Maximum Difference by Remapping a Digit — Easy Problem & Solution

Problem statement

Pick one digit d and one digit e (possibly the same) and replace every occurrence of d in num with e. Leading zeros are allowed in the result.

Do this once to get the largest possible value and once to get the smallest, and return the difference.

Example 1

Input: num = 11891
Output: 99009
Explanation: Mapping 1 → 9 gives 99899; mapping 1 → 0 gives 00890, i.e. 890.

Example 2

Input: num = 90
Output: 99
Explanation: Mapping 0 → 9 gives 99; mapping 9 → 0 gives 00.

Example 3

Input: num = 999
Output: 999
Explanation: Already maximal; mapping 9 → 0 gives 0.

Constraints

• 1 <= num <= 1000000000

How to solve Maximum Difference by Remapping a Digit

Place value decides everything: raising the most significant digit that can be raised beats any change further right, and lowering the leading digit to 0 is the biggest possible reduction.

Approach

1. Render num as a string.
2. For the maximum, find the first character that is not '9' and replace every copy of it with '9'; if there is none, the number is already maximal.
3. For the minimum, replace every copy of the leading character with '0'.
4. Return the difference of the two parsed values.

Why it works

Changing a digit at position i alters the value by at least 10^(len-1-i), which dominates any change at a later position — so the leftmost changeable digit is the one to pick. Mapping it to 9 is the largest increase available and mapping the leading digit to 0 the largest decrease; other occurrences of the same digit only help, since they move in the same direction.

Complexity

• Time — O(d) in the number of digits
• Space — O(d)

Pitfalls

• A number of all 9s has no digit to raise — the maximum is the number itself.
• Leading zeros are permitted, so "00890" parses to 890 rather than being rejected.
• The replacement is global: every copy of the chosen digit changes, not just the first.

Reference solution

Python

def minMaxDifference(num: int) -> int:
    s = str(num)
    hi = s
    for ch in s:
        if ch != "9":
            hi = s.replace(ch, "9")
            break
    lo = s.replace(s[0], "0")
    return int(hi) - int(lo)

JavaScript

var minMaxDifference = function(num) {
    var s = String(num);
    var maxS = s;
    for (var i = 0; i < s.length; i++) {
        if (s.charAt(i) !== "9") {
            maxS = s.split(s.charAt(i)).join("9");
            break;
        }
    }
    var minS = s.split(s.charAt(0)).join("0");
    return parseInt(maxS, 10) - parseInt(minS, 10);
};

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