# Minimum number of days required to complete the work

Given N works numbered from 1 to N. Given two arrays D1[] and D2[] of N elements each. Also, each work number W(i) is assigned days, D1[i] and D2[i](*Such that, D2[i] < D1[i]*) either on which it can be completed.

Also, it is mentioned that each work has to completed according to **non-decreasing date of the array D1[]**.

The task is to find the **minimum number of days** required to complete the work in a non-decreasing order of days in D1[].

**Examples**:

Input :

N = 3

D1[] = {5, 3, 4}

D2[] = {2, 1, 2}

Output :2

Explanation:

3 works are to be completed. The first value on Line(i) is D1(i) and the second value is D2(i) where D2(i) < D1(i). The smart worker can finish the second work on Day 1 and then both third work and first work in Day 2, thus maintaining the non-decreasing order of D1[], [3 4 5].

Input :

N = 6

D1[] = {3, 3, 4, 4, 5, 5}

D2[] = {1, 2, 1, 2, 4, 4}

Output :4

### Recommended: Please try your approach on __{IDE}__ first, before moving on to the solution.

__{IDE}__**Approach:** The solution is greedy. The work(i) can be sorted by increasing D1[i], breaking the ties by increasing D2[i]. If we consider the works in this order, we can try to finish the works as early as possible. First of all complete the first work on D2[1]. Move to the second work. If we can complete it on day D2[2] such that (D2[1]<=D2[2]), do it. Otherwise, do the work on day D[2]. Repeat the process until we complete the N-th work, keeping the day of the latest work.

Below is the implementation of the above approach

## C++

`// C++ program to find the minimum ` `// number days required ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` `#define inf INT_MAX ` ` ` `// Function to find the minimum ` `// number days required ` `int` `minimumDays(` `int` `N, ` `int` `D1[], ` `int` `D2[]) ` `{ ` ` ` `// initialising ans to least value possible ` ` ` `int` `ans = -inf; ` ` ` ` ` `// vector to store the pair of D1(i) and D2(i) ` ` ` `vector<pair<` `int` `, ` `int` `> > vect; ` ` ` ` ` `for` `(` `int` `i = 0; i < N; i++) ` ` ` `vect.push_back(make_pair(D1[i], D2[i])); ` ` ` ` ` ` ` `// sort by first i.e D(i) ` ` ` `sort(vect.begin(), vect.end()); ` ` ` ` ` `// Calculate the minimum possible days ` ` ` `for` `(` `int` `i = 0; i < N; i++) { ` ` ` `if` `(vect[i].second >= ans) ` ` ` `ans = vect[i].second; ` ` ` `else` ` ` `ans = vect[i].first; ` ` ` `} ` ` ` ` ` `// return the answer ` ` ` `return` `ans; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `// Number of works ` ` ` `int` `N = 3; ` ` ` ` ` `// D1[i] ` ` ` `int` `D1[] = { 6, 5, 4 }; ` ` ` ` ` `// D2[i] ` ` ` `int` `D2[] = { 1, 2, 3 }; ` ` ` ` ` `cout<<minimumDays(N, D1, D2); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find the minimum ` `// number days required ` `import` `java.util.*; ` `import` `java.lang.*; ` `import` `java.io.*; ` ` ` `// pair class for number of days ` `class` `Pair ` `{ ` ` ` `int` `x, y; ` ` ` ` ` `Pair(` `int` `a, ` `int` `b) ` ` ` `{ ` ` ` `this` `.x = a; ` ` ` `this` `.y = b; ` ` ` `} ` `} ` ` ` `class` `GFG ` `{ ` `static` `int` `inf = Integer.MIN_VALUE; ` ` ` `// Function to find the minimum ` `// number days required ` `public` `static` `int` `minimumDays(` `int` `N, ` `int` `D1[], ` ` ` `int` `D2[]) ` `{ ` ` ` `// initialising ans to ` ` ` `// least value possible ` ` ` `int` `ans = -inf; ` ` ` ` ` `ArrayList<Pair> ` ` ` `list = ` `new` `ArrayList<Pair>(); ` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < N; i++) ` ` ` `list.add(` `new` `Pair(D1[i], D2[i])); ` ` ` ` ` `// sort by first i.e D(i) ` ` ` `Collections.sort(list, ` `new` `Comparator<Pair>() ` ` ` `{ ` ` ` `@Override` ` ` `public` `int` `compare(Pair p1, Pair p2) ` ` ` `{ ` ` ` `return` `p1.x - p2.x; ` ` ` `} ` ` ` `}); ` ` ` `// Calculate the minimum possible days ` `for` `(` `int` `i = ` `0` `; i < N; i++) ` `{ ` ` ` `if` `(list.get(i).y >= ans) ` ` ` `ans = list.get(i).y; ` ` ` `else` ` ` `ans = list.get(i).x; ` `} ` ` ` `return` `ans; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main (String[] args) ` `{ ` ` ` `// Number of works ` ` ` `int` `N = ` `3` `; ` ` ` ` ` `// D1[i] ` ` ` `int` `D1[] = ` `new` `int` `[]{` `6` `, ` `5` `, ` `4` `}; ` ` ` ` ` `// D2[i] ` ` ` `int` `D2[] = ` `new` `int` `[]{` `1` `, ` `2` `, ` `3` `}; ` ` ` ` ` `System.out.print(minimumDays(N, D1, D2)); ` `} ` `} ` ` ` `// This code is contributed by Kirti_Mangal ` |

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**Output:**

6

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