最大子数组问题－Swift 3.0 实现

主要使用分治算法
FindMaxSubArray.swift如下：

//Max SubArray

func findMaxCrossingSubarray(arr: [Int], low: Int, mid: Int, high: Int) -> (max_left: Int, max_right: Int, sum: Int) {
    print("start findMaxCrossingSubarray: arr is \(arr), low is \(low), mid is \(mid),high is \(high)")
    
    var max_left = low
    var max_right = high
    var left_sum = 0
    var right_sum = 0
    var sum = 0

    for index in (low...mid).reversed() {
        //尝试从 mid 到 low 去遍历
        sum = sum + arr[index]
        if sum > left_sum {
            //如果加上的和更大，那么就增加
            left_sum = sum
            max_left = index
        }
    }

    sum = 0
    
    for index in mid+1...high {
        //尝试从 mid 到 high 遍历
        sum = sum + arr[index]
        if sum > right_sum {
            //如果加上的和更大，那么就增加
            right_sum = sum
            max_right = index
        }
    }
    
    print("finish findMaxCrossingSubarray. max_left is \(max_left), max_right is \(max_right), sum is \(left_sum + right_sum)")

    return (max_left, max_right, left_sum + right_sum)
}

func findMaximumSubarray(arr: [Int], low: Int, high: Int) -> (max_left: Int, max_right: Int, sum: Int) {

    print("start findMaximumSubarray: arr is \(arr), low is \(low), high is \(high)")
    
    var left_low, left_high, left_sum: Int
    var right_low, right_high, right_sum: Int
    var cross_low, cross_high, cross_sum: Int
    var mid: Int

    if high == low {
        print("high is equal to low, are \(high)")
        print("")
        return (low, high, arr[low])
    } else {
        mid = (low + high) / 2

        (left_low, left_high, left_sum) = findMaximumSubarray(arr: arr, low: low, high: mid)
        (right_low, right_high, right_sum) = findMaximumSubarray(arr: arr, low: mid + 1, high: high)
        (cross_low, cross_high, cross_sum) = findMaxCrossingSubarray(arr: arr, low: low, mid: mid, high: high)
    }

    print("finish findMaximumSubarray.")
    print("")
    
    if left_sum >= right_sum && left_sum >= cross_sum {
        print("left_low is \(left_low), left_high is \(left_high), left_sum is \(left_sum))")
        print("")
        
        return (left_low, left_high, left_sum)
    } else if right_sum >= left_sum && right_sum >= cross_sum {
        print("right_low is \(right_low), right_high is \(right_high), right_sum is \(right_sum)")
        print("")
        
        return (right_low, right_high, right_sum)
    } else {
        print("cross_low is \(cross_low), cross_high is \(cross_high), cross_sum is \(cross_sum)")
        print("")
        
        return (cross_low, cross_high, cross_sum)
    }
}

//Test Code
var arrayForTest: [Int] = [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7]

var (max_left, max_right, sum) = findMaximumSubarray(arr: arrayForTest, low: 0, high: arrayForTest.count - 1)

print("max_left is \(max_left), max_right is \(max_right), sum is \(sum)")

//List num
print("max sum SubArray is \(arrayForTest[max_left...max_right])")

Terminal运行swift FindMaxSubArray.swift可见：

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, high is 15
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, high is 7
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, high is 3
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, high is 1
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, high is 0
high is equal to low, are 0

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 1, high is 1
high is equal to low, are 1

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, mid is 0,high is 1
finish findMaxCrossingSubarray. max_left is 0, max_right is 1, sum is 13
finish findMaximumSubarray.

left_low is 0, left_high is 0, left_sum is 13)

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 2, high is 3
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 2, high is 2
high is equal to low, are 2

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 3, high is 3
high is equal to low, are 3

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 2, mid is 2,high is 3
finish findMaxCrossingSubarray. max_left is 2, max_right is 3, sum is 20
finish findMaximumSubarray.

right_low is 3, right_high is 3, right_sum is 20

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, mid is 1,high is 3
finish findMaxCrossingSubarray. max_left is 0, max_right is 3, sum is 10
finish findMaximumSubarray.

