Question

为什么分区方法的循环体永远不会抛出ArrayIndexOutOfBounds异常？

public static int partition( int[] a, low, high ) {

    int k = low, m = low;


    /* loop invariant:
    *     low <= k <= m <= high  and
    *     all elements in a[low..k-1] are RED (i.e., < pivot) and
    *     all elements in a[k..m-1] are BLUE (i.e., >= pivot)
    */
    while (m != high)  {
       if (a[m] >= pivot)     // a[m] is BLUE
          { }
       else  {                // a[m] is RED
          swap(a,k,m);
          k = k+1;
       }
       m = m+1;
    }
    return k;
 }

Answer 1

// m <= high (loop invariant)
while (m != high)  {
    // m < high, hence correct index
    a[m] ...

    m = m + 1;
    // m <= high (loop invariant)
}

心灵交换不会改变m。也许你认为k和m在哪里交换，但可能是[k]和[m]。由于m是局部int变量，因此int按值传递。

即使m和k在哪里交换：m <=高

循环不变量k <= m是helt：

// k <= m
if (...) {
    swap(a, k, m);
    // m <= old m // if call-by-reference

    k = k + 1;
    // k - 1 <= m if call-by-value
}
m = m + 1;
// k <= m again; if call-by-value

分区循环理解

1 个答案: