LeetCode #1423 — MEDIUM

Maximum Points You Can Obtain from Cards

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode
The Problem

Problem Statement

There are several cards arranged in a row, and each card has an associated number of points. The points are given in the integer array cardPoints.

In one step, you can take one card from the beginning or from the end of the row. You have to take exactly k cards.

Your score is the sum of the points of the cards you have taken.

Given the integer array cardPoints and the integer k, return the maximum score you can obtain.

Example 1:

Input: cardPoints = [1,2,3,4,5,6,1], k = 3
Output: 12
Explanation: After the first step, your score will always be 1. However, choosing the rightmost card first will maximize your total score. The optimal strategy is to take the three cards on the right, giving a final score of 1 + 6 + 5 = 12.

Example 2:

Input: cardPoints = [2,2,2], k = 2
Output: 4
Explanation: Regardless of which two cards you take, your score will always be 4.

Example 3:

Input: cardPoints = [9,7,7,9,7,7,9], k = 7
Output: 55
Explanation: You have to take all the cards. Your score is the sum of points of all cards.

Constraints:

  • 1 <= cardPoints.length <= 105
  • 1 <= cardPoints[i] <= 104
  • 1 <= k <= cardPoints.length
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: There are several cards arranged in a row, and each card has an associated number of points. The points are given in the integer array cardPoints. In one step, you can take one card from the beginning or from the end of the row. You have to take exactly k cards. Your score is the sum of the points of the cards you have taken. Given the integer array cardPoints and the integer k, return the maximum score you can obtain.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Sliding Window

Example 1

[1,2,3,4,5,6,1]
3

Example 2

[2,2,2]
2

Example 3

[9,7,7,9,7,7,9]
7

Related Problems

  • Maximum Score from Performing Multiplication Operations (maximum-score-from-performing-multiplication-operations)
  • Removing Minimum and Maximum From Array (removing-minimum-and-maximum-from-array)
  • Minimum Recolors to Get K Consecutive Black Blocks (minimum-recolors-to-get-k-consecutive-black-blocks)
  • Maximum Spending After Buying Items (maximum-spending-after-buying-items)
Step 02

Core Insight

What unlocks the optimal approach

  • Let the sum of all points be total_pts. You need to remove a sub-array from cardPoints with length n - k.
  • Keep a window of size n - k over the array. The answer is max(answer, total_pts - sumOfCurrentWindow)
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1423: Maximum Points You Can Obtain from Cards
class Solution {
    public int maxScore(int[] cardPoints, int k) {
        int s = 0, n = cardPoints.length;
        for (int i = n - k; i < n; ++i) {
            s += cardPoints[i];
        }
        int ans = s;
        for (int i = 0; i < k; ++i) {
            s += cardPoints[i] - cardPoints[n - k + i];
            ans = Math.max(ans, s);
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(k)

Approach Breakdown

BRUTE FORCE
O(n × k) time
O(1) space

For each starting index, scan the next k elements to compute the window aggregate. There are n−k+1 starting positions, each requiring O(k) work, giving O(n × k) total. No extra space since we recompute from scratch each time.

SLIDING WINDOW
O(n) time
O(k) space

The window expands and contracts as we scan left to right. Each element enters the window at most once and leaves at most once, giving 2n total operations = O(n). Space depends on what we track inside the window (a hash map of at most k distinct elements, or O(1) for a fixed-size window).

Shortcut: Each element enters and exits the window once → O(n) amortized, regardless of window size.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Shrinking the window only once

Wrong move: Using `if` instead of `while` leaves the window invalid for multiple iterations.

Usually fails on: Over-limit windows stay invalid and produce wrong lengths/counts.

Fix: Shrink in a `while` loop until the invariant is valid again.