LeetCode #1849 — MEDIUM

Splitting a String Into Descending Consecutive Values

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

The Problem

Problem Statement

You are given a string s that consists of only digits.

Check if we can split s into two or more non-empty substrings such that the numerical values of the substrings are in descending order and the difference between numerical values of every two adjacent substrings is equal to 1.

For example, the string s = "0090089" can be split into ["0090", "089"] with numerical values [90,89]. The values are in descending order and adjacent values differ by 1, so this way is valid.
Another example, the string s = "001" can be split into ["0", "01"], ["00", "1"], or ["0", "0", "1"]. However all the ways are invalid because they have numerical values [0,1], [0,1], and [0,0,1] respectively, all of which are not in descending order.

Return true if it is possible to split s as described above, or false otherwise.

A substring is a contiguous sequence of characters in a string.

Example 1:

Input: s = "1234"
Output: false
Explanation: There is no valid way to split s.

Example 2:

Input: s = "050043"
Output: true
Explanation: s can be split into ["05", "004", "3"] with numerical values [5,4,3].
The values are in descending order with adjacent values differing by 1.

Example 3:

Input: s = "9080701"
Output: false
Explanation: There is no valid way to split s.

Constraints:

1 <= s.length <= 20
s only consists of digits.

Step 01

Brute Force Baseline

Problem summary: You are given a string s that consists of only digits. Check if we can split s into two or more non-empty substrings such that the numerical values of the substrings are in descending order and the difference between numerical values of every two adjacent substrings is equal to 1. For example, the string s = "0090089" can be split into ["0090", "089"] with numerical values [90,89]. The values are in descending order and adjacent values differ by 1, so this way is valid. Another example, the string s = "001" can be split into ["0", "01"], ["00", "1"], or ["0", "0", "1"]. However all the ways are invalid because they have numerical values [0,1], [0,1], and [0,0,1] respectively, all of which are not in descending order. Return true if it is possible to split s as described above, or false otherwise. A substring is a contiguous sequence of characters in a string.

Baseline thinking

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

Pattern signal: Backtracking

Example 1

"1234"

Example 2

"050043"

Example 3

"9080701"

Step 02

Core Insight

What unlocks the optimal approach

One solution is to try all possible splits using backtrack
Look out for trailing zeros in string

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 #1849: Splitting a String Into Descending Consecutive Values
class Solution {
    private char[] s;

    public boolean splitString(String s) {
        this.s = s.toCharArray();
        return dfs(0, -1);
    }

    private boolean dfs(int i, long x) {
        if (i >= s.length) {
            return true;
        }
        long y = 0;
        int r = x < 0 ? s.length - 1 : s.length;
        for (int j = i; j < r; ++j) {
            y = y * 10 + s[j] - '0';
            if ((x < 0 || x - y == 1) && dfs(j + 1, y)) {
                return true;
            }
        }
        return false;
    }
}

// Accepted solution for LeetCode #1849: Splitting a String Into Descending Consecutive Values
func splitString(s string) bool {
	var dfs func(i, x int) bool
	dfs = func(i, x int) bool {
		if i >= len(s) {
			return true
		}
		y := 0
		r := len(s)
		if x < 0 {
			r--
		}
		for j := i; j < r; j++ {
			y = y*10 + int(s[j]-'0')
			if (x < 0 || x-y == 1) && dfs(j+1, y) {
				return true
			}
		}
		return false
	}
	return dfs(0, -1)
}

# Accepted solution for LeetCode #1849: Splitting a String Into Descending Consecutive Values
class Solution:
    def splitString(self, s: str) -> bool:
        def dfs(i: int, x: int) -> bool:
            if i >= len(s):
                return True
            y = 0
            r = len(s) - 1 if x < 0 else len(s)
            for j in range(i, r):
                y = y * 10 + int(s[j])
                if (x < 0 or x - y == 1) and dfs(j + 1, y):
                    return True
            return False

        return dfs(0, -1)

