LeetCode #1049 — MEDIUM

Last Stone Weight II

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

The Problem

Problem Statement

You are given an array of integers stones where stones[i] is the weight of the i^th stone.

We are playing a game with the stones. On each turn, we choose any two stones and smash them together. Suppose the stones have weights x and y with x <= y. The result of this smash is:

If x == y, both stones are destroyed, and
If x != y, the stone of weight x is destroyed, and the stone of weight y has new weight y - x.

At the end of the game, there is at most one stone left.

Return the smallest possible weight of the left stone. If there are no stones left, return 0.

Example 1:

Input: stones = [2,7,4,1,8,1]
Output: 1
Explanation:
We can combine 2 and 4 to get 2, so the array converts to [2,7,1,8,1] then,
we can combine 7 and 8 to get 1, so the array converts to [2,1,1,1] then,
we can combine 2 and 1 to get 1, so the array converts to [1,1,1] then,
we can combine 1 and 1 to get 0, so the array converts to [1], then that's the optimal value.

Example 2:

Input: stones = [31,26,33,21,40]
Output: 5

Constraints:

1 <= stones.length <= 30
1 <= stones[i] <= 100

Step 01

Brute Force Baseline

Problem summary: You are given an array of integers stones where stones[i] is the weight of the ith stone. We are playing a game with the stones. On each turn, we choose any two stones and smash them together. Suppose the stones have weights x and y with x <= y. The result of this smash is: If x == y, both stones are destroyed, and If x != y, the stone of weight x is destroyed, and the stone of weight y has new weight y - x. At the end of the game, there is at most one stone left. Return the smallest possible weight of the left stone. If there are no stones left, return 0.

Baseline thinking

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

Pattern signal: Array · Dynamic Programming

Example 1

[2,7,4,1,8,1]

Example 2

[31,26,33,21,40]

Core Insight

What unlocks the optimal approach

Think of the final answer as a sum of weights with + or - sign symbols infront of each weight. Actually, all sums with 1 of each sign symbol are possible.
Use dynamic programming: for every possible sum with N stones, those sums +x or -x is possible with N+1 stones, where x is the value of the newest stone. (This overcounts sums that are all positive or all negative, but those don't matter.)

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 #1049: Last Stone Weight II
class Solution {
    public int lastStoneWeightII(int[] stones) {
        int s = 0;
        for (int v : stones) {
            s += v;
        }
        int m = stones.length;
        int n = s >> 1;
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 1; i <= m; ++i) {
            for (int j = 0; j <= n; ++j) {
                dp[i][j] = dp[i - 1][j];
                if (stones[i - 1] <= j) {
                    dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - stones[i - 1]] + stones[i - 1]);
                }
            }
        }
        return s - dp[m][n] * 2;
    }
}

// Accepted solution for LeetCode #1049: Last Stone Weight II
func lastStoneWeightII(stones []int) int {
	s := 0
	for _, v := range stones {
		s += v
	}
	m, n := len(stones), s>>1
	dp := make([][]int, m+1)
	for i := range dp {
		dp[i] = make([]int, n+1)
	}
	for i := 1; i <= m; i++ {
		for j := 0; j <= n; j++ {
			dp[i][j] = dp[i-1][j]
			if stones[i-1] <= j {
				dp[i][j] = max(dp[i][j], dp[i-1][j-stones[i-1]]+stones[i-1])
			}
		}
	}
	return s - dp[m][n]*2
}

# Accepted solution for LeetCode #1049: Last Stone Weight II
class Solution:
    def lastStoneWeightII(self, stones: List[int]) -> int:
        s = sum(stones)
        m, n = len(stones), s >> 1
        dp = [[0] * (n + 1) for _ in range(m + 1)]
        for i in range(1, m + 1):
            for j in range(n + 1):
                dp[i][j] = dp[i - 1][j]
                if stones[i - 1] <= j:
                    dp[i][j] = max(
                        dp[i][j], dp[i - 1][j - stones[i - 1]] + stones[i - 1]
                    )
        return s - 2 * dp[-1][-1]

// Accepted solution for LeetCode #1049: Last Stone Weight II
impl Solution {
    #[allow(dead_code)]
    pub fn last_stone_weight_ii(stones: Vec<i32>) -> i32 {
        let n = stones.len();
        let mut sum = 0;

        for e in &stones {
            sum += *e;
        }

        let m = (sum / 2) as usize;
        let mut dp: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];

        // Begin the actual dp process
        for i in 1..=n {
            for j in 1..=m {
                dp[i][j] = if stones[i - 1] > (j as i32) {
                    dp[i - 1][j]
                } else {
                    std::cmp::max(
                        dp[i - 1][j],
                        dp[i - 1][j - (stones[i - 1] as usize)] + stones[i - 1],
                    )
                };
            }
        }

        sum - 2 * dp[n][m]
    }
}

// Accepted solution for LeetCode #1049: Last Stone Weight II
function lastStoneWeightII(stones: number[]): number {
    const sum = stones.reduce((a, b) => a + b);
    const target = Math.ceil(sum / 2);

    let dp = Array.from({ length: sum + 1 }, (_, i) => {
        return Math.abs(i - (sum - i));
    });

    for (let i = 0; i < stones.length; i++) {
        const current: number[] = Array.from({ length: sum + 1 });
        for (let j = current.length - 1; j >= 0; j--) {
            if (j >= target) {
                current[j] = Math.abs(j - (sum - j));
            } else {
                current[j] = Math.min(dp[j], dp[j + stones[i]]);
            }
        }

        dp = current;
    }

    return dp[0];
}

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.