right_low is 3, right_high is 3, right_sum is 20

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 4, high is 7
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 4, high is 5
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 4, high is 4
high is equal to low, are 4

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 5, high is 5
high is equal to low, are 5

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 4, mid is 4,high is 5
finish findMaxCrossingSubarray. max_left is 4, max_right is 5, sum is 0
finish findMaximumSubarray.

cross_low is 4, cross_high is 5, cross_sum is 0

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 6, high is 7
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 6, high is 6
high is equal to low, are 6

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 7, high is 7
high is equal to low, are 7

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 6, mid is 6,high is 7
finish findMaxCrossingSubarray. max_left is 6, max_right is 7, sum is 18
finish findMaximumSubarray.

right_low is 7, right_high is 7, right_sum is 18

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 4, mid is 5,high is 7
finish findMaxCrossingSubarray. max_left is 4, max_right is 7, sum is 0
finish findMaximumSubarray.

right_low is 7, right_high is 7, right_sum is 18

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, mid is 3,high is 7
finish findMaxCrossingSubarray. max_left is 3, max_right is 7, sum is 20
finish findMaximumSubarray.

left_low is 3, left_high is 3, left_sum is 20)

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 8, high is 15
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 8, high is 11
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 8, high is 9
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 8, high is 8
high is equal to low, are 8

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 9, high is 9
high is equal to low, are 9

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 8, mid is 8,high is 9
finish findMaxCrossingSubarray. max_left is 8, max_right is 9, sum is 20
finish findMaximumSubarray.

left_low is 8, left_high is 8, left_sum is 20)

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 10, high is 11
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 10, high is 10
high is equal to low, are 10

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 11, high is 11
high is equal to low, are 11

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 10, mid is 10,high is 11
finish findMaxCrossingSubarray. max_left is 10, max_right is 11, sum is 12
finish findMaximumSubarray.

left_low is 10, left_high is 10, left_sum is 12)

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 8, mid is 9,high is 11
finish findMaxCrossingSubarray. max_left is 8, max_right is 10, sum is 25
finish findMaximumSubarray.

cross_low is 8, cross_high is 10, cross_sum is 25

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 12, high is 15
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 12, high is 13
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 12, high is 12
high is equal to low, are 12

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 13, high is 13
high is equal to low, are 13

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 12, mid is 12,high is 13
finish findMaxCrossingSubarray. max_left is 12, max_right is 13, sum is 15
finish findMaximumSubarray.

right_low is 13, right_high is 13, right_sum is 15

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 14, high is 15
start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 14, high is 14
high is equal to low, are 14

start findMaximumSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 15, high is 15
high is equal to low, are 15

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 14, mid is 14,high is 15
finish findMaxCrossingSubarray. max_left is 14, max_right is 15, sum is 7
finish findMaximumSubarray.

right_low is 15, right_high is 15, right_sum is 7

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 12, mid is 13,high is 15
finish findMaxCrossingSubarray. max_left is 13, max_right is 15, sum is 18
finish findMaximumSubarray.

cross_low is 13, cross_high is 15, cross_sum is 18

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 8, mid is 11,high is 15
finish findMaxCrossingSubarray. max_left is 8, max_right is 15, sum is 20
finish findMaximumSubarray.

left_low is 8, left_high is 10, left_sum is 25)

start findMaxCrossingSubarray: arr is [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7], low is 0, mid is 7,high is 15
finish findMaxCrossingSubarray. max_left is 7, max_right is 10, sum is 43
finish findMaximumSubarray.

cross_low is 7, cross_high is 10, cross_sum is 43

max_left is 7, max_right is 10, sum is 43
max sum SubArray is [18, 20, -7, 12]

其中比较有意思的地方，Swift 3.0不支持了常见的方式，如果我们要逆序遍历，需要使用for index in (low...mid).reversed() {...}，其中reversed()就是逆序排列。

引用 Swift 2.x 源码[https://segmentfault.com/a/1190000002418778]

最后编辑于：2017.12.03 14:57:00

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最大子数组问题－Swift 3.0 实现

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