Algorithm 5 Insert an Element into a Young Matrix

1:procedure YoungInsert( $Y, key$ )

2: $m = Y.\text{row-num}$

3: $n = Y.\text{col-num}$

4:if $Y[m, n] < \infty$ then

5:error "young matrix overflow"

6:end if

7:YoungDecreaseKey( $Y, m, n, key$ )

8:end procedure

10: // decrease $Y[i, j]$ down to $key$

11:procedure YoungDecreaseKey( $Y, i, j, key$ )

12:if $key > Y[i, j]$ then

13:error "new key is larger than the current key"

14:end if

15: $Y[i, j] = key$

16:while ( $i > 1$ and $Y[i - 1, j] > Y[i, j]$ ) or ( $j > 1$ and $Y[i, j - 1] > Y[i, j]$ ) do

17:if $Y[i - 1, j] > Y[i, j - 1]$ then

18:exchange $Y[i, j]$ with $Y[i - 1, j]$

19: $i = i - 1$

20:else

21:exchange $Y[i, j]$ with $Y[i, j - 1]$

22: $j = j - 1$

23:end if

24:end while

25:end procedure