LeetCode #1436 — EASY

Destination City

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

You are given the array paths, where paths[i] = [cityA_i, cityB_i] means there exists a direct path going from cityA_i to cityB_i. Return the destination city, that is, the city without any path outgoing to another city.

It is guaranteed that the graph of paths forms a line without any loop, therefore, there will be exactly one destination city.

Example 1:

Input: paths = [["London","New York"],["New York","Lima"],["Lima","Sao Paulo"]]
Output: "Sao Paulo" 
Explanation: Starting at "London" city you will reach "Sao Paulo" city which is the destination city. Your trip consist of: "London" -> "New York" -> "Lima" -> "Sao Paulo".

Example 2:

Input: paths = [["B","C"],["D","B"],["C","A"]]
Output: "A"
Explanation: All possible trips are: 
"D" -> "B" -> "C" -> "A". 
"B" -> "C" -> "A". 
"C" -> "A". 
"A". 
Clearly the destination city is "A".

Example 3:

Input: paths = [["A","Z"]]
Output: "Z"

Constraints:

1 <= paths.length <= 100
paths[i].length == 2
1 <= cityA_i.length, cityB_i.length <= 10
cityA_i != cityB_i
All strings consist of lowercase and uppercase English letters and the space character.

Step 01

Brute Force Baseline

Problem summary: You are given the array paths, where paths[i] = [cityAi, cityBi] means there exists a direct path going from cityAi to cityBi. Return the destination city, that is, the city without any path outgoing to another city. It is guaranteed that the graph of paths forms a line without any loop, therefore, there will be exactly one destination city.

Baseline thinking

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

Pattern signal: Array · Hash Map

Example 1

[["London","New York"],["New York","Lima"],["Lima","Sao Paulo"]]

Example 2

[["B","C"],["D","B"],["C","A"]]

Example 3

[["A","Z"]]

Step 02

Core Insight

What unlocks the optimal approach

Start in any city and use the path to move to the next city.
Eventually, you will reach a city with no path outgoing, this is the destination city.

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 #1436: Destination City
class Solution {
    public String destCity(List<List<String>> paths) {
        Set<String> s = new HashSet<>();
        for (var p : paths) {
            s.add(p.get(0));
        }
        for (int i = 0;; ++i) {
            var b = paths.get(i).get(1);
            if (!s.contains(b)) {
                return b;
            }
        }
    }
}

// Accepted solution for LeetCode #1436: Destination City
func destCity(paths [][]string) string {
	s := map[string]bool{}
	for _, p := range paths {
		s[p[0]] = true
	}
	for _, p := range paths {
		if !s[p[1]] {
			return p[1]
		}
	}
	return ""
}

# Accepted solution for LeetCode #1436: Destination City
class Solution:
    def destCity(self, paths: List[List[str]]) -> str:
        s = {a for a, _ in paths}
        return next(b for _, b in paths if b not in s)

// Accepted solution for LeetCode #1436: Destination City
use std::collections::HashSet;

impl Solution {
    pub fn dest_city(paths: Vec<Vec<String>>) -> String {
        let s = paths
            .iter()
            .map(|p| p[0].clone())
            .collect::<HashSet<String>>();
        paths.into_iter().find(|p| !s.contains(&p[1])).unwrap()[1].clone()
    }
}

// Accepted solution for LeetCode #1436: Destination City
function destCity(paths: string[][]): string {
    const s = new Set<string>(paths.map(([a, _]) => a));
    return paths.find(([_, b]) => !s.has(b))![1];
}

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)

Space

O(n)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

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.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.