857639. Grinding Geek
Here is the Markdown blog post for the Grinding Geek problem:
Grinding Geek
Summary
The Grinding Geek problem involves simulating a grinding process where a geek's skill level increases based on their current level and effort. The goal is to determine when the geek will finally reach a target skill level, considering the effort required to increase their skills at each step.
This problem requires an understanding of dynamic programming concepts, as it involves breaking down a complex problem into smaller subproblems and solving them recursively.
Detailed Explanation
To solve this problem, we can use dynamic programming. We create a 2D array dp where dp[i][j] represents the skill level the geek will reach after j efforts when their current skill level is i.
Here's the step-by-step breakdown of the solution:
- Initialize the
dparray with zeros, wheredp[0][j] = 0for allj, anddp[i][0] = ifor alli. - For each effort level
jfrom 1 toefforts, iterate through the skill levels from0tocurrent_skill. For each skill leveli, calculate the new skill levelnew_skillusing the formulai + (effort - current_skill) / 3. - Update the
dparray by settingdp[i][j] = max(dp[i-1][j-1], dp[new_skill][j-1]). This represents the maximum skill level the geek can reach afterjefforts, given their current skill level isi. - Find the smallest
jsuch thatdp[current_skill][j] >= target_skill, which represents the minimum number of efforts required to reach the target skill level.
Time complexity: O(efforts * current_skill) Space complexity: O(efforts * current_skill)
Optimized Solutions
Java
public int grindingGeek(int currentSkill, int efforts, int targetSkill) {
int[][] dp = new int[currentSkill + 1][efforts + 1];
for (int i = 0; i <= currentSkill; i++) {
dp[i][0] = i;
}
for (int j = 1; j <= efforts; j++) {
for (int i = 0; i <= currentSkill; i++) {
int newSkill = Math.max(i, (i + (j - 1) / 3));
dp[i][j] = Math.max(dp[i-1][j-1], dp[newSkill][j-1]);
}
}
for (int j = efforts; j >= 0; j--) {
if (dp[currentSkill][j] >= targetSkill) {
return j;
}
}
return -1; // not reachable
}