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50 lines
2.2 KiB
HTML
50 lines
2.2 KiB
HTML
<!DOCTYPE html>
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
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<h1>1136. A Delayed Palindrome (20)</h1>
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<div id="problemContent">
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<p>Consider a positive integer N written in standard notation with k+1 digits a<sub>i</sub> as a<sub>k</sub>...a<sub>1</sub>a<sub>0</sub> with 0 <= a<sub>i</sub> < 10 for all i and a<sub>k</sub> > 0. Then N is <b>palindromic</b> if and only if a<sub>i</sub> = a<sub>k-i</sub> for all i. Zero is written 0 and is also palindromic by definition.
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</p>
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<p>
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Non-palindromic numbers can be paired with palindromic ones via a series of operations. First, the non-palindromic number is reversed and the result is added to the original number. If the result is not a palindromic number, this is repeated until it gives a palindromic number. Such number is called <b>a delayed palindrome</b>. (Quoted from https://en.wikipedia.org/wiki/Palindromic_number)
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</p>
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<p>
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Given any positive integer, you are supposed to find its paired palindromic number.
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</p>
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<p><b>
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Input Specification:
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</b></p>
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<p>Each input file contains one test case which gives a positive integer no more than 1000 digits.</p>
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<p><b>
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Output Specification:
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</b></p>
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<p>For each test case, print line by line the process of finding the palindromic number. The format of each line is the following:</p><pre>
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A + B = C
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</pre>
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<p>
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where A is the original number, B is the reversed A, and C is their sum. A starts being the input number, and this process ends until C becomes a palindromic number -- in this case we print in the last line "C is a palindromic number."; or if a palindromic number cannot be found in 10 iterations, print "Not found in 10 iterations." instead.
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</p>
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<b>Sample Input 1:</b><pre>
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97152
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</pre>
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<b>Sample Output 1:</b><pre>
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97152 + 25179 = 122331
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122331 + 133221 = 255552
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255552 is a palindromic number.
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</pre>
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<b>Sample Input 2:</b><pre>
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196
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</pre>
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<b>Sample Output 2:</b><pre>
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196 + 691 = 887
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887 + 788 = 1675
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1675 + 5761 = 7436
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7436 + 6347 = 13783
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13783 + 38731 = 52514
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52514 + 41525 = 94039
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94039 + 93049 = 187088
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187088 + 880781 = 1067869
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1067869 + 9687601 = 10755470
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10755470 + 07455701 = 18211171
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Not found in 10 iterations.
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</pre>
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</div> |