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1428. 至少有一个 1 的最左端列

English Version

题目描述

（这是一个交互题）

我们称只包含元素 0 或 1 的矩阵为二进制矩阵。矩阵中每个单独的行都按非递减顺序排序。

给定一个这样的二进制矩阵，返回至少包含一个 1 的最左端列的索引（从 0 开始）。如果这样的列不存在，返回 -1。

您不能直接访问该二进制矩阵。你只可以通过 BinaryMatrix 接口来访问。

• BinaryMatrix.get(row, col) 返回位于索引 (row, col) （从 0 开始）的元素。
• BinaryMatrix.dimensions() 返回含有 2 个元素的列表 [rows, cols]，表示这是一个 rows * cols的矩阵。

如果提交的答案调用 BinaryMatrix.get 超过 1000 次，则该答案会被判定为错误答案。提交任何试图规避判定机制的答案将会被取消资格。

下列示例中， mat 为给定的二进制矩阵。您不能直接访问该矩阵。

 

示例 1:

输入: mat = [[0,0],[1,1]]
输出: 0

示例 2:

输入: mat = [[0,0],[0,1]]
输出: 1

示例 3:

输入: mat = [[0,0],[0,0]]
输出: -1

示例 4:

输入: mat = [[0,0,0,1],[0,0,1,1],[0,1,1,1]]
输出: 1

 

提示:

• rows == mat.length
• cols == mat[i].length
• 1 <= rows, cols <= 100
• mat[i][j] 只会是 0 或 1。
• mat[i] 已按非递减顺序排序。

解法

二分查找。

Python3

# """
# This is BinaryMatrix's API interface.
# You should not implement it, or speculate about its implementation
# """
#class BinaryMatrix(object):
#    def get(self, row: int, col: int) -> int:
#    def dimensions(self) -> list[]:

class Solution:
    def leftMostColumnWithOne(self, binaryMatrix: 'BinaryMatrix') -> int:
        rows, cols = binaryMatrix.dimensions()
        res = -1
        for row in range(rows):
            left, right = 0, cols - 1
            while left < right:
                mid = (left + right) >> 1
                if binaryMatrix.get(row, mid) == 1:
                    right = mid
                else:
                    left = mid + 1
            if binaryMatrix.get(row, left) == 1:
                if res == -1:
                    res = left
                else:
                    res = min(res, left)
        return res

Java

/**
 * // This is the BinaryMatrix's API interface.
 * // You should not implement it, or speculate about its implementation
 * interface BinaryMatrix {
 *     public int get(int row, int col) {}
 *     public List<Integer> dimensions {}
 * };
 */

class Solution {
    public int leftMostColumnWithOne(BinaryMatrix binaryMatrix) {
        List<Integer> scale = binaryMatrix.dimensions();
        int rows = scale.get(0), cols = scale.get(1);
        int res = -1;
        for (int row = 0; row < rows; ++row) {
            int left = 0, right = cols - 1;
            while (left < right) {
                int mid = (left + right) >> 1;
                if (binaryMatrix.get(row, mid) == 1) {
                    right = mid;
                } else {
                    left = mid + 1;
                }
            }
            if (binaryMatrix.get(row, left) == 1) {
                if (res == -1) {
                    res = left;
                } else {
                    res = Math.min(res, left);
                }
            }
        }
        return res;
    }
}

C++

/**
 * // This is the BinaryMatrix's API interface.
 * // You should not implement it, or speculate about its implementation
 * class BinaryMatrix {
 *   public:
 *     int get(int row, int col);
 *     vector<int> dimensions();
 * };
 */

class Solution {
public:
    int leftMostColumnWithOne(BinaryMatrix &binaryMatrix) {
        vector<int> scale = binaryMatrix.dimensions();
        int rows = scale[0], cols = scale[1];
        int res = -1;
        for (int row = 0; row < rows; ++row) {
            int left = 0, right = cols - 1;
            while (left < right) {
                int mid = left + right >> 1;
                if (binaryMatrix.get(row, mid) == 1) {
                    right = mid;
                } else {
                    left = mid + 1;
                }
            }
            if (binaryMatrix.get(row, left) == 1) {
                if (res == -1) {
                    res = left;
                } else {
                    res = min(res, left);
                }
            }
        }
        return res;
    }
};

Go

/**
 * // This is the BinaryMatrix's API interface.
 * // You should not implement it, or speculate about its implementation
 * type BinaryMatrix struct {
 *     Get func(int, int) int
 *     Dimensions func() []int
 * }
 */

func leftMostColumnWithOne(binaryMatrix BinaryMatrix) int {
	scale := binaryMatrix.Dimensions()
	rows, cols := scale[0], scale[1]
	res := -1
	for row := 0; row < rows; row++ {
		left, right := 0, cols-1
		for left < right {
			mid := (left + right) >> 1
			if binaryMatrix.Get(row, mid) == 1 {
				right = mid
			} else {
				left = mid + 1
			}
		}
		if binaryMatrix.Get(row, left) == 1 {
			if res == -1 {
				res = left
			} else {
				res = min(res, left)
			}
		}
	}
	return res
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

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