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Can you find the computational complexity of this problem?

Input: An array A of numbers

Output: An array B of numbers such that B[i] is the smallest number larger than A[i] in the subarray starting from A[i+1]. (X if no such number exists)

Example:

Input: [11, 69, 16, 81, 78, 94, 21, 20, 82, 91]

Output: [16, 78, 20, 82, 82, X, 82, 82, 91, X ]

Good upper bounds and lower bounds would do.

Input: An array A of numbers

Output: An array B of numbers such that B[i] is the smallest number larger than A[i] in the subarray starting from A[i+1]. (X if no such number exists)

Example:

Input: [11, 69, 16, 81, 78, 94, 21, 20, 82, 91]

Output: [16, 78, 20, 82, 82, X, 82, 82, 91, X ]

Good upper bounds and lower bounds would do.

Here's a question some friends and I had fun solving:

There's an infinite chess board (infinite in both dimensions), you have an army and the opponent has only a king left. You have to place your army on the board, then the opponent will place the king on the board. Your task is to capture the king (checkmate, no stalemate) in a finite number of moves.

How many pieces would you need in your army if your army is made up of:

Part a: only queens

Part b: only rooks

Part c: only bishops

Part d: only knights

There's an infinite chess board (infinite in both dimensions), you have an army and the opponent has only a king left. You have to place your army on the board, then the opponent will place the king on the board. Your task is to capture the king (checkmate, no stalemate) in a finite number of moves.

How many pieces would you need in your army if your army is made up of:

Part a: only queens

Part b: only rooks

Part c: only bishops

Part d: only knights

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Nexus 7 (2012, WiFi) battery problems!

tl;dr not even awake and charging, but battery still drains. Also, battery did not charge while tablet was off despite the tablet showing itself as charging.

I'm having serious trouble with my Nexus 7. First, the battery drained, the tablet went off and I couldn't charge it or turn it on. After doing some magic connecting to computer stuff Google recommended, it started working. I charged it fully and turned it on. As you can see in the pic, the battery continued draining while it was not awake and kept for charging (albeit with a MotoG charger). Somehow it charged a bit after waking it up. (Or maybe anomaly in data).

Confused, I turned it off and put it for charge so that I can get proper data. To my shock, when I turned it on hours later after leaving it on charge, it had not charged at all despite the screen showing charging symbols.

Has anybody had these problems? Any idea what I should do?

tl;dr not even awake and charging, but battery still drains. Also, battery did not charge while tablet was off despite the tablet showing itself as charging.

I'm having serious trouble with my Nexus 7. First, the battery drained, the tablet went off and I couldn't charge it or turn it on. After doing some magic connecting to computer stuff Google recommended, it started working. I charged it fully and turned it on. As you can see in the pic, the battery continued draining while it was not awake and kept for charging (albeit with a MotoG charger). Somehow it charged a bit after waking it up. (Or maybe anomaly in data).

Confused, I turned it off and put it for charge so that I can get proper data. To my shock, when I turned it on hours later after leaving it on charge, it had not charged at all despite the screen showing charging symbols.

Has anybody had these problems? Any idea what I should do?

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"The best reporting on social science statistics, like the best reporting in most areas, comes from The Onion"

- SlateStarCodex

- SlateStarCodex

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For what values of r can a circle of radius r intersect the graph of ln(x) 4 times?

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http://qr.ae/GKXLi

A very well written article on mapping patterns to integers.

A very well written article on mapping patterns to integers.

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http://qr.ae/GKXLi

A very very well written explanation of how you can map bitmaps to integers.

A very very well written explanation of how you can map bitmaps to integers.

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Oh no they didn't!! :D

**Google has epic comeback for Microsoft's latest smear campaign t-shirts**

“Microsoft’s latest venture comes as no surprise; competition in the wearables space is really heating up.” -Google

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Busy day in analytic number theory; Harald Helfgott has complemented his previous paper http://arxiv.org/abs/1205.5252 (obtaining minor arc estimates for the odd Goldbach problem) with major arc estimates, thus finally obtaining an unconditional proof of the odd Goldbach conjecture that every odd number greater than five is the sum of three primes. (This improves upon a result of mine from last year http://terrytao.wordpress.com/2012/02/01/every-odd-integer-larger-than-1-is-the-sum-of-at-most-five-primes/ showing that such numbers are the sum of five or fewer primes, though at the cost of a significantly lengthier argument.) As with virtually all successful partial results on the Goldbach problem, the argument proceeds by the Hardy-Littlewood-Vinogradov circle method; the challenge is to make all the estimates completely effective and to optimise all parameters (which, among other things, requires a certain amount of computer-assisted computation).

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I remember having a lot of fun when I was young playing this flight game where you have your homebase and your team of jets and you have to shoot down the opponents. You were safe at your homebase and had to go back to refuel. Graphics were obviously not good but gameplay was. My team kept alerting me where the enemy was, etc. I don't remember the name, if anyone here knows of any such or similar game, could you let me know?

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