Book allocation problem leetcode

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Binary Search : Allocate books Binary search problem: Allocate library books with a minimum of a maximum number of pages. Given: N number of books are available. ( 1 . . . N ) Each book ‘x’ from 1 .. N has B [ x ] number of pages There are ‘S’ students. Book allocation criteria Criteria 1 : Allocate all the books. Criteria 2 : Each student is issued at least one book. Criteria 3 : Allocate the books in continuous order. Criteria 4 : Allocate the books such that the maximum number of pages of books issued to a student is minimum. Example: Consider 4 books with pages [ 10 , 32 , 70, 88 ] Number of students : 2 Possible allocations as below: Allocation 1 -> S1 : ( 10 ) S2 : ( 32 + 70 + 88 ) Max pages = 190 Allocation 2 -> S1 : ( 10 + 32 ) S2 : ( 70 + 88 ) Max pages = 158 Allocation 3 -> S1 : ( 10 + 32 + 70 ) S2 : ( 88 ) Max pages = 112 From the above 4 allocations, the minimum of max pages after the allocation is 112. Idea for solving the book allocation problem using binary search Case a) If the number of books is less than the number of students, then at least 1 student is not issued any book. Case b) If the number of books equals number of students, then each student gets a book. Thus the minimum of maximum pages allocated is maximum of ( B[1], B[2], … B[N] ). Use binary search to find the minimum of the maximum number of pages Example : Consider 4 books with pages [ 1, 2, 3, 4 ], and 2 students. Choose a very large number (INT_MAX) say 100 (maxpages) that we can allocate ...

Binary Search : Allocate books Binary search problem: Allocate library books with a minimum of a maximum number of pages. Given: N number of books are available. ( 1 . . . N ) Each book ‘x’ from 1 .. N has B [ x ] number of pages There are ‘S’ students. Book allocation criteria Criteria 1 : Allocate all the books. Criteria 2 : Each student is issued at least one book. Criteria 3 : Allocate the books in continuous order. Criteria 4 : Allocate the books such that the maximum number of pages of books issued to a student is minimum. Example: Consider 4 books with pages [ 10 , 32 , 70, 88 ] Number of students : 2 Possible allocations as below: Allocation 1 -> S1 : ( 10 ) S2 : ( 32 + 70 + 88 ) Max pages = 190 Allocation 2 -> S1 : ( 10 + 32 ) S2 : ( 70 + 88 ) Max pages = 158 Allocation 3 -> S1 : ( 10 + 32 + 70 ) S2 : ( 88 ) Max pages = 112 From the above 4 allocations, the minimum of max pages after the allocation is 112. Idea for solving the book allocation problem using binary search Case a) If the number of books is less than the number of students, then at least 1 student is not issued any book. Case b) If the number of books equals number of students, then each student gets a book. Thus the minimum of maximum pages allocated is maximum of ( B[1], B[2], … B[N] ). Use binary search to find the minimum of the maximum number of pages Example : Consider 4 books with pages [ 1, 2, 3, 4 ], and 2 students. Choose a very large number (INT_MAX) say 100 (maxpages) that we can allocate ...

• Xplore • • • • • • • A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. © Copyright 2023 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.

Binary Search : Allocate books Binary search problem: Allocate library books with a minimum of a maximum number of pages. Given: N number of books are available. ( 1 . . . N ) Each book ‘x’ from 1 .. N has B [ x ] number of pages There are ‘S’ students. Book allocation criteria Criteria 1 : Allocate all the books. Criteria 2 : Each student is issued at least one book. Criteria 3 : Allocate the books in continuous order. Criteria 4 : Allocate the books such that the maximum number of pages of books issued to a student is minimum. Example: Consider 4 books with pages [ 10 , 32 , 70, 88 ] Number of students : 2 Possible allocations as below: Allocation 1 -> S1 : ( 10 ) S2 : ( 32 + 70 + 88 ) Max pages = 190 Allocation 2 -> S1 : ( 10 + 32 ) S2 : ( 70 + 88 ) Max pages = 158 Allocation 3 -> S1 : ( 10 + 32 + 70 ) S2 : ( 88 ) Max pages = 112 From the above 4 allocations, the minimum of max pages after the allocation is 112. Idea for solving the book allocation problem using binary search Case a) If the number of books is less than the number of students, then at least 1 student is not issued any book. Case b) If the number of books equals number of students, then each student gets a book. Thus the minimum of maximum pages allocated is maximum of ( B[1], B[2], … B[N] ). Use binary search to find the minimum of the maximum number of pages Example : Consider 4 books with pages [ 1, 2, 3, 4 ], and 2 students. Choose a very large number (INT_MAX) say 100 (maxpages) that we can allocate ...

