/* Search for the position of "value".
*
* 在集合is的底层数组中查找值value所在的索引。
*
* Return 1 when the value was found and
* sets "pos" to the position of the value within the intset.
*
* 成功找到value时，函数返回1，并将*pos的值设为value所在的索引。
*
* Return 0 when
* the value is not present in the intset and sets "pos" to the position
* where "value" can be inserted.
*
* 当在数组中没找到value时，返回0。
* 并将*pos的值设为value可以插入到数组中的位置。
*
* T = O(logN)
*/
static uint8_t intsetSearch(intset *is, int64_t value, uint32_t *pos) {
int min = 0, max = intrev32ifbe(is->length)-1, mid = -1;
int64_t cur = -1;
/* The value can never be found when the set is empty */
// 处理is为空时的函数
if (intrev32ifbe(is->length) == 0) {
if (pos) *pos = 0;
return 0;
} else {
/* Check for the case where we know we cannot find the value,
* but do know the insert position. */
// 因为底层数组是有序的，如果value比数组中最后一个值都要大
// 那么value肯定不存在于集合中，并且应该将value添加到底层数组的最末端
if (value > _intsetGet(is,intrev32ifbe(is->length)-1)) {
if (pos) *pos = intrev32ifbe(is->length);
return 0;
// 因为底层数组是有序的，如果value比数组中最前一个值都要小
// 那么value肯定不存在于集合中，并且应该将它添加到底层数组的最前端
} else if (value < _intsetGet(is,0)) {
if (pos) *pos = 0;
return 0;
}
}
// 在有序数组中进行二分查找
// T = O(logN)
while(max >= min) {
mid = ((unsigned int)min + (unsigned int)max) >> 1;
cur = _intsetGet(is,mid);
if (value > cur) {
min = mid+1;
} else if (value < cur) {
max = mid-1;
} else {
break;
}
}
// 检查是否已经找到了value
if (value == cur) {
if (pos) *pos = mid;
return 1;
} else {
if (pos) *pos = min;
return 0;
}
}
void intsetRepr(intset *is) {
int i;
for (i = 0; i < is->length; i++) {
printf("%lld\n", (uint64_t)_intsetGet(is,i));
}
printf("\n");
}
/* Sets the value to the value at the given position. When this position is
* out of range the function returns 0, when in range it returns 1. */
uint8_t intsetGet(intset *is, uint32_t pos, int64_t *value) {
if (pos < is->length) {
*value = _intsetGet(is,pos);
return 1;
}
return 0;
}
/*
* 查找 value 在 is 中的索引
*
* 查找成功时，将索引保存到 pos ，并返回 1 。
* 查找失败时，返回 0 ，并将 value 可以插入的索引保存到 pos 。
*
* T = O(lg N)
*/
static uint8_t intsetSearch(intset *is, int64_t value, uint32_t *pos) {
int min = 0,
max = intrev32ifbe(is->length)-1,
mid = -1;
int64_t cur = -1;
/* The value can never be found when the set is empty */
if (intrev32ifbe(is->length) == 0) {
// is 为空时，总是查找失败
if (pos) *pos = 0;
return 0;
} else {
/* Check for the case where we know we cannot find the value,
* but do know the insert position. */
if (value > _intsetGet(is,intrev32ifbe(is->length)-1)) {
// 值比 is 中的最后一个值(所有元素中的最大值)要大
// 那么这个值应该插入到 is 最后
if (pos) *pos = intrev32ifbe(is->length);
return 0;
} else if (value < _intsetGet(is,0)) {
// value 作为新的最小值，插入到 is 最前
if (pos) *pos = 0;
return 0;
}
}
// 在 is 元素数组中进行二分查找
while(max >= min) {
mid = (min+max)/2;
cur = _intsetGet(is,mid);
if (value > cur) {
min = mid+1;
} else if (value < cur) {
max = mid-1;
} else {
break;
}
}
if (value == cur) {
if (pos) *pos = mid;
return 1;
} else {
if (pos) *pos = min;
return 0;
}
}
/* Search for the position of "value". Return 1 when the value was found and
* sets "pos" to the position of the value within the intset. Return 0 when
* the value is not present in the intset and sets "pos" to the position
* where "value" can be inserted.
