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Minimum Difficulty of a Job Schedule in C++
Suppose we want to schedule a list of tasks in d days. The tasks are dependent so, to work on the i-th task, we have to finish all the tasks j where 0 <= j < i.
We have to finish at least one task in each day. The difficulty of a task schedule is actually the sum of difficulties of each day of the d number of days. The difficulty of a day is the maximum difficulty of a task that done in that day.
So we have an array of integers called taskDifficulty and an integer d. The difficulty of the i-th job is taskDifficulty[i]. We have to find the minimum difficulty of a task schedule. If we cannot find a schedule for the tasks, then return -1.
So, if the input is like taskDifficulty = [6,5,4,3,2,1], d = 2,
then the output will be 7, as on the day 1 we can finish the first 5 jobs, the total difficulty is 6. Now on day 2 we can finish the last job, total difficulty is 1, so the difficulty of the schedule will be 6 + 1 = 7.
To solve this, we will follow these steps −
Define a function solve(), this will take an array v, idx, k, one 2D dp,
if idx is same as size of v and k is same as 0, then −
return 0
if k < 0 or idx is same as size of v and k > 0, then −
return 1^6
if dp[idx, k] is not equal to -1, then −
return dp[idx, k]
maxVal := 0
ret := inf
for initialize i := idx, when i < size of v, update (increase i by 1), do −
maxVal := maximum of v[i] and maxVal
ret := minimum of ret and maxVal + solve(v, i + 1, k - 1, dp)
dp[idx, k] := ret
return ret
From the main method do the following −
n := size of j
if d > n, then −
return -1
Define one 2D array dp of size n x (d + 1) and fill this with -1
return solve(j, 0, d, dp)
Let us see the following implementation to get better understanding −
Example
#include <bits/stdc++.h> using namespace std; class Solution { public: int solve(vector<int>& v, int idx, int k, vector<vector<int> >& dp){ if (idx == v.size() && k == 0) return 0; if (k < 0 || idx == v.size() && k > 0) return 1e6; if (dp[idx][k] != -1) return dp[idx][k]; int maxVal = 0; int ret = INT_MAX; for (int i = idx; i < v.size(); i++) { maxVal = max(v[i], maxVal); ret = min(ret, maxVal + solve(v, i + 1, k - 1, dp)); } return dp[idx][k] = ret; } int minDifficulty(vector<int>& j, int d){ int n = j.size(); if (d > n) return -1; vector<vector<int> > dp(n, vector<int>(d + 1, -1)); return solve(j, 0, d, dp); } }; main(){ Solution ob; vector<int> v = {6,5,4,3,2,1}; cout << (ob.minDifficulty(v, 2)); }
Input
{6,5,4,3,2,1}, 2
Output
7
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