NSArray -> 找到最接近的值 - 最快的方法

Question

假设我已经订购了NSArray 的NSNumbers：

2, 4, 8, 15, 16, 20 // for simplicity let's treat it as array of int's instead of NSNumbers

现在我需要找到最接近的索引，比如value == 19。

searchValue = 19;
minIndex = 0;
maxIndex = array.count - 1;
currentIndex = (int)floorf(maxIndex / 2.f);

while (maxIndex - minIndex == 1) {
    if (array[currentIndex] < searchValue) { // go right
        minIndex = currentIndex;
    } else if (array[currentIndex] > searchValue) { // go left
        maxIndex = currentIndex;
    } else { // exact value, rather low probability of happening
        return currentIndex;
    }

    currentIndex = (int)floorf((maxIndex - minIndex) / 2.f);
}

// let's check values around, who has smaller difference
int leftDifference = (currentIndex - 1 >= 0) ? abs(array[currentIndex - 1] - searchValue) : INT_MAX;
int rightDifference = (currentIndex + 1 < array.count) ? abs(array[currentIndex + 1] - searchValue) : INT_MAX;
int centralDifference = abs(array[currentIndex] - searchValue);
if (leftDifference < rightDifference && leftDifference < centralDifference) {
    return currentIndex - 1;
} else if () {
    return currentIndex + 1;
} else {
    return currentIndex;
}

这是我能想象到的最快的方式，也许有人有不同的想法？如何改进算法？

我查看了 egSOF question，但它搜索值而不是索引，并通过浏览所有值来实现。在索引的情况下，我们不必浏览整个数组。

Answer 1

假设你有一个 NSNumbers 数组：

NSArray *array = @[@(2), @(4), @(8), @(15), @(16), @(20)];

您正在寻找myValue，如下所示：

NSNumber *myValue = @(17);

使用indexOfObject:inSortedRange:options:usingComparator 方法查找最接近您的值的数组索引。二进制搜索具有 O(log n) 性能，因此非常快。

NSInteger searchIndex = MIN([array indexOfObject: myValue inSortedRange:NSMakeRange(0, array.count)
                                   options:NSBinarySearchingFirstEqual | NSBinarySearchingInsertionIndex
                           usingComparator:^NSComparisonResult(NSNumber *obj1, NSNumber *obj2) {
                               return [obj1 compare:obj2];
                           }], [array count] - 1);

然后在searchIndex - 1 索引上检查是否存在与您的myValue 最接近的数字：

if (searchIndex > 0) {
    CGFloat leftHandDiff = ABS(((NSNumber *)array[searchIndex - 1]).floatValue - myValue.floatValue);
    CGFloat rightHandDiff = ABS(((NSNumber *)array[searchIndex]).floatValue - myValue.floatValue);

    if (leftHandDiff == rightHandDiff) {
        //here you can add behaviour when your value is in the middle of range
        NSLog(@"given value is in the middle");
    } else if (leftHandDiff < rightHandDiff) {
        searchIndex--;
    }
}

NSLog(@"The nearest value to %f is %d in array at index %d", myValue.floatValue, array[searchIndex], searchIndex);

瞧！现在你现在是最接近myValue 的值。

记住您的array 必须按升序排序才能实现此技巧。