Leetcode #2019: The Score of Students Solving Math Expression
In this guide, we solve Leetcode #2019 The Score of Students Solving Math Expression in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given a string s that contains digits 0-9, addition symbols '+', and multiplication symbols '' only, representing a valid math expression of single digit numbers (e.g., 3+52). This expression was given to n elementary school students.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Stack, Memoization, Array, Hash Table, Math, String, Dynamic Programming
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: s = "7+3*1*2", answers = [20,13,42]
Output: 7
Explanation: As illustrated above, the correct answer of the expression is 13, therefore one student is rewarded 5 points: [20,13,42]
A student might have applied the operators in this wrong order: ((7+3)*1)*2 = 20. Therefore one student is rewarded 2 points: [20,13,42]
The points for the students are: [2,5,0]. The sum of the points is 2+5+0=7.
Python Solution
class Solution:
def scoreOfStudents(self, s: str, answers: List[int]) -> int:
def cal(s: str) -> int:
res, pre = 0, int(s[0])
for i in range(1, n, 2):
if s[i] == "*":
pre *= int(s[i + 1])
else:
res += pre
pre = int(s[i + 1])
res += pre
return res
n = len(s)
x = cal(s)
m = (n + 1) >> 1
f = [[set() for _ in range(m)] for _ in range(m)]
for i in range(m):
f[i][i] = {int(s[i << 1])}
for i in range(m - 1, -1, -1):
for j in range(i, m):
for k in range(i, j):
for l in f[i][k]:
for r in f[k + 1][j]:
if s[k << 1 | 1] == "+" and l + r <= 1000:
f[i][j].add(l + r)
elif s[k << 1 | 1] == "*" and l * r <= 1000:
f[i][j].add(l * r)
cnt = Counter(answers)
ans = cnt[x] * 5
for k, v in cnt.items():
if k != x and k in f[0][m - 1]:
ans += v << 1
return ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.