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.
Move from brute-force thinking to an efficient approach using array strategy.
You are given a 0-indexed integer array piles, where piles[i] represents the number of stones in the ith pile, and an integer k. You should apply the following operation exactly k times:
piles[i] and remove floor(piles[i] / 2) stones from it.Notice that you can apply the operation on the same pile more than once.
Return the minimum possible total number of stones remaining after applying the k operations.
floor(x) is the largest integer that is smaller than or equal to x (i.e., rounds x down).
Example 1:
Input: piles = [5,4,9], k = 2 Output: 12 Explanation: Steps of a possible scenario are: - Apply the operation on pile 2. The resulting piles are [5,4,5]. - Apply the operation on pile 0. The resulting piles are [3,4,5]. The total number of stones in [3,4,5] is 12.
Example 2:
Input: piles = [4,3,6,7], k = 3 Output: 12 Explanation: Steps of a possible scenario are: - Apply the operation on pile 2. The resulting piles are [4,3,3,7]. - Apply the operation on pile 3. The resulting piles are [4,3,3,4]. - Apply the operation on pile 0. The resulting piles are [2,3,3,4]. The total number of stones in [2,3,3,4] is 12.
Constraints:
1 <= piles.length <= 1051 <= piles[i] <= 1041 <= k <= 105Problem summary: You are given a 0-indexed integer array piles, where piles[i] represents the number of stones in the ith pile, and an integer k. You should apply the following operation exactly k times: Choose any piles[i] and remove floor(piles[i] / 2) stones from it. Notice that you can apply the operation on the same pile more than once. Return the minimum possible total number of stones remaining after applying the k operations. floor(x) is the largest integer that is smaller than or equal to x (i.e., rounds x down).
Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.
Pattern signal: Array · Greedy
[5,4,9] 2
[4,3,6,7] 3
minimum-operations-to-halve-array-sum)maximal-score-after-applying-k-operations)take-gifts-from-the-richest-pile)Source-backed implementations are provided below for direct study and interview prep.
// Accepted solution for LeetCode #1962: Remove Stones to Minimize the Total
class Solution {
public int minStoneSum(int[] piles, int k) {
PriorityQueue<Integer> pq = new PriorityQueue<>((a, b) -> b - a);
for (int x : piles) {
pq.offer(x);
}
while (k-- > 0) {
int x = pq.poll();
pq.offer(x - x / 2);
}
int ans = 0;
while (!pq.isEmpty()) {
ans += pq.poll();
}
return ans;
}
}
// Accepted solution for LeetCode #1962: Remove Stones to Minimize the Total
func minStoneSum(piles []int, k int) (ans int) {
pq := &hp{piles}
heap.Init(pq)
for ; k > 0; k-- {
x := pq.pop()
pq.push(x - x/2)
}
for pq.Len() > 0 {
ans += pq.pop()
}
return
}
type hp struct{ sort.IntSlice }
func (h hp) Less(i, j int) bool { return h.IntSlice[i] > h.IntSlice[j] }
func (h *hp) Push(v any) { h.IntSlice = append(h.IntSlice, v.(int)) }
func (h *hp) Pop() any {
a := h.IntSlice
v := a[len(a)-1]
h.IntSlice = a[:len(a)-1]
return v
}
func (h *hp) push(v int) { heap.Push(h, v) }
func (h *hp) pop() int { return heap.Pop(h).(int) }
# Accepted solution for LeetCode #1962: Remove Stones to Minimize the Total
class Solution:
def minStoneSum(self, piles: List[int], k: int) -> int:
pq = [-x for x in piles]
heapify(pq)
for _ in range(k):
heapreplace(pq, pq[0] // 2)
return -sum(pq)
// Accepted solution for LeetCode #1962: Remove Stones to Minimize the Total
/**
* [1962] Remove Stones to Minimize the Total
*
* You are given a 0-indexed integer array piles, where piles[i] represents the number of stones in the i^th pile, and an integer k. You should apply the following operation exactly k times:
*
* Choose any piles[i] and remove floor(piles[i] / 2) stones from it.
*
* Notice that you can apply the operation on the same pile more than once.
* Return the minimum possible total number of stones remaining after applying the k operations.
* floor(x) is the greatest integer that is smaller than or equal to x (i.e., rounds x down).
*
* Example 1:
*
* Input: piles = [5,4,9], k = 2
* Output: 12
* Explanation: Steps of a possible scenario are:
* - Apply the operation on pile 2. The resulting piles are [5,4,<u>5</u>].
* - Apply the operation on pile 0. The resulting piles are [<u>3</u>,4,5].
* The total number of stones in [3,4,5] is 12.
*
* Example 2:
*
* Input: piles = [4,3,6,7], k = 3
* Output: 12
* Explanation: Steps of a possible scenario are:
* - Apply the operation on pile 2. The resulting piles are [4,3,<u>3</u>,7].
* - Apply the operation on pile 3. The resulting piles are [4,3,3,<u>4</u>].
* - Apply the operation on pile 0. The resulting piles are [<u>2</u>,3,3,4].
* The total number of stones in [2,3,3,4] is 12.
*
*
* Constraints:
*
* 1 <= piles.length <= 10^5
* 1 <= piles[i] <= 10^4
* 1 <= k <= 10^5
*
*/
pub struct Solution {}
// problem: https://leetcode.com/problems/remove-stones-to-minimize-the-total/
// discuss: https://leetcode.com/problems/remove-stones-to-minimize-the-total/discuss/?currentPage=1&orderBy=most_votes&query=
// submission codes start here
impl Solution {
pub fn min_stone_sum(piles: Vec<i32>, k: i32) -> i32 {
0
}
}
// submission codes end
#[cfg(test)]
mod tests {
use super::*;
#[test]
#[ignore]
fn test_1962_example_1() {
let piles = vec![5, 4, 9];
let k = 2;
let result = 12;
assert_eq!(Solution::min_stone_sum(piles, k), result);
}
#[test]
#[ignore]
fn test_1962_example_2() {
let piles = vec![4, 3, 6, 7];
let k = 3;
let result = 12;
assert_eq!(Solution::min_stone_sum(piles, k), result);
}
}
// Accepted solution for LeetCode #1962: Remove Stones to Minimize the Total
function minStoneSum(piles: number[], k: number): number {
const pq = new MaxPriorityQueue<number>();
for (const x of piles) {
pq.enqueue(x);
}
while (k--) {
pq.enqueue((pq.dequeue() + 1) >> 1);
}
return pq.toArray().reduce((a, b) => a + b, 0);
}
Use this to step through a reusable interview workflow for this problem.
Try every possible combination of choices. With n items each having two states (include/exclude), the search space is 2ⁿ. Evaluating each combination takes O(n), giving O(n × 2ⁿ). The recursion stack or subset storage uses O(n) space.
Greedy algorithms typically sort the input (O(n log n)) then make a single pass (O(n)). The sort dominates. If the input is already sorted or the greedy choice can be computed without sorting, time drops to O(n). Proving greedy correctness (exchange argument) is harder than the implementation.
Review these before coding to avoid predictable interview regressions.
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.
Wrong move: Locally optimal choices may fail globally.
Usually fails on: Counterexamples appear on crafted input orderings.
Fix: Verify with exchange argument or monotonic objective before committing.