Problem Statement :-

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934

96983520312774506326239578318016984801869478851843

85861560789112949495459501737958331952853208805511

12540698747158523863050715693290963295227443043557

66896648950445244523161731856403098711121722383113

62229893423380308135336276614282806444486645238749

30358907296290491560440772390713810515859307960866

70172427121883998797908792274921901699720888093776

65727333001053367881220235421809751254540594752243

52584907711670556013604839586446706324415722155397

53697817977846174064955149290862569321978468622482

83972241375657056057490261407972968652414535100474

82166370484403199890008895243450658541227588666881

16427171479924442928230863465674813919123162824586

17866458359124566529476545682848912883142607690042

24219022671055626321111109370544217506941658960408

07198403850962455444362981230987879927244284909188

84580156166097919133875499200524063689912560717606

05886116467109405077541002256983155200055935729725

71636269561882670428252483600823257530420752963450

Solution :

One way to solve is :-

starting from the beginning 5 numbers (strating from the 1st), multiplying them, storing it in as max, continuing the process for the next 5 numbers(starting from the 2nd), replacing the max value if the current product is more than the max stored earlier and so on till we reach the last 5 elements.

We may minimize the number of iterations based on the fact that for every zero found we don't need to calculate the product.

Lucky Solution :-

I started looking for 99999 using "ctrl+F" (as I knew if I find this any where), this would be the max no matter what the other numbers are.

Since it was not there, I started looking for the combination of for 9's and one 8 (it was also not there) and so on, and eventually found 99879. Definitely, i was lucky to get the number in a minute or so (The data set for the problem was friendly, otherwise I would have probably coded it.

You may use another fact to code your logic. If you know the sum of n numbers x1+x2+..xn, the maximum value of their product is when x1=x2=..=xn.

For e.g. sum of 9,9,8,8,8 and 9,9,8,7,9 is equal, the product of 9,9,8,8,8 would be

larger (8+7+9 = 24 = 8+8+8).

## Saturday, November 14, 2009

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