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| 1 | +package leetcode |
| 2 | + |
| 3 | +import ( |
| 4 | + "math" |
| 5 | +) |
| 6 | + |
| 7 | +// 解法一 二分搜索 |
| 8 | +func maxSumSubmatrix(matrix [][]int, k int) int { |
| 9 | + // 转换为前缀和 |
| 10 | + for i := 0; i < len(matrix); i++ { |
| 11 | + for j := 1; j < len(matrix[0]); j++ { |
| 12 | + matrix[i][j] += matrix[i][j-1] |
| 13 | + } |
| 14 | + } |
| 15 | + sum, absMax, absMaxFound := make([]int, len(matrix)), 0, false |
| 16 | + for y1 := 0; y1 < len(matrix[0]); y1++ { |
| 17 | + for y2 := y1; y2 < len(matrix[0]); y2++ { |
| 18 | + for x := 0; x < len(matrix); x++ { |
| 19 | + if y1 == 0 { |
| 20 | + sum[x] = matrix[x][y2] |
| 21 | + } else { |
| 22 | + sum[x] = matrix[x][y2] - matrix[x][y1-1] |
| 23 | + } |
| 24 | + } |
| 25 | + curMax := kadaneK(sum, k) |
| 26 | + if !absMaxFound || curMax > absMax { |
| 27 | + absMax = curMax |
| 28 | + absMaxFound = true |
| 29 | + } |
| 30 | + } |
| 31 | + } |
| 32 | + return absMax |
| 33 | +} |
| 34 | + |
| 35 | +func kadaneK(a []int, k int) int { |
| 36 | + sum, sums, maxSoFar := 0, []int{}, math.MinInt32 |
| 37 | + for _, v := range a { |
| 38 | + // 第一次循环会先插入 0,因为 sum 有可能等于 k |
| 39 | + sums = insertSort(sums, sum) |
| 40 | + sum += v |
| 41 | + pos := binarySearchOfKadane(sums, sum-k) |
| 42 | + if pos < len(sums) && sum-sums[pos] > maxSoFar { |
| 43 | + maxSoFar = sum - sums[pos] |
| 44 | + } |
| 45 | + } |
| 46 | + return maxSoFar |
| 47 | +} |
| 48 | + |
| 49 | +func binarySearchOfKadane(a []int, v int) int { |
| 50 | + low, high := 0, len(a) |
| 51 | + for low < high { |
| 52 | + mid := low + (high-low)>>1 |
| 53 | + if a[mid] < v { |
| 54 | + low = mid + 1 |
| 55 | + } else { |
| 56 | + high = mid |
| 57 | + } |
| 58 | + } |
| 59 | + return low |
| 60 | +} |
| 61 | + |
| 62 | +func insertSort(a []int, v int) []int { |
| 63 | + // 类似插入排序,将元素按照从小到大的顺序插入数组 |
| 64 | + p := binarySearchOfKadane(a, v) |
| 65 | + a = append(a, 0) |
| 66 | + // 把 p 后面的元素全部往后移,把 p 位置空出来放 v |
| 67 | + copy(a[p+1:], a[p:len(a)-1]) |
| 68 | + a[p] = v |
| 69 | + return a |
| 70 | +} |
| 71 | + |
| 72 | +// 解法二 暴力解法,超时 |
| 73 | +func maxSumSubmatrix1(matrix [][]int, k int) int { |
| 74 | + minNum := math.MaxInt64 |
| 75 | + for row := range matrix { |
| 76 | + for col := 1; col < len(matrix[row]); col++ { |
| 77 | + if matrix[row][col] < minNum { |
| 78 | + minNum = matrix[row][col] |
| 79 | + } |
| 80 | + } |
| 81 | + } |
| 82 | + for row := range matrix { |
| 83 | + for col := 1; col < len(matrix[row]); col++ { |
| 84 | + matrix[row][col] += matrix[row][col-1] |
| 85 | + } |
| 86 | + } |
| 87 | + for i := k; ; i-- { |
| 88 | + if findSumSubmatrix(matrix, i) > 0 { |
| 89 | + return i |
| 90 | + } |
| 91 | + } |
| 92 | +} |
| 93 | + |
| 94 | +func findSumSubmatrix(matrix [][]int, target int) int { |
| 95 | + m, n, res := len(matrix), len(matrix[0]), 0 |
| 96 | + for i := 0; i < n; i++ { |
| 97 | + for j := i; j < n; j++ { |
| 98 | + counterMap, sum := make(map[int]int, m), 0 |
| 99 | + counterMap[0] = 1 // 题目保证一定有解,所以这里初始化是 1 |
| 100 | + for row := 0; row < m; row++ { |
| 101 | + if i > 0 { |
| 102 | + sum += matrix[row][j] - matrix[row][i-1] |
| 103 | + } else { |
| 104 | + sum += matrix[row][j] |
| 105 | + } |
| 106 | + res += counterMap[sum-target] |
| 107 | + counterMap[sum]++ |
| 108 | + } |
| 109 | + } |
| 110 | + } |
| 111 | + return res |
| 112 | +} |
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