/**
 * @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.
 * 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.
 * @author [Rakshaa Viswanathan](https://github.com/rakshaa2000)
*/

#include <vector>
#include <iostream>
#include <cassert>


 /**
 * @brief This function implements the above algorithm
 * @param array of numbers 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 Function to test above algorithm
 * @returns void
 */
static void test(){
  //Test 1
  std::vector<int> num1={4,3,1,0,5};
  assert(canJump(num1)==true);
  std::cout<<"Input: ";
  for(auto i: num1){
    std::cout<<i<<" ";
  }
  std::cout<<"Output: true"<<std::endl;
  //Test 2
  std::vector<int> num2={3,2,1,0,4};
  assert(canJump(num2)==false);
  std::cout<<"Input: ";
  for(auto i: num2){
    std::cout<<i<<" ";
  }
  std::cout<<"Output: false"<<std::endl;
}


/**
 * @brief Main function
 * @returns 0 on exit
 */
int main(){
    test();
    return 0;
}