Young tableaux. Suppose you have an n-by-n array of integers a [] [] such that, for all i and j, a[i] [j]< a[i+l] [j] and a[i] [j]< a[i] [j+1], as in the following the 5-by-5 array.
5 | 23 | 54 | 67 | 89 |
6 | 69 | 73 | 74 | 90 |
10 | 71 | 83 | 84 | 91 |
60 | 73 | 84 | 86 | 92 |
99 | 91 | 92 | 93 | 94 |
A two-dimensional array with this property is known as a Young tableaux. Write a function that takes as arguments an n-by-n Young tableaux and an integer, and determines whether the integer is in the Young tableaux. The order of growth of the running time of your function should be linear in n.
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