int> num={4,3,1,0,5};
    std::cout<<canJump(num);  //Should display true, as when you take one step from position 0, you reach position 1, from which 3 steps lead you to the destination
    return 0;
}