题目链接:https://leetcode.com/contest/7/problems/split-array-largest-sum/]
补充链接:https://leetcode.com/problems/split-array-largest-sum
contest所有题目最后都会出现在problems上
题目:
Given an array which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays.
Write an algorithm to minimize the largest sum among these m subarrays.Note:Given m satisfies the following constraint: 1 ≤ m ≤ length(nums) ≤ 14,000.
思路:
先计算subarrays sum的上下界,在该范围内二分法搜索满足条件的sum(以该sum贪心划分array 看能否满足sum>=所有subarray的sum)。并记录最小的sum。
本次contest只做出来这三题。
算法:
public int splitArray(int[] nums, int m) {
int high = 0, low = 0, mid = 0, ans = 0;
for (int num : nums) {
high += num;
low = Math.max(num, low);
}
if (m == 1)
return high;
if (m == nums.length)
return low;
ans = high;
while (low <= high) {
mid = low + (high - low) / 2;
boolean flag = true;
int sum = nums[0];
int count = 1;
for (int i = 1; i < nums.length; i++) {
sum += nums[i];
if (sum > mid) {
count++;
sum = nums[i];
}
if (count > m) {
flag = false;
break;
}
}
if (flag) {
high = mid - 1;
ans = mid;
} else {
low = mid + 1;
}
}
return ans;
}