prithivMLmods/Coder-Stat

1 2<script type="text/x-mathjax-config">3  MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});4</script>5<script type='text/javascript' src='http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></script>6</script>7 8 9<h2>Problem A10Decimal Sequences</h2>11 12<p>13Hanako learned the conjecture that all the non-negative integers appear in the infinite digit sequence of the decimal representation of $\pi$ = 3.14159265..., the ratio of a circle's circumference to its diameter. After that, whenever she watches a sequence of digits, she tries to count up non-negative integers whose decimal representations appear as its subsequences.14</p>15 16<p>17For example, given a sequence "<span>3 0 1</span>", she finds representations of five non-negative integers 3, 0, 1, 30 and 301 that appear as its subsequences.18</p>19 20<p>21Your job is to write a program that, given a finite sequence of digits, outputs the smallest non-negative integer not appearing in the sequence. In the above example, 0 and 1 appear, but 2 does not. So, 2 should be the answer.22</p>23 24 25<h3>Input</h3>26<p>27The input consists of a single test case.<br>28<br>29 30$n$<br>31$d_1$ $d_2$ ... $d_n$<br>32<br>33 34$n$ is a positive integer that indicates the number of digits. Each of $d_k$'s $(k = 1, ... ,  n)$ is a digit. There is a space or a newline between $d_k$ and $d_{k+1}$ $(k = 1, ..., n - 1)$.35</p>36 37<p>38You can assume that $1 \leq n \leq 1000$.39</p>40 41 42<h3>Output</h3>43 44<p>45Print the smallest non-negative integer not appearing in the sequence.46</p>47 48 49<h3>Sample Input 1</h3>50 51<pre>3523 0 1</pre>53 54<h3>Sample Output 1</h3>55 56<pre>2</pre>57 58 59 60<h3>Sample Input 2</h3>61 62<pre>11639 8 7 6 5 4 3 2 1 1 0</pre>64 65<h3>Sample Output 2</h3>66 67<pre>12</pre>68 69 70 71<h3>Sample Input 3</h3>72 73<pre>10749 0 8 7 6 5 4 3 2 1</pre>75 76<h3>Sample Output 3</h3>77 78<pre>10</pre>79 80 81<h3>Sample Input 4</h3>82 83<pre>100843 6 7 5 3 5 6 2 9 1 2 7 0 9 3 6 0 6 2856 1 8 7 9 2 0 2 3 7 5 9 2 2 8 9 7 3 6861 2 9 3 1 9 4 7 8 4 5 0 3 6 1 0 6 3 2870 6 1 5 5 4 7 6 5 6 9 3 7 4 5 2 5 4 7884 4 3 0 7 8 6 8 8 4 3 1 4 9 2 0 6 8 9892 6 6 4 9</pre>90 91<h3>Sample Output 4</h3>92 93<pre>11</pre>94 95 96<h3>Sample Input 5</h3>97 98<pre>100997 2 7 5 4 7 4 4 5 8 1 5 7 7 0 5 6 2 01004 3 4 1 1 0 6 1 6 6 2 1 7 9 2 4 6 9 31016 2 8 0 5 9 7 6 3 1 4 9 1 9 1 2 6 4 21029 7 8 3 9 5 5 2 3 3 8 4 0 6 8 2 5 5 01036 7 1 8 5 1 4 8 1 3 7 3 3 5 3 0 6 0 61045 3 2 2 2</pre>105 106<h3>Sample Output 5</h3>107 108<pre>86</pre>109 110 111<h3>Sample Input 6</h3>112 113<pre>11143</pre>115 116<h3>Sample Output 6</h3>117 118<pre>0</pre>119