LeetCode #3502 — EASY

Minimum Cost to Reach Every Position

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

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The Problem

Problem Statement

You are given an integer array cost of size n. You are currently at position n (at the end of the line) in a line of n + 1 people (numbered from 0 to n).

You wish to move forward in the line, but each person in front of you charges a specific amount to swap places. The cost to swap with person i is given by cost[i].

You are allowed to swap places with people as follows:

  • If they are in front of you, you must pay them cost[i] to swap with them.
  • If they are behind you, they can swap with you for free.

Return an array answer of size n, where answer[i] is the minimum total cost to reach each position i in the line.

Example 1:

Input: cost = [5,3,4,1,3,2]

Output: [5,3,3,1,1,1]

Explanation:

We can get to each position in the following way:

  • i = 0. We can swap with person 0 for a cost of 5.
  • i = 1. We can swap with person 1 for a cost of 3.
  • i = 2. We can swap with person 1 for a cost of 3, then swap with person 2 for free.
  • i = 3. We can swap with person 3 for a cost of 1.
  • i = 4. We can swap with person 3 for a cost of 1, then swap with person 4 for free.
  • i = 5. We can swap with person 3 for a cost of 1, then swap with person 5 for free.

Example 2:

Input: cost = [1,2,4,6,7]

Output: [1,1,1,1,1]

Explanation:

We can swap with person 0 for a cost of 1, then we will be able to reach any position i for free.

Constraints:

  • 1 <= n == cost.length <= 100
  • 1 <= cost[i] <= 100

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: You are given an integer array cost of size n. You are currently at position n (at the end of the line) in a line of n + 1 people (numbered from 0 to n). You wish to move forward in the line, but each person in front of you charges a specific amount to swap places. The cost to swap with person i is given by cost[i]. You are allowed to swap places with people as follows: If they are in front of you, you must pay them cost[i] to swap with them. If they are behind you, they can swap with you for free. Return an array answer of size n, where answer[i] is the minimum total cost to reach each position i in the line.

Baseline thinking

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

Pattern signal: Array

Example 1

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

Example 2

[1,2,4,6,7]
Step 02

Core Insight

What unlocks the optimal approach

  • Note that once you swap to a position with a lower cost, you can reach any later position for free.
  • Use a min prefix array.
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 #3502: Minimum Cost to Reach Every Position
class Solution {
    public int[] minCosts(int[] cost) {
        int n = cost.length;
        int[] ans = new int[n];
        int mi = cost[0];
        for (int i = 0; i < n; ++i) {
            mi = Math.min(mi, cost[i]);
            ans[i] = mi;
        }
        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(1)

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.