计数阵列号对索引的总数,使得改编[1] - ; ARR [J]和I&LT; Ĵ [英] Count total number pairs of indices in array such that arr[i] < arr[j] and i < j
问题描述
为了问这个<一href="http://stackoverflow.com/questions/13791288/count-all-pairs-of-indices-in-array-such-that-arri-arrj">here但因为我忘了提及对指数的条件下,创造了新的问题。
Meant to ask this here but since I forgot to mention the condition on the indices, creating a new question.
现在的问题是给予排序的数组,找到对指数 I,J
,使得总数I&LT; Ĵ
和改编[1] - ; ARR [J]
。复杂性应该是线性的或接近它。
The question is given an unsorted array, find the total number of pairs of indices i, j
such that i < j
and arr[i] < arr[j]
. Complexity should be linear or as close to it.
推荐答案
如果目标是要找到对 I&LT数量; Ĵ
,使得改编[1] - GT;改编[j]的
,这将是反转计数,可通过合并排序阵列和计数多少值的每个项目被移动过去被确定。
If the target were to find the number of pairs i < j
such that arr[i] > arr[j]
, it would be the inversion count, that can be determined by merge-sorting the array and counting how many values each item is moved past.
在这里,我们可以做同样的,如果我们按降序排序。
Here, we can do the same, if we sort in descending order.
int pairs_count(int[] arr, int lo, int hi) {
if (hi <= lo) return 0;
int mid = (lo+hi)/2;
int count = pairs_count(arr, lo, mid);
count += pairs_count(arr, mid+1,hi);
count += merge(arr, lo, mid, hi);
return count;
}
int merge(int[] arr, int lo, int mid, int hi) {
int[] scratch = new int[hi-lo+1];
int l = lo, r = mid+1, k = 0, count = 0;
while(l <= mid && r <= hi) {
if (arr[r] > arr[l]) {
scratch[k++] = arr[r++];
count += mid-l+1;
} else {
scratch[k++] = arr[l++];
}
}
while(l <= mid) {
scratch[k++] = arr[l++];
}
while(r <= hi) {
scratch[k++] = arr[r++];
}
for(k = 0; k < scratch.length; ++k) {
arr[lo+k] = scratch[k];
}
retrun count;
}
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