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Undergraduate
By
JeffE
on June 6, 2012 | Updated Dec. 6, 2017
Longest increasing digital subsequence
Let \(S[1..n]\) be a sequence of integers between \(0\) and \(9\). A digital subsequence of \(S\) is a sequence \(D[1..k]\) of integers such that each integer \(D[i]\) is the numerical value of a sub…
Computer Science
Algorithms
dynamic programming
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Undergraduate
By
Shiva Kintali
on June 10, 2012 | Updated Dec. 6, 2017
Efficient cash register
You have a cash register that contains coins of denominations \(1 = d_{1} < d_{2} < \dots < d_{n}\). The register contains infinite number of coins of each denomination. A customer needs to get \(M\)…
Computer Science
Algorithms
dynamic programming
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Undergraduate
By
True Putnam
on June 7, 2012 | Updated Jan. 4, 2018
Putnam 2005 A1
Prove that every positive integer can be expressed as a sum of numbers of the kind \(2^i3^j\), where no term in the summation divides the other. For example : 1) 14 = 8 + 6 is a valid represent…
Computer Science
Mathematics
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dynamic programming
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Graduate
By
Shiva Kintali
on June 8, 2012 | Updated Dec. 6, 2017
Exact Algorithms for Subset Sum
Let \(a_1, a_2, \dots, a_n\) be natural numbers in the range \([1,M]\). Let \(b\) be another natural number. Subset Sum Problem is to decide if there is a subset \(S\) of indices \(1,2,\dots,n\) such …
Computer Science
Algorithms
dynamic programming
exponential algorithms
subset sum
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Undergraduate
By
Shiva Kintali
on Oct. 20, 2012 | Updated Dec. 6, 2017
Longest increasing subsequence
Give an \(O(n{\log}n)\) time algorithm to find the longest monotonically increasing subsequence of a sequence of \(n\) numbers.
Computer Science
Algorithms
dynamic programming
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