# QUESTION

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.

Your goal is to reach the last index in the minimum number of jumps.

For example:

Given array A = [2,3,1,1,4]

The minimum number of jumps to reach the last index is 2. (Jump 1 step from index 0 to 1, then 3 steps to the last index.)

This question is provided by LeetCode.

# SOLUTION

Greedy search algorithm is implied to solve this problem. This first idea comes into mind is Dynamic programming, while it fails when judge large. This question indicates I might be able to make my solution of Jump Game better.

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class Solution { public: int jump(int A[], int n) { // Start typing your C/C++ solution below // DO NOT write int main() function if (n == 1) return 0; int jumps = 0; int currMax = 0; int i = 0; while (i < n) { currMax = A[i] + i; if (A[i] > 0) ++jumps; else return 0; if (currMax >= n - 1) return jumps; int tmpMax = 0; for (int j = i + 1; j <= currMax; ++j) { if (A[j] + j >= tmpMax) { tmpMax = A[j] + j; i = j; } } } return jumps; } }; |

Hi, Liu Yang:

I tried DP method, it works. You can check at my website. But your solution is better, I love this method! Greedy Algorithm!

Sorry, I messed up. I did not use DP!