Python (Simple DP + Sliding Window)
Intuition\n Describe your first thoughts on how to solve this problem. \n\n# Approach\n Describe your approach to solving the problem. \n\n# Complexity\n- Time 
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\n\n# Code\n```\nclass Solution:\n    def maximizeWin(self, prizePositions, k):\n        n = len(prizePositions)\n\n        left, dp, max_val = 0, [0]*(n+1), 0\n\n        for right in range(n):\n            while prizePositions[right] - prizePositions[left] > k:\n                left += 1\n\n            dp[right+1] = max(dp[right],right-left+1)\n\n            max_val = max(max_val,dp[left] + right - left + 1)\n\n        return max_val\n\n\n\n\n\n        \n```
['Python3']