Minimum Number of Operations to Make String Sorted — LeetCode 1830 Python Solution

The problem

You are given a string s (0-indexed)​​​​​​. You are asked to perform the following operation on s​​​​​​ until you get a sorted string: Find the largest index i such that 1 <= i < s.length and s[i] < s[i - 1].

Example

Input

s = "cba"

Output

5

Explanation

The simulation goes as follows:

Python solution

n = 3010
mod = 10**9 + 7
f = [1] + [0] * n
g = [1] + [0] * n

for i in range(1, n):
    f[i] = f[i - 1] * i % mod
    g[i] = pow(f[i], mod - 2, mod)


class Solution:
    def makeStringSorted(self, s: str) -> int:
        cnt = Counter(s)
        ans, n = 0, len(s)
        for i, c in enumerate(s):
            m = sum(v for a, v in cnt.items() if a < c)
            t = f[n - i - 1] * m
            for v in cnt.values():
                t = t * g[v] % mod
            ans = (ans + t) % mod
            cnt[c] -= 1
            if cnt[c] == 0:
                cnt.pop(c)
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1830. Minimum Number of Operations to Make String Sorted is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Combinatorics.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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