Binary Search : Allocate books Binary search problem: Allocate library books with a minimum of a maximum number of pages. Given: N number of books are available. ( 1 . . . N ) Each book ‘x’ from 1 .. N has B [ x ] number of pages There are ‘S’ students. Book allocation criteria Criteria 1 : Allocate all the books. Criteria 2 : Each student is issued at least one book. Criteria 3 : Allocate the books in continuous order. Criteria 4 : Allocate the books such that the maximum number of pages of books issued to a student is minimum. Example: Consider 4 books with pages [ 10 , 32 , 70, 88 ] Number of students : 2 Possible allocations as below: Allocation 1 -> S1 : ( 10 ) S2 : ( 32 + 70 + 88 ) Max pages = 190 Allocation 2 -> S1 : ( 10 + 32 ) S2 : ( 70 + 88 ) Max pages = 158 Allocation 3 -> S1 : ( 10 + 32 + 70 ) S2 : ( 88 ) Max pages = 112 From the above 4 allocations, the minimum of max pages after the allocation is 112. Idea for solving the book allocation problem using binary search Case a) If the number of books is less than the number of students, then at least 1 student is not issued any book. Case b) If the number of books equals number of students, then each student gets a book. Thus the minimum of maximum pages allocated is maximum of ( B[1], B[2], … B[N] ). Use binary search to find the minimum of the maximum number of pages Example : Consider 4 books with pages [ 1, 2, 3, 4 ], and 2 students. Choose a very large number (INT_MAX) say 100 (maxpages) that we can allocate ...

• Xplore • • • • • • • A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. © Copyright 2023 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.

• Xplore • • • • • • • A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. © Copyright 2023 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.

Binary Search : Allocate books Binary search problem: Allocate library books with a minimum of a maximum number of pages. Given: N number of books are available. ( 1 . . . N ) Each book ‘x’ from 1 .. N has B [ x ] number of pages There are ‘S’ students. Book allocation criteria Criteria 1 : Allocate all the books. Criteria 2 : Each student is issued at least one book. Criteria 3 : Allocate the books in continuous order. Criteria 4 : Allocate the books such that the maximum number of pages of books issued to a student is minimum. Example: Consider 4 books with pages [ 10 , 32 , 70, 88 ] Number of students : 2 Possible allocations as below: Allocation 1 -> S1 : ( 10 ) S2 : ( 32 + 70 + 88 ) Max pages = 190 Allocation 2 -> S1 : ( 10 + 32 ) S2 : ( 70 + 88 ) Max pages = 158 Allocation 3 -> S1 : ( 10 + 32 + 70 ) S2 : ( 88 ) Max pages = 112 From the above 4 allocations, the minimum of max pages after the allocation is 112. Idea for solving the book allocation problem using binary search Case a) If the number of books is less than the number of students, then at least 1 student is not issued any book. Case b) If the number of books equals number of students, then each student gets a book. Thus the minimum of maximum pages allocated is maximum of ( B[1], B[2], … B[N] ). Use binary search to find the minimum of the maximum number of pages Example : Consider 4 books with pages [ 1, 2, 3, 4 ], and 2 students. Choose a very large number (INT_MAX) say 100 (maxpages) that we can allocate ...

• Xplore • • • • • • • A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. © Copyright 2023 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.