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POThe puzzle of Liars
 

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    <p>I have been trying to solve a puzzle in <a href="https://www.interviewstreet.com/challenges/dashboard/#problem/4f9ea7df7d5c6" rel="nofollow">Interviewstreet</a>. But I don't have a clue for the problem by now. It'll be great if someone can give me a hint.</p> <p>The puzzle is: You have N soldiers numbered from 1 to N. Each of your soldiers is either a liar or a truthful person. You have M sets of information about them. The information is of the following form:</p> <p>Each line contains 3 integers - A, B and C. This means that in the set of soldiers numbered as {A, A+1, A+2, ..., B}, exactly C of them are liars. There are M lines like the above.</p> <p>Let L be the total number of your liar soldiers. Since you can't find the exact value of L, you want to find the minimum and maximum value of L.</p> <p>Input:</p> <p>The first line of the input contains two integers N and M. Each of next M lines contains three integers - A, B and C (1 &lt;= Ai &lt;= Bi &lt;= n) and (0 &lt;= Ci &lt;= Bi-Ai). where Ai, B i and C i refers to the values of A, B and C in the ith line respectively N and M are not more than 101, and it is guaranteed the given informations are satisfiable. You can always find a situation that satisfies the given information .</p> <p>Output:</p> <p>Print two integers Lmin and Lmax to the output.</p> <p>Sample Input</p> <pre><code>3 2 1 2 1 2 3 1 </code></pre> <p>Sample Output</p> <pre><code>1 2 </code></pre> <p>Sample Input</p> <pre><code>20 11 3 8 4 1 9 6 1 13 9 5 11 5 4 19 12 8 13 5 4 8 4 7 9 2 10 13 3 7 16 7 14 19 4 </code></pre> <p>Sample Output</p> <pre><code>13 14 </code></pre> <p>Explanation</p> <p>In the first sample testcase the first line is "3 2", meaning that there are 3 soldiers and we have two sets of information. The first information is that in the set of soldiers {1, 2} one is a liar and the second piece of information is that in the set of soldiers {2,3} again there is one liar. Now there are two possibilities for this scenario: Soldiers number 1 and 3 are liars or soldier number 2 is liar. So the minimum number of liars is 1 and maximum number of liars is 2. Hence the answer, 1 2.</p>
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