LeetCode #1053 — MEDIUM

Previous Permutation With One Swap

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

The Problem

Problem Statement

Given an array of positive integers arr (not necessarily distinct), return the lexicographically largest permutation that is smaller than arr, that can be made with exactly one swap. If it cannot be done, then return the same array.

Note that a swap exchanges the positions of two numbers arr[i] and arr[j]

Example 1:

Input: arr = [3,2,1]
Output: [3,1,2]
Explanation: Swapping 2 and 1.

Example 2:

Input: arr = [1,1,5]
Output: [1,1,5]
Explanation: This is already the smallest permutation.

Example 3:

Input: arr = [1,9,4,6,7]
Output: [1,7,4,6,9]
Explanation: Swapping 9 and 7.

Constraints:

1 <= arr.length <= 10⁴
1 <= arr[i] <= 10⁴

Step 01

Brute Force Baseline

Problem summary: Given an array of positive integers arr (not necessarily distinct), return the lexicographically largest permutation that is smaller than arr, that can be made with exactly one swap. If it cannot be done, then return the same array. Note that a swap exchanges the positions of two numbers arr[i] and arr[j]

Baseline thinking

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

Pattern signal: Array · Greedy

Example 1

[3,2,1]

Example 2

[1,1,5]

Example 3

[1,9,4,6,7]

Step 02

Core Insight

What unlocks the optimal approach

You need to swap two values, one larger than the other. Where is the larger one located?

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 #1053: Previous Permutation With One Swap
class Solution {
    public int[] prevPermOpt1(int[] arr) {
        int n = arr.length;
        for (int i = n - 1; i > 0; --i) {
            if (arr[i - 1] > arr[i]) {
                for (int j = n - 1; j > i - 1; --j) {
                    if (arr[j] < arr[i - 1] && arr[j] != arr[j - 1]) {
                        int t = arr[i - 1];
                        arr[i - 1] = arr[j];
                        arr[j] = t;
                        return arr;
                    }
                }
            }
        }
        return arr;
    }
}

// Accepted solution for LeetCode #1053: Previous Permutation With One Swap
func prevPermOpt1(arr []int) []int {
	n := len(arr)
	for i := n - 1; i > 0; i-- {
		if arr[i-1] > arr[i] {
			for j := n - 1; j > i-1; j-- {
				if arr[j] < arr[i-1] && arr[j] != arr[j-1] {
					arr[i-1], arr[j] = arr[j], arr[i-1]
					return arr
				}
			}
		}
	}
	return arr
}

# Accepted solution for LeetCode #1053: Previous Permutation With One Swap
class Solution:
    def prevPermOpt1(self, arr: List[int]) -> List[int]:
        n = len(arr)
        for i in range(n - 1, 0, -1):
            if arr[i - 1] > arr[i]:
                for j in range(n - 1, i - 1, -1):
                    if arr[j] < arr[i - 1] and arr[j] != arr[j - 1]:
                        arr[i - 1], arr[j] = arr[j], arr[i - 1]
                        return arr
        return arr

// Accepted solution for LeetCode #1053: Previous Permutation With One Swap
struct Solution;

impl Solution {
    fn prev_perm_opt1(mut a: Vec<i32>) -> Vec<i32> {
        let n = a.len();
        if n < 2 {
            return a;
        }
        let mut i = n - 2;
        while i > 0 && a[i] <= a[i + 1] {
            i -= 1;
        }
        if i == 0 && a[0] <= a[1] {
            return a;
        }
        let mut j = n - 1;
        while a[j] >= a[i] || a[j] == a[j - 1] {
            j -= 1;
        }
        a.swap(i, j);
        a
    }
}

#[test]
fn test() {
    let a = vec![3, 2, 1];
    let res = vec![3, 1, 2];
    assert_eq!(Solution::prev_perm_opt1(a), res);
    let a = vec![1, 1, 5];
    let res = vec![1, 1, 5];
    assert_eq!(Solution::prev_perm_opt1(a), res);
    let a = vec![1, 9, 4, 6, 7];
    let res = vec![1, 7, 4, 6, 9];
    assert_eq!(Solution::prev_perm_opt1(a), res);
    let a = vec![3, 1, 1, 3];
    let res = vec![1, 3, 1, 3];
    assert_eq!(Solution::prev_perm_opt1(a), res);
}

// Accepted solution for LeetCode #1053: Previous Permutation With One Swap
function prevPermOpt1(arr: number[]): number[] {
    const n = arr.length;
    for (let i = n - 1; i > 0; --i) {
        if (arr[i - 1] > arr[i]) {
            for (let j = n - 1; j > i - 1; --j) {
                if (arr[j] < arr[i - 1] && arr[j] !== arr[j - 1]) {
                    const t = arr[i - 1];
                    arr[i - 1] = arr[j];
                    arr[j] = t;
                    return arr;
                }
            }
        }
    }
    return arr;
}

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 log n)

Space

O(1)

Approach Breakdown

EXHAUSTIVE

O(2ⁿ) time

O(n) space

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

O(n log n) time

O(1) 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.

Shortcut: Sort + single pass → O(n log n). If no sort needed → O(n). The hard part is proving it works.

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.

Using greedy without proof

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.