// Accepted solution for LeetCode #1849: Splitting a String Into Descending Consecutive Values
/**
 * [1849] Splitting a String Into Descending Consecutive Values
 *
 * You are given a string s that consists of only digits.
 * Check if we can split s into two or more non-empty substrings such that the numerical values of the substrings are in descending order and the difference between numerical values of every two adjacent substrings is equal to 1.
 *
 * 	For example, the string s = "0090089" can be split into ["0090", "089"] with numerical values [90,89]. The values are in descending order and adjacent values differ by 1, so this way is valid.
 * 	Another example, the string s = "001" can be split into ["0", "01"], ["00", "1"], or ["0", "0", "1"]. However all the ways are invalid because they have numerical values [0,1], [0,1], and [0,0,1] respectively, all of which are not in descending order.
 *
 * Return true if it is possible to split s as described above, or false otherwise.
 * A substring is a contiguous sequence of characters in a string.
 *  
 * Example 1:
 *
 * Input: s = "1234"
 * Output: false
 * Explanation: There is no valid way to split s.
 *
 * Example 2:
 *
 * Input: s = "050043"
 * Output: true
 * Explanation: s can be split into ["05", "004", "3"] with numerical values [5,4,3].
 * The values are in descending order with adjacent values differing by 1.
 *
 * Example 3:
 *
 * Input: s = "9080701"
 * Output: false
 * Explanation: There is no valid way to split s.
 *
 *  
 * Constraints:
 *
 * 	1 <= s.length <= 20
 * 	s only consists of digits.
 *
 */
pub struct Solution {}

// problem: https://leetcode.com/problems/splitting-a-string-into-descending-consecutive-values/
// discuss: https://leetcode.com/problems/splitting-a-string-into-descending-consecutive-values/discuss/?currentPage=1&orderBy=most_votes&query=

// submission codes start here

impl Solution {
    pub fn split_string(s: String) -> bool {
        false
    }
}

// submission codes end

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    #[ignore]
    fn test_1849_example_1() {
        let s = "1234".to_string();

        let result = false;

        assert_eq!(Solution::split_string(s), result);
    }

    #[test]
    #[ignore]
    fn test_1849_example_2() {
        let s = "050043".to_string();

        let result = true;

        assert_eq!(Solution::split_string(s), result);
    }

    #[test]
    #[ignore]
    fn test_1849_example_3() {
        let s = "9080701".to_string();

        let result = false;

        assert_eq!(Solution::split_string(s), result);
    }
}

// Accepted solution for LeetCode #1849: Splitting a String Into Descending Consecutive Values
function splitString(s: string): boolean {
    const dfs = (i: number, x: number): boolean => {
        if (i >= s.length) {
            return true;
        }
        let y = 0;
        const r = x < 0 ? s.length - 1 : s.length;
        for (let j = i; j < r; ++j) {
            y = y * 10 + +s[j];
            if ((x < 0 || x - y === 1) && dfs(j + 1, y)) {
                return true;
            }
        }
        return false;
    };
    return dfs(0, -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^2)

Space

O(n)

Approach Breakdown

EXHAUSTIVE

O(nⁿ) time

O(n) space

Generate every possible combination without any filtering. At each of n positions we choose from up to n options, giving nⁿ total candidates. Each candidate takes O(n) to validate. No pruning means we waste time on clearly invalid partial solutions.

BACKTRACKING + PRUNING

O(n!) time

O(n) space

Backtracking explores a decision tree, but prunes branches that violate constraints early. Worst case is still factorial or exponential, but pruning dramatically reduces the constant factor in practice. Space is the recursion depth (usually O(n) for n-level decisions).

Shortcut: Backtracking time = size of the pruned search tree. Focus on proving your pruning eliminates most branches.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Missing undo step on backtrack

Wrong move: Mutable state leaks between branches.

Usually fails on: Later branches inherit selections from earlier branches.

Fix: Always revert state changes immediately after recursive call.