[fix/docs]: improve the Jump Game algorithm (#2514)

* [fix/docs]: improve the Jump Game algorithm

* fix: pass `index` by reference and `const` it

* fix: use previous algorithm

* chore: apply suggestions from code review

Co-authored-by: Caeden Perelli-Harris <[email protected]>
Co-authored-by: Piotr Idzik <[email protected]>

---------

Co-authored-by: Caeden Perelli-Harris <[email protected]>
Co-authored-by: Piotr Idzik <[email protected]>
Co-authored-by: realstealthninja <[email protected]>

Author: 4 people

greedy_algorithms/jump_game.cpp

@@ -0,0 +1,74 @@
+/**
+ * @file
+ * @brief [Jumping Game](https://leetcode.com/problems/jump-game/)
+ * algorithm implementation
+ * @details
+ *
+ * Given an array of non-negative integers, you are initially positioned at the
+ * first index of the array. Each element in the array represents your maximum
+ * jump length at that position. Determine if you are able to reach the last
+ * index. 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)
+ * @author [David Leal](https://github.com/Panquesito7)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for std::cout
+#include <vector>    /// for std::vector
+
+/**
+ * @namespace
+ * @brief Greedy Algorithms
+ */
+namespace greedy_algorithms {
+/**
+ * @brief Checks whether the given element (default is `1`) can jump to the last
+ * index.
+ * @param nums array of numbers containing the maximum jump (in steps) from that
+ * index
+ * @returns true  if the index can be reached
+ * @returns false if the index can NOT be reached
+ */
+bool can_jump(const std::vector<int> &nums) {
+    size_t lastPos = nums.size() - 1;
+    for (size_t i = lastPos; i != static_cast<size_t>(-1); i--) {
+        if (i + nums[i] >= lastPos) {
+            lastPos = i;
+        }
+    }
+    return lastPos == 0;
+}
+}  // namespace greedy_algorithms
+
+/**
+ * @brief Function to test the above algorithm
+ * @returns void
+ */
+static void test() {
+    assert(greedy_algorithms::can_jump(std::vector<int>({4, 3, 1, 0, 5})));
+    assert(!greedy_algorithms::can_jump(std::vector<int>({3, 2, 1, 0, 4})));
+    assert(greedy_algorithms::can_jump(std::vector<int>({5, 9, 4, 7, 15, 3})));
+    assert(!greedy_algorithms::can_jump(std::vector<int>({1, 0, 5, 8, 12})));
+    assert(greedy_algorithms::can_jump(std::vector<int>({2, 1, 4, 7})));
+
+    std::cout << "All tests have successfully passed!\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}