LeetCode #3332 — MEDIUM

Maximum Points Tourist Can Earn

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

The Problem

Problem Statement

You are given two integers, n and k, along with two 2D integer arrays, stayScore and travelScore.

A tourist is visiting a country with n cities, where each city is directly connected to every other city. The tourist's journey consists of exactly k 0-indexed days, and they can choose any city as their starting point.

Each day, the tourist has two choices:

Stay in the current city: If the tourist stays in their current city curr during day i, they will earn stayScore[i][curr] points.
Move to another city: If the tourist moves from their current city curr to city dest, they will earn travelScore[curr][dest] points.

Return the maximum possible points the tourist can earn.

Example 1:

Input: n = 2, k = 1, stayScore = [[2,3]], travelScore = [[0,2],[1,0]]

Output: 3

Explanation:

The tourist earns the maximum number of points by starting in city 1 and staying in that city.

Example 2:

Input: n = 3, k = 2, stayScore = [[3,4,2],[2,1,2]], travelScore = [[0,2,1],[2,0,4],[3,2,0]]

Output: 8

Explanation:

The tourist earns the maximum number of points by starting in city 1, staying in that city on day 0, and traveling to city 2 on day 1.

Constraints:

1 <= n <= 200
1 <= k <= 200
n == travelScore.length == travelScore[i].length == stayScore[i].length
k == stayScore.length
1 <= stayScore[i][j] <= 100
0 <= travelScore[i][j] <= 100
travelScore[i][i] == 0

Step 01

Brute Force Baseline

Problem summary: You are given two integers, n and k, along with two 2D integer arrays, stayScore and travelScore. A tourist is visiting a country with n cities, where each city is directly connected to every other city. The tourist's journey consists of exactly k 0-indexed days, and they can choose any city as their starting point. Each day, the tourist has two choices: Stay in the current city: If the tourist stays in their current city curr during day i, they will earn stayScore[i][curr] points. Move to another city: If the tourist moves from their current city curr to city dest, they will earn travelScore[curr][dest] points. Return the maximum possible points the tourist can earn.

Baseline thinking

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

Pattern signal: Array · Dynamic Programming

Example 1

2
1
[[2,3]]
[[0,2],[1,0]]

Example 2

3
2
[[3,4,2],[2,1,2]]
[[0,2,1],[2,0,4],[3,2,0]]

Step 02

Core Insight

What unlocks the optimal approach

Use DP.
<code>dp[i][j]</code> is the maximum score that you can achieve in your last <code>i</code> actions by starting from city <code>j</code>.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
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 #3332: Maximum Points Tourist Can Earn
class Solution {
    public int maxScore(int n, int k, int[][] stayScore, int[][] travelScore) {
        int[][] f = new int[k + 1][n];
        for (var g : f) {
            Arrays.fill(g, Integer.MIN_VALUE);
        }
        Arrays.fill(f[0], 0);
        for (int i = 1; i <= k; ++i) {
            for (int j = 0; j < n; ++j) {
                for (int h = 0; h < n; ++h) {
                    f[i][j] = Math.max(
                        f[i][j], f[i - 1][h] + (j == h ? stayScore[i - 1][j] : travelScore[h][j]));
                }
            }
        }
        return Arrays.stream(f[k]).max().getAsInt();
    }
}

// Accepted solution for LeetCode #3332: Maximum Points Tourist Can Earn
func maxScore(n int, k int, stayScore [][]int, travelScore [][]int) (ans int) {
	f := make([][]int, k+1)
	for i := range f {
		f[i] = make([]int, n)
		for j := range f[i] {
			f[i][j] = math.MinInt32
		}
	}
	for j := 0; j < n; j++ {
		f[0][j] = 0
	}
	for i := 1; i <= k; i++ {
		for j := 0; j < n; j++ {
			f[i][j] = f[i-1][j] + stayScore[i-1][j]
			for h := 0; h < n; h++ {
				if h != j {
					f[i][j] = max(f[i][j], f[i-1][h]+travelScore[h][j])
				}
			}
		}
	}
	for j := 0; j < n; j++ {
		ans = max(ans, f[k][j])
	}
	return
}

# Accepted solution for LeetCode #3332: Maximum Points Tourist Can Earn
class Solution:
    def maxScore(
        self, n: int, k: int, stayScore: List[List[int]], travelScore: List[List[int]]
    ) -> int:
        f = [[-inf] * n for _ in range(k + 1)]
        f[0] = [0] * n
        for i in range(1, k + 1):
            for j in range(n):
                for h in range(n):
                    f[i][j] = max(
                        f[i][j],
                        f[i - 1][h]
                        + (stayScore[i - 1][j] if j == h else travelScore[h][j]),
                    )
        return max(f[k])

// Accepted solution for LeetCode #3332: Maximum Points Tourist Can Earn
// Rust example auto-generated from java reference.
// Replace the signature and local types with the exact LeetCode harness for this problem.
impl Solution {
    pub fn rust_example() {
        // Port the logic from the reference block below.
    }
}

// Reference (java):
// // Accepted solution for LeetCode #3332: Maximum Points Tourist Can Earn
// class Solution {
//     public int maxScore(int n, int k, int[][] stayScore, int[][] travelScore) {
//         int[][] f = new int[k + 1][n];
//         for (var g : f) {
//             Arrays.fill(g, Integer.MIN_VALUE);
//         }
//         Arrays.fill(f[0], 0);
//         for (int i = 1; i <= k; ++i) {
//             for (int j = 0; j < n; ++j) {
//                 for (int h = 0; h < n; ++h) {
//                     f[i][j] = Math.max(
//                         f[i][j], f[i - 1][h] + (j == h ? stayScore[i - 1][j] : travelScore[h][j]));
//                 }
//             }
//         }
//         return Arrays.stream(f[k]).max().getAsInt();
//     }
// }

// Accepted solution for LeetCode #3332: Maximum Points Tourist Can Earn
function maxScore(n: number, k: number, stayScore: number[][], travelScore: number[][]): number {
    const f: number[][] = Array.from({ length: k + 1 }, () => Array(n).fill(-Infinity));
    f[0].fill(0);
    for (let i = 1; i <= k; ++i) {
        for (let j = 0; j < n; ++j) {
            for (let h = 0; h < n; ++h) {
                f[i][j] = Math.max(
                    f[i][j],
                    f[i - 1][h] + (j == h ? stayScore[i - 1][j] : travelScore[h][j]),
                );
            }
        }
    }
    return Math.max(...f[k]);
}

Step 06

Interactive Study Demo

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

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n × m)

Space

O(n × m)

Approach Breakdown

RECURSIVE

O(2ⁿ) time

O(n) space

Pure recursion explores every possible choice at each step. With two choices per state (take or skip), the decision tree has 2ⁿ leaves. The recursion stack uses O(n) space. Many subproblems are recomputed exponentially many times.

DYNAMIC PROGRAMMING

O(n × m) time

O(n × m) space

Each cell in the DP table is computed exactly once from previously solved subproblems. The table dimensions determine both time and space. Look for the state variables — each unique combination of state values is one cell. Often a rolling array can reduce space by one dimension.

Shortcut: Count your DP state dimensions → that’s your time. Can you drop one? That’s your space optimization.

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.

State misses one required dimension

Wrong move: An incomplete state merges distinct subproblems and caches incorrect answers.

Usually fails on: Correctness breaks on cases that differ only in hidden state.

Fix: Define state so each unique subproblem maps to one DP cell.