*
* 在intset中找到value所在位置。
* 如果找到就返回1并且将pos的值设为value所在位置
* 如果没找到就返回0并且将pos的值设为value应该插入的位置
* */
static uint8_t intsetSearch(intset *is, int64_t value, uint32_t *pos) {
int min = 0, max = intrev32ifbe(is->length)-1, mid = -1;
int64_t cur = -1;
/* The value can never be found when the set is empty */
if (intrev32ifbe(is->length) == 0) {
//空集时直接返回0
if (pos) *pos = 0;
return 0;
} else {
/* Check for the case where we know we cannot find the value,
* but do know the insert position. */
if (value > _intsetGet(is,intrev32ifbe(is->length)-1)) {
//整数集为有序集，最后一个元素为最大的数，比它还大则说明value不在集合中
if (pos) *pos = intrev32ifbe(is->length);
return 0;
} else if (value < _intsetGet(is,0)) {
//第一个元素为最小值，比它小则说明value不在集合中
if (pos) *pos = 0;
return 0;
}
}
//使用二分法查找元素
while(max >= min) {
mid = (min+max)/2;
cur = _intsetGet(is,mid);
if (value > cur) {
min = mid+1;
} else if (value < cur) {
max = mid-1;
} else {
break;
}
}
if (value == cur) {
//找到元素，将pos设为mid
if (pos) *pos = mid;
return 1;
} else {
//没找到元素，将pos设为min即该插入得位置
if (pos) *pos = min;
return 0;
}
}
/* Search for the position of "value". Return 1 when the value was found and
* sets "pos" to the position of the value within the intset. Return 0 when
* the value is not present in the intset and sets "pos" to the position
* where "value" can be inserted. */
static uint8_t intsetSearch(intset *is, int64_t value, uint32_t *pos) {
int min = 0, max = intrev32ifbe(is->length)-1, mid = -1;
int64_t cur = -1;
/* The value can never be found when the set is empty */
// 集合为空
if (intrev32ifbe(is->length) == 0) {
if (pos) *pos = 0;
return 0;
} else {
/* Check for the case where we know we cannot find the value,
* but do know the insert position. */
// value 比最大元素还大
if (value > _intsetGet(is,intrev32ifbe(is->length)-1)) {
if (pos) *pos = intrev32ifbe(is->length);
return 0;
// value 比最小元素还小
} else if (value < _intsetGet(is,0)) {
if (pos) *pos = 0;
return 0;
}
}
// 二分查找
while(max >= min) {
mid = (min+max)/2;
cur = _intsetGet(is,mid);
if (value > cur) {
min = mid+1;
} else if (value < cur) {
max = mid-1;
} else {
break;
}
}
if (value == cur) {
if (pos) *pos = mid;
return 1;
} else {
if (pos) *pos = min;
return 0;
}
}
static uint8_t intsetSearch(intset *is, int64_t value, uint32_t *pos) {
int min = 0, max = intrev32ifbe(is->length)-1, mid = -1;
int64_t cur = -1;
/* The value can never be found when the set is empty */
if (intrev32ifbe(is->length) == 0) { // set 为空
if (pos) *pos = 0;
return 0;
} else { // set 不为空
/* Check for the case where we know we cannot find the value,
* but do know the insert position. */
// intset 中存储的数是按从小到大的顺序存储的
if (value > _intsetGet(is,intrev32ifbe(is->length)-1)) {
if (pos) *pos = intrev32ifbe(is->length);
return 0;
} else if (value < _intsetGet(is,0)) {
if (pos) *pos = 0;
return 0;
}
}
// 二分查找
while(max >= min) {
mid = ((unsigned int)min + (unsigned int)max) >> 1; // 除2
cur = _intsetGet(is,mid); // 获取值得大小
if (value > cur) {
min = mid+1; // 每次加减一位
} else if (value < cur) {
max = mid-1;
} else {
break;
}
} // 跳出循环 max < min
if (value == cur) {
if (pos) *pos = mid;
return 1; // 找到
} else {
if (pos) *pos = min;
return 0; // 没有找到
}
}
/*
* 取出集合底层数组指定位置中的值，并将它保存到value指针中。
*
* 如果pos没超过数组的索引范围，那么返回-1，如果超出索引，那么返回0。
*
* p.s.上面原文的文档说这个函数用于设置值，这是错误的。
*
* T = O(1)
*/
uint8_t intsetGet(intset *is, uint32_t pos, int64_t *value) {
// pos < intrev32ifbe(is->length)
// 检查pos是否符合数组的范围
if (pos < intrev32ifbe(is->length)) {
// 保存值到指针
*value = _intsetGet(is,pos);
// 返回成功指示值
return 1;
}
// 超出索引范围
return 0;
}
/* Return random member */
int64_t intsetRandom(intset *is) {
return _intsetGet(is,rand()%is->length);
}
/*
* 随机返回一个 intset 里的元素
*
* T = theta(1)
*/
int64_t intsetRandom(intset *is) {
return _intsetGet(is,rand()%intrev32ifbe(is->length));
}
static void intsetRepr(intset *is) {
for (uint32_t i = 0; i < intrev32ifbe(is->length); i++) {
printf("%lld\n", (uint64_t)_intsetGet(is,i));
}
printf("\n");
}
/* Return random member
*
* 从整数集合中随机返回一个元素
*
* 只能在集合非空时使用
*
* T = O(1)
*/
int64_t intsetRandom(intset *is) {
// intrev32ifbe(is->length)取出集合的元素数量
// 而rand() % intrev32ifbe(is->length)根据元素数量计算一个随机索引
// 然后_intsetGet负责根据随机索引来查找值
return _intsetGet(is,rand()%intrev32ifbe(is->length));
}