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ISI2014PCBA1a
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Let $x=(x_1, x_2, \dots x_n) \in \{0,1\}^n$ By $H(x)$ we mean the number of 1's in $(x_1, x_2, \dots x_n)$. Prove that $H(x) = \frac{1}{2} (n\Sigma^n_{i=1} (1)^{x_i})$.
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May 30, 2016
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What do we mean by 'x'? Is it the set of n, nbit binary numbers? How do we build set x? How do we consider the elements in set x?
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ISI2014PCBA2a
Let $A$ be a $30 \times 40$ matrix having $500$ nonzero entries. For $1 \leq i \leq 30$, let $r_i$ be the number of nonzero entries in the $i$th row, and for $1 \leq j \leq 40$, let $m_j$ be the number of nonzero entries in the $j$th column. Show that there is a k such that $1 \leq k \leq 30$, $r_k \geq 17$ and there is an $l$ such that $1 \leq l \leq 40$, $m_l \leq 12$.
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May 31, 2016
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Numerical Ability
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ISI2014PCBA1b
Let $x, y$ be two nonnegative integers $< 2^{32}$. By $x \wedge y$ we mean the integer represented by the bitwise logical $AND$ of the 32 bit binary representations of $x$ and $y$. For example, if $x = 13$ and $y = 6$, then $x \wedge y$ ... the pseudocode for the input $x = 13$? What will be the output of the pseudocode for an arbitrary nonnegative integer $x < 2^{32}$?
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May 30, 2016
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Algorithms
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jothee
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ISI2014PCBA2b
Let $A$ be a 30 40 matrix having 500 nonzero entries. For $1 \leq i \leq 30$, let $r_i$ be the number of nonzero entries in the $i$th row, and for $1 \leq j \leq 40$, let $m_j$ be the number of nonzero entries in the $j$th column ... of the stack contains the value $max_{1\leq i \leq 30} r_i$. Write pseudocode for creating such a stack using a single scan of the matrix $A$.
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Jun 8, 2016
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Arjun
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ISI2012PCBA1a
A group of $15$ boys plucked a total of $100$ apples. Prove that two of those boys plucked the same number of apples.
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Jun 2, 